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MIPLearn
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Merge branch 'feature/tsp'

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pull/1/head
Alinson S. Xavier 6 years ago
parent 477e7677ed 0b04fa93da
commit 9a2dd52566
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GPG Key ID: A796166E4E218E02
37 changed files with 1617 additions and 643 deletions
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3
benchmark/Makefile
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@ -5,7 +5,8 @@
CHALLENGES := \ CHALLENGES := \
stab/ChallengeA \ stab/ChallengeA \
knapsack/ChallengeA knapsack/ChallengeA \
tsp/ChallengeA
main: $(addsuffix /performance.png, $(CHALLENGES)) main: $(addsuffix /performance.png, $(CHALLENGES))

23
benchmark/benchmark.py
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@ -20,9 +20,16 @@ from miplearn import (LearningSolver, BenchmarkRunner)
from numpy import median from numpy import median
import pyomo.environ as pe import pyomo.environ as pe
import pickle import pickle
import logging import logging
import sys
logging.basicConfig(format='%(asctime)s %(levelname).1s %(name)s: %(message)12s',
datefmt='%H:%M:%S',
level=logging.INFO,
stream=sys.stdout)
logging.getLogger('pyomo.core').setLevel(logging.ERROR) logging.getLogger('pyomo.core').setLevel(logging.ERROR)
logging.getLogger('miplearn').setLevel(logging.INFO)
logger = logging.getLogger("benchmark")
n_jobs = 10 n_jobs = 10
time_limit = 900 time_limit = 900
@ -34,7 +41,7 @@ pathlib.Path(basepath).mkdir(parents=True, exist_ok=True)
def save(obj, filename): def save(obj, filename):
print("Writing %s..." % filename) logger.info("Writing %s..." % filename)
with open(filename, "wb") as file: with open(filename, "wb") as file:
pickle.dump(obj, file) pickle.dump(obj, file)
@ -55,7 +62,6 @@ def train():
solver=internal_solver, solver=internal_solver,
components={}) components={})
solver.parallel_solve(train_instances, n_jobs=n_jobs) solver.parallel_solve(train_instances, n_jobs=n_jobs)
solver.fit(n_jobs=n_jobs)
save(train_instances, "%s/train_instances.bin" % basepath) save(train_instances, "%s/train_instances.bin" % basepath)
save(test_instances, "%s/test_instances.bin" % basepath) save(test_instances, "%s/test_instances.bin" % basepath)
@ -65,6 +71,7 @@ def test_baseline():
solvers = { solvers = {
"baseline": LearningSolver( "baseline": LearningSolver(
time_limit=time_limit, time_limit=time_limit,
solver=internal_solver,
components={}, components={},
), ),
} }
@ -74,22 +81,28 @@ def test_baseline():
def test_ml(): def test_ml():
logger.info("Loading instances...")
train_instances = load("%s/train_instances.bin" % basepath) train_instances = load("%s/train_instances.bin" % basepath)
test_instances = load("%s/test_instances.bin" % basepath) test_instances = load("%s/test_instances.bin" % basepath)
solvers = { solvers = {
"ml-exact": LearningSolver( "ml-exact": LearningSolver(
time_limit=time_limit, time_limit=time_limit,
solver=internal_solver,
), ),
"ml-heuristic": LearningSolver( "ml-heuristic": LearningSolver(
time_limit=time_limit, time_limit=time_limit,
solver=internal_solver,
mode="heuristic", mode="heuristic",
), ),
} }
benchmark = BenchmarkRunner(solvers) benchmark = BenchmarkRunner(solvers)
logger.info("Loading results...")
benchmark.load_results("%s/benchmark_baseline.csv" % basepath) benchmark.load_results("%s/benchmark_baseline.csv" % basepath)
logger.info("Fitting...")
benchmark.fit(train_instances) benchmark.fit(train_instances)
logger.info("Solving...")
benchmark.parallel_solve(test_instances, n_jobs=n_jobs) benchmark.parallel_solve(test_instances, n_jobs=n_jobs)
benchmark.save_results("%s/benchmark_ml.csv" % basepath) benchmark.save_results("%s/benchmark_ml.csv" % basepath)
def charts(): def charts():

51
benchmark/tsp/ChallengeA/benchmark_baseline.csv
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@ -0,0 +1,51 @@
,Solver,Instance,Wallclock Time,Lower Bound,Upper Bound,Gap,Nodes,Mode,Relative Lower Bound,Relative Upper Bound,Relative Wallclock Time,Relative Gap,Relative Nodes
0,baseline,0,88.44052076339722,13538.699999999997,13540.0,9.602103599333102e-05,1,exact,1.0,1.0,1.0,1.0,1.0
1,baseline,1,74.86838150024414,13565.666666666666,13567.0,9.828734304744377e-05,1,exact,1.0,1.0,1.0,1.0,1.0
2,baseline,2,113.96127772331238,13560.699999999997,13562.0,9.586525769340157e-05,1,exact,1.0,1.0,1.0,1.0,1.0
3,baseline,3,91.72307801246643,13520.666666666666,13522.0,9.861446674231594e-05,1,exact,1.0,1.0,1.0,1.0,1.0
4,baseline,4,75.7019145488739,13532.98571428571,13534.0,7.494914542165241e-05,1,exact,1.0,1.0,1.0,1.0,1.0
5,baseline,5,148.34671473503113,13530.670398009952,13532.0,9.82657880901199e-05,1,exact,1.0,1.0,1.0,1.0,1.0
6,baseline,6,128.75406980514526,13533.647058823528,13535.0,9.99687054488398e-05,1,exact,1.0,1.0,1.0,1.0,1.0
7,baseline,7,89.82294702529907,13611.833333333334,13613.0,8.57097378506001e-05,1,exact,1.0,1.0,1.0,1.0,1.0
8,baseline,8,163.10344243049622,13578.666666666664,13580.0,9.819324430497046e-05,1,exact,1.0,1.0,1.0,1.0,1.0
9,baseline,9,110.7302086353302,13582.666666666664,13584.0,9.816432708371643e-05,1,exact,1.0,1.0,1.0,1.0,1.0
10,baseline,10,969.3387920856476,13576.642857142855,13578.0,9.996159370362496e-05,1,exact,1.0,1.0,1.0,1.0,1.0
11,baseline,11,74.61696720123291,13575.0,13575.0,0.0,1,exact,1.0,1.0,1.0,,1.0
12,baseline,12,83.92108988761902,13542.649999999998,13544.0,9.968506902284139e-05,1,exact,1.0,1.0,1.0,1.0,1.0
13,baseline,13,71.3746600151062,13532.75,13534.0,9.2368513421145e-05,1,exact,1.0,1.0,1.0,1.0,1.0
14,baseline,14,95.41746068000793,13549.66666666667,13551.0,9.840340475758086e-05,1,exact,1.0,1.0,1.0,1.0,1.0
15,baseline,15,119.16796040534973,13592.724074074078,13594.0,9.386830181858343e-05,1,exact,1.0,1.0,1.0,1.0,1.0
16,baseline,16,236.61669611930847,13592.65,13594.0,9.931838162539047e-05,1,exact,1.0,1.0,1.0,1.0,1.0
17,baseline,17,151.28878140449524,13542.65,13544.0,9.968506902270707e-05,1,exact,1.0,1.0,1.0,1.0,1.0
18,baseline,18,85.78852319717407,13523.833333333332,13525.0,8.62674537545725e-05,1,exact,1.0,1.0,1.0,1.0,1.0
19,baseline,19,101.29387998580933,13562.666666666662,13564.0,9.830908375965233e-05,1,exact,1.0,1.0,1.0,1.0,1.0
20,baseline,20,158.05654454231262,13567.666666666666,13569.0,9.827285458078813e-05,1,exact,1.0,1.0,1.0,1.0,1.0
21,baseline,21,142.137060880661,13564.750000000002,13566.0,9.215061095841655e-05,1,exact,1.0,1.0,1.0,1.0,1.0
22,baseline,22,75.79312753677368,13563.714285714286,13565.0,9.479072314785627e-05,1,exact,1.0,1.0,1.0,1.0,1.0
23,baseline,23,125.0184965133667,13578.651041666662,13580.0,9.934406070221867e-05,1,exact,1.0,1.0,1.0,1.0,1.0
24,baseline,24,110.1647527217865,13541.666666666666,13543.0,9.846153846158324e-05,1,exact,1.0,1.0,1.0,1.0,1.0
25,baseline,25,107.13047480583191,13540.75,13542.0,9.231394125140778e-05,1,exact,1.0,1.0,1.0,1.0,1.0
26,baseline,26,86.15372657775879,13530.672413793101,13532.0,9.811679466463352e-05,1,exact,1.0,1.0,1.0,1.0,1.0
27,baseline,27,94.40602779388428,13520.7,13522.0,9.614886803192678e-05,1,exact,1.0,1.0,1.0,1.0,1.0
28,baseline,28,65.10137605667114,13569.749999999998,13571.0,9.21166565339685e-05,1,exact,1.0,1.0,1.0,1.0,1.0
29,baseline,29,62.560155391693115,13593.777777777777,13595.0,8.991041653046851e-05,1,exact,1.0,1.0,1.0,1.0,1.0
30,baseline,30,123.58262610435486,13575.666666666668,13577.0,9.821494340354953e-05,1,exact,1.0,1.0,1.0,1.0,1.0
31,baseline,31,77.88054895401001,13580.75,13582.0,9.204204480606741e-05,1,exact,1.0,1.0,1.0,1.0,1.0
32,baseline,32,91.31177544593811,13523.0,13524.0,7.394808844191378e-05,1,exact,1.0,1.0,1.0,1.0,1.0
33,baseline,33,125.20542597770691,13546.724137931033,13548.0,9.418233190376748e-05,1,exact,1.0,1.0,1.0,1.0,1.0
34,baseline,34,93.4059066772461,13555.999999999996,13557.0,7.376807317819698e-05,1,exact,1.0,1.0,1.0,1.0,1.0
35,baseline,35,133.77592086791992,13566.671171171172,13568.0,9.794803839953082e-05,1,exact,1.0,1.0,1.0,1.0,1.0
36,baseline,36,105.60492086410522,13552.674418604645,13554.0,9.780958019141685e-05,1,exact,1.0,1.0,1.0,1.0,1.0
37,baseline,37,106.68410634994507,13530.666666666666,13532.0,9.854158454872436e-05,1,exact,1.0,1.0,1.0,1.0,1.0
38,baseline,38,76.45212483406067,13512.666666666666,13514.0,9.86728501653219e-05,1,exact,1.0,1.0,1.0,1.0,1.0
39,baseline,39,66.65553593635559,13536.666666666666,13538.0,9.849790691952276e-05,1,exact,1.0,1.0,1.0,1.0,1.0
40,baseline,40,72.2125403881073,13578.0,13578.0,0.0,1,exact,1.0,1.0,1.0,,1.0
41,baseline,41,68.3276731967926,13526.0,13526.0,0.0,1,exact,1.0,1.0,1.0,,1.0
42,baseline,42,91.24437737464905,13527.7,13529.0,9.609911514886287e-05,1,exact,1.0,1.0,1.0,1.0,1.0
43,baseline,43,197.3597583770752,13563.65151515152,13565.0,9.941901315984782e-05,1,exact,1.0,1.0,1.0,1.0,1.0
44,baseline,44,68.33869886398315,13551.749999999995,13553.0,9.223900972239434e-05,1,exact,1.0,1.0,1.0,1.0,1.0
45,baseline,45,88.19205832481384,13519.66666666667,13521.0,9.862176089131646e-05,1,exact,1.0,1.0,1.0,1.0,1.0
46,baseline,46,85.30370616912842,13541.745070422534,13543.0,9.267118609455138e-05,1,exact,1.0,1.0,1.0,1.0,1.0
47,baseline,47,80.86965203285217,13562.678333333333,13564.0,9.744879545055802e-05,1,exact,1.0,1.0,1.0,1.0,1.0
48,baseline,48,88.52302312850952,13550.6875,13552.0,9.685855422464727e-05,1,exact,1.0,1.0,1.0,1.0,1.0
49,baseline,49,130.87233448028564,13523.000000000002,13524.0,7.394808844177925e-05,1,exact,1.0,1.0,1.0,1.0,1.0
1 Solver Instance Wallclock Time Lower Bound Upper Bound Gap Nodes Mode Relative Lower Bound Relative Upper Bound Relative Wallclock Time Relative Gap Relative Nodes
2 0 baseline 0 88.44052076339722 13538.699999999997 13540.0 9.602103599333102e-05 1 exact 1.0 1.0 1.0 1.0 1.0
3 1 baseline 1 74.86838150024414 13565.666666666666 13567.0 9.828734304744377e-05 1 exact 1.0 1.0 1.0 1.0 1.0
4 2 baseline 2 113.96127772331238 13560.699999999997 13562.0 9.586525769340157e-05 1 exact 1.0 1.0 1.0 1.0 1.0
5 3 baseline 3 91.72307801246643 13520.666666666666 13522.0 9.861446674231594e-05 1 exact 1.0 1.0 1.0 1.0 1.0
6 4 baseline 4 75.7019145488739 13532.98571428571 13534.0 7.494914542165241e-05 1 exact 1.0 1.0 1.0 1.0 1.0
7 5 baseline 5 148.34671473503113 13530.670398009952 13532.0 9.82657880901199e-05 1 exact 1.0 1.0 1.0 1.0 1.0
8 6 baseline 6 128.75406980514526 13533.647058823528 13535.0 9.99687054488398e-05 1 exact 1.0 1.0 1.0 1.0 1.0
9 7 baseline 7 89.82294702529907 13611.833333333334 13613.0 8.57097378506001e-05 1 exact 1.0 1.0 1.0 1.0 1.0
10 8 baseline 8 163.10344243049622 13578.666666666664 13580.0 9.819324430497046e-05 1 exact 1.0 1.0 1.0 1.0 1.0
11 9 baseline 9 110.7302086353302 13582.666666666664 13584.0 9.816432708371643e-05 1 exact 1.0 1.0 1.0 1.0 1.0
12 10 baseline 10 969.3387920856476 13576.642857142855 13578.0 9.996159370362496e-05 1 exact 1.0 1.0 1.0 1.0 1.0
13 11 baseline 11 74.61696720123291 13575.0 13575.0 0.0 1 exact 1.0 1.0 1.0 1.0
14 12 baseline 12 83.92108988761902 13542.649999999998 13544.0 9.968506902284139e-05 1 exact 1.0 1.0 1.0 1.0 1.0
15 13 baseline 13 71.3746600151062 13532.75 13534.0 9.2368513421145e-05 1 exact 1.0 1.0 1.0 1.0 1.0
16 14 baseline 14 95.41746068000793 13549.66666666667 13551.0 9.840340475758086e-05 1 exact 1.0 1.0 1.0 1.0 1.0
17 15 baseline 15 119.16796040534973 13592.724074074078 13594.0 9.386830181858343e-05 1 exact 1.0 1.0 1.0 1.0 1.0
18 16 baseline 16 236.61669611930847 13592.65 13594.0 9.931838162539047e-05 1 exact 1.0 1.0 1.0 1.0 1.0
19 17 baseline 17 151.28878140449524 13542.65 13544.0 9.968506902270707e-05 1 exact 1.0 1.0 1.0 1.0 1.0
20 18 baseline 18 85.78852319717407 13523.833333333332 13525.0 8.62674537545725e-05 1 exact 1.0 1.0 1.0 1.0 1.0
21 19 baseline 19 101.29387998580933 13562.666666666662 13564.0 9.830908375965233e-05 1 exact 1.0 1.0 1.0 1.0 1.0
22 20 baseline 20 158.05654454231262 13567.666666666666 13569.0 9.827285458078813e-05 1 exact 1.0 1.0 1.0 1.0 1.0
23 21 baseline 21 142.137060880661 13564.750000000002 13566.0 9.215061095841655e-05 1 exact 1.0 1.0 1.0 1.0 1.0
24 22 baseline 22 75.79312753677368 13563.714285714286 13565.0 9.479072314785627e-05 1 exact 1.0 1.0 1.0 1.0 1.0
25 23 baseline 23 125.0184965133667 13578.651041666662 13580.0 9.934406070221867e-05 1 exact 1.0 1.0 1.0 1.0 1.0
26 24 baseline 24 110.1647527217865 13541.666666666666 13543.0 9.846153846158324e-05 1 exact 1.0 1.0 1.0 1.0 1.0
27 25 baseline 25 107.13047480583191 13540.75 13542.0 9.231394125140778e-05 1 exact 1.0 1.0 1.0 1.0 1.0
28 26 baseline 26 86.15372657775879 13530.672413793101 13532.0 9.811679466463352e-05 1 exact 1.0 1.0 1.0 1.0 1.0
29 27 baseline 27 94.40602779388428 13520.7 13522.0 9.614886803192678e-05 1 exact 1.0 1.0 1.0 1.0 1.0
30 28 baseline 28 65.10137605667114 13569.749999999998 13571.0 9.21166565339685e-05 1 exact 1.0 1.0 1.0 1.0 1.0
31 29 baseline 29 62.560155391693115 13593.777777777777 13595.0 8.991041653046851e-05 1 exact 1.0 1.0 1.0 1.0 1.0
32 30 baseline 30 123.58262610435486 13575.666666666668 13577.0 9.821494340354953e-05 1 exact 1.0 1.0 1.0 1.0 1.0
33 31 baseline 31 77.88054895401001 13580.75 13582.0 9.204204480606741e-05 1 exact 1.0 1.0 1.0 1.0 1.0
34 32 baseline 32 91.31177544593811 13523.0 13524.0 7.394808844191378e-05 1 exact 1.0 1.0 1.0 1.0 1.0
35 33 baseline 33 125.20542597770691 13546.724137931033 13548.0 9.418233190376748e-05 1 exact 1.0 1.0 1.0 1.0 1.0
36 34 baseline 34 93.4059066772461 13555.999999999996 13557.0 7.376807317819698e-05 1 exact 1.0 1.0 1.0 1.0 1.0
37 35 baseline 35 133.77592086791992 13566.671171171172 13568.0 9.794803839953082e-05 1 exact 1.0 1.0 1.0 1.0 1.0
38 36 baseline 36 105.60492086410522 13552.674418604645 13554.0 9.780958019141685e-05 1 exact 1.0 1.0 1.0 1.0 1.0
39 37 baseline 37 106.68410634994507 13530.666666666666 13532.0 9.854158454872436e-05 1 exact 1.0 1.0 1.0 1.0 1.0
40 38 baseline 38 76.45212483406067 13512.666666666666 13514.0 9.86728501653219e-05 1 exact 1.0 1.0 1.0 1.0 1.0
41 39 baseline 39 66.65553593635559 13536.666666666666 13538.0 9.849790691952276e-05 1 exact 1.0 1.0 1.0 1.0 1.0
42 40 baseline 40 72.2125403881073 13578.0 13578.0 0.0 1 exact 1.0 1.0 1.0 1.0
43 41 baseline 41 68.3276731967926 13526.0 13526.0 0.0 1 exact 1.0 1.0 1.0 1.0
44 42 baseline 42 91.24437737464905 13527.7 13529.0 9.609911514886287e-05 1 exact 1.0 1.0 1.0 1.0 1.0
45 43 baseline 43 197.3597583770752 13563.65151515152 13565.0 9.941901315984782e-05 1 exact 1.0 1.0 1.0 1.0 1.0
46 44 baseline 44 68.33869886398315 13551.749999999995 13553.0 9.223900972239434e-05 1 exact 1.0 1.0 1.0 1.0 1.0
47 45 baseline 45 88.19205832481384 13519.66666666667 13521.0 9.862176089131646e-05 1 exact 1.0 1.0 1.0 1.0 1.0
48 46 baseline 46 85.30370616912842 13541.745070422534 13543.0 9.267118609455138e-05 1 exact 1.0 1.0 1.0 1.0 1.0
49 47 baseline 47 80.86965203285217 13562.678333333333 13564.0 9.744879545055802e-05 1 exact 1.0 1.0 1.0 1.0 1.0
50 48 baseline 48 88.52302312850952 13550.6875 13552.0 9.685855422464727e-05 1 exact 1.0 1.0 1.0 1.0 1.0
51 49 baseline 49 130.87233448028564 13523.000000000002 13524.0 7.394808844177925e-05 1 exact 1.0 1.0 1.0 1.0 1.0

151
benchmark/tsp/ChallengeA/benchmark_ml.csv
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@ -0,0 +1,151 @@
,Solver,Instance,Wallclock Time,Lower Bound,Upper Bound,Gap,Nodes,Mode,Relative Lower Bound,Relative Upper Bound,Relative Wallclock Time,Relative Gap,Relative Nodes
0,baseline,0,88.44052076339722,13538.699999999995,13540.0,9.602103599333102e-05,1,exact,0.999990151785604,1.0,41.72369503515307,1.1142966881214733,1.0
1,baseline,1,74.86838150024414,13565.666666666664,13567.0,9.828734304744377e-05,1,exact,0.9999017223164048,1.0,76.61356087521061,inf,1.0
2,baseline,2,113.96127772331238,13560.699999999995,13562.0,9.586525769340156e-05,1,exact,0.9999235465104994,1.0,76.24000609297043,1.0400038346080955,1.0
3,baseline,3,91.72307801246643,13520.666666666664,13522.0,9.861446674231594e-05,1,exact,0.9999013952571116,1.0,94.94335769471294,inf,1.0
4,baseline,4,75.70191454887392,13532.98571428571,13534.0,7.49491454216524e-05,1,exact,0.9999250564715317,1.0,41.48575715983321,inf,1.0
5,baseline,5,148.34671473503113,13530.670398009952,13532.0,9.82657880901199e-05,1,exact,0.9999978122351358,1.0,119.90309626530366,1.0227729991614376,1.0
6,baseline,6,128.75406980514526,13533.647058823528,13535.0,9.99687054488398e-05,1,exact,0.9999000412872943,1.0,89.50928932403158,inf,1.0
7,baseline,7,89.82294702529906,13611.833333333336,13613.0,8.570973785060009e-05,1,exact,0.9999142976076791,1.0,58.998624886131445,inf,1.0
8,baseline,8,163.10344243049622,13578.666666666664,13580.0,9.819324430497046e-05,1,exact,0.9999999999999999,1.0,89.45505955167431,1.0000000000013642,1.0
9,baseline,9,110.7302086353302,13582.666666666664,13584.0,9.816432708371644e-05,1,exact,0.9999018453082056,1.0,69.69178446747482,inf,1.0
10,baseline,10,969.3387920856476,13576.642857142857,13578.0,9.996159370362496e-05,1,exact,0.9999000483976179,1.0,515.7574545488682,inf,1.0
11,baseline,11,74.61696720123291,13575.0,13575.0,0.0,1,exact,1.0,1.0,89.50190791176391,,1.0
12,baseline,12,83.92108988761902,13542.649999999998,13544.0,9.968506902284139e-05,1,exact,0.9999003248670997,1.0,55.69203928988848,inf,1.0
13,baseline,13,71.3746600151062,13532.75,13534.0,9.236851342114499e-05,1,exact,0.9999076400177331,1.0,52.71414831739878,inf,1.0
14,baseline,14,95.41746068000792,13549.66666666667,13551.0,9.840340475758086e-05,1,exact,0.9999016062775197,1.0,64.56994873575405,inf,1.0
15,baseline,15,119.16796040534972,13592.724074074076,13594.0,9.386830181858343e-05,1,exact,0.9999061405086124,1.0,65.40523211338186,inf,1.0
16,baseline,16,236.61669611930847,13592.65,13594.0,9.931838162539048e-05,1,exact,0.9999742514529537,1.0,92.34020750352192,1.3500347614339328,1.0
17,baseline,17,151.28878140449527,13542.65,13544.0,9.968506902270708e-05,1,exact,0.9999741563907554,1.0000738388835562,91.4641415949715,1.350034889774522,1.0
18,baseline,18,85.78852319717406,13523.833333333332,13525.0,8.62674537545725e-05,1,exact,0.9999137399876771,1.0,96.1413272100395,inf,1.0
19,baseline,19,101.29387998580931,13562.666666666662,13564.0,9.830908375965231e-05,1,exact,0.9999017005799663,1.0,75.05436661902205,inf,1.0
20,baseline,20,158.05654454231262,13567.666666666664,13569.0,9.827285458078812e-05,1,exact,0.999901736802024,1.0,90.31845612470958,inf,1.0
21,baseline,21,142.13706088066098,13564.750000000002,13566.0,9.215061095841657e-05,1,exact,0.9999078578799943,1.0,145.5161989355379,inf,1.0
22,baseline,22,75.7931275367737,13563.714285714286,13565.0,9.479072314785627e-05,1,exact,0.9999052182612816,1.0,103.67687261190537,inf,1.0
23,baseline,23,125.0184965133667,13578.651041666662,13580.0,9.934406070221867e-05,1,exact,0.9999006658075599,1.0,76.27885738292231,inf,1.0
24,baseline,24,110.1647527217865,13541.666666666664,13543.0,9.846153846158324e-05,1,exact,0.9999015481552583,1.0,137.78651586217427,inf,1.0
25,baseline,25,107.13047480583192,13540.75,13542.0,9.231394125140777e-05,1,exact,0.9999815375526179,1.0,81.76214710854182,1.2500230784875868,1.0
26,baseline,26,86.15372657775879,13530.672413793101,13532.0,9.811679466463352e-05,1,exact,0.9999018928312963,1.0,95.4669269129848,inf,1.0
27,baseline,27,94.40602779388428,13520.7,13522.0,9.614886803192679e-05,1,exact,0.9999778122919903,1.0,54.71143091363273,1.3000288446596822,1.0
28,baseline,28,65.10137605667114,13569.749999999998,13571.0,9.21166565339685e-05,1,exact,0.9999078918281629,1.0,50.24970031074932,inf,1.0
29,baseline,29,62.560155391693115,13593.777777777776,13595.0,8.991041653046851e-05,1,exact,0.9999100976666256,1.0,46.92879617539241,inf,1.0
30,baseline,30,123.58262610435486,13575.666666666668,13577.0,9.821494340354953e-05,1,exact,0.9999754468670203,1.0,71.13568329179179,1.3333660716465885,1.0
31,baseline,31,77.88054895401002,13580.75,13582.0,9.20420448060674e-05,1,exact,0.9999079664261522,1.0,101.52119482807224,inf,1.0
32,baseline,32,91.31177544593812,13523.0,13524.0,7.394808844191378e-05,1,exact,1.0,1.0,58.01274392159489,1.0,1.0
33,baseline,33,125.20542597770692,13546.724137931033,13548.0,9.418233190376748e-05,1,exact,0.9999796366672351,1.0,91.02421056827991,1.275888050298017,1.0
34,baseline,34,93.4059066772461,13555.999999999995,13557.0,7.376807317819698e-05,1,exact,0.9999262373681489,1.0,75.47322729615996,inf,1.0
35,baseline,35,133.77592086791992,13566.671171171172,13568.0,9.794803839953082e-05,1,exact,0.9999020615544791,1.0,84.38612997732044,inf,1.0
36,baseline,36,105.60492086410522,13552.674418604644,13554.0,9.780958019141684e-05,1,exact,0.9999759771714486,1.0,58.58183671223716,1.3256132403342726,1.0
37,baseline,37,106.68410634994508,13530.666666666664,13532.0,9.854158454872437e-05,1,exact,0.9999014681249382,1.0,136.8255659357326,inf,1.0
38,baseline,38,76.45212483406067,13512.666666666664,13514.0,9.867285016532191e-05,1,exact,0.9999901328123457,1.0,84.32910693002859,1.1111220747609611,1.0
39,baseline,39,66.65553593635559,13536.666666666664,13538.0,9.849790691952276e-05,1,exact,0.9999015117939625,1.0,85.20374060262657,inf,1.0
40,baseline,40,72.2125403881073,13578.0,13578.0,0.0,1,exact,1.0,1.0,102.32184109577935,,1.0
41,baseline,41,68.3276731967926,13526.0,13526.0,0.0,1,exact,1.0,1.0,36.988942309740004,,1.0
42,baseline,42,91.24437737464905,13527.7,13529.0,9.609911514886287e-05,1,exact,0.9999039101190037,1.0,60.45086955649546,inf,1.0
43,baseline,43,197.3597583770752,13563.651515151521,13565.0,9.941901315984781e-05,1,exact,0.9999743081061281,1.0,97.77650283861117,1.3485194945001757,1.0
44,baseline,44,68.33869886398314,13551.749999999995,13553.0,9.223900972239434e-05,1,exact,0.9999907761841069,1.0,92.29526354225831,1.1111213598948202,1.0
45,baseline,45,88.19205832481384,13519.66666666667,13521.0,9.862176089131646e-05,1,exact,0.9999013879644013,1.0,113.90345047382237,inf,1.0
46,baseline,46,85.30370616912842,13541.745070422534,13543.0,9.267118609455138e-05,1,exact,0.9999073374010584,1.0,67.75852498047483,inf,1.0
47,baseline,47,80.86965203285217,13562.678333333333,13564.0,9.744879545055802e-05,1,exact,0.9999025606998919,1.0,116.23732479169651,inf,1.0
48,baseline,48,88.52302312850952,13550.6875,13552.0,9.685855422464728e-05,1,exact,0.9999031508264463,1.0,122.53937560747,inf,1.0
49,baseline,49,130.87233448028564,13523.000000000002,13524.0,7.394808844177925e-05,1,exact,0.9999260573794737,1.0,97.84851972743084,inf,1.0
50,ml-exact,0,9.014199018478394,13538.699999999999,13540.0,9.602103599319664e-05,1,exact,0.9999901517856042,1.0,4.252639939099353,1.114296688119914,1.0
51,ml-exact,1,5.4113500118255615,13565.709677419356,13567.0,9.511648202170943e-05,1,exact,0.999904892564263,1.0,5.537488392836666,inf,1.0
52,ml-exact,2,7.311800241470337,13560.749999999995,13562.0,9.217779252662703e-05,1,exact,0.9999272333539017,1.0,4.891588670265028,1.0,1.0
53,ml-exact,3,22.324601411819458,13520.72222222222,13522.0,9.450514231252222e-05,1,exact,0.9999055037880654,1.0,23.108389547788498,inf,1.0
54,ml-exact,4,7.276817560195923,13534.0,13534.0,0.0,1,exact,1.0,1.0,3.987802527818481,,1.0
55,ml-exact,5,6.725529432296753,13530.699999999999,13532.0,9.607780824355662e-05,1,exact,1.0,1.0,5.435993674657236,1.0,1.0
56,ml-exact,6,8.695855855941772,13533.665041782733,13535.0,9.863981509409236e-05,1,exact,0.9999013699137593,1.0,6.045322519960155,inf,1.0
57,ml-exact,7,6.677775144577026,13612.0,13613.0,7.346459006758743e-05,1,exact,0.9999265408065819,1.0,4.386179299125712,inf,1.0
58,ml-exact,8,11.08420991897583,13578.642857142859,13580.0,9.994687034775287e-05,1,exact,0.999998246549209,1.0,6.079201294649372,1.0178589276210523,1.0
59,ml-exact,9,16.643534421920776,13582.66666666667,13584.0,9.816432708331462e-05,1,exact,0.9999018453082059,1.0,10.475168682554177,inf,1.0
60,ml-exact,10,16.841771364212036,13576.691176470587,13578.0,9.640224649735783e-05,1,exact,0.999903607046,1.0,8.961024978903895,inf,1.0
61,ml-exact,11,4.076904058456421,13573.75,13575.0,9.208951100469657e-05,1,exact,0.9999079189686925,1.0,4.89018389907214,inf,1.0
62,ml-exact,12,6.3809661865234375,13542.750000000002,13544.0,9.230030828289534e-05,1,exact,0.9999077082102777,1.0,4.234561539217345,inf,1.0
63,ml-exact,13,4.139940500259399,13532.999999999998,13534.0,7.389344565150514e-05,1,exact,0.9999261120141864,1.0,3.0575758610926025,inf,1.0
64,ml-exact,14,7.238400936126709,13549.66666666667,13551.0,9.840340475758086e-05,1,exact,0.9999016062775197,1.0,4.898298215480208,inf,1.0
65,ml-exact,15,7.4390175342559814,13592.6875,13594.0,9.655927129936593e-05,1,exact,0.9999034500514933,1.0,4.082898346741258,inf,1.0
66,ml-exact,16,45.386595487594604,13592.666666666664,13594.0,9.809210849005043e-05,1,exact,0.9999754775742414,1.0,17.712222822558893,1.3333660307052555,1.0
67,ml-exact,17,7.782220363616943,13541.750000000002,13543.0,9.230712426371635e-05,1,exact,0.9999077013955551,1.0,4.704870372100049,1.2501153839035106,1.0
68,ml-exact,18,3.7182631492614746,13525.0,13525.0,0.0,1,exact,1.0,1.0,4.166976429522626,,1.0
69,ml-exact,19,5.698674201965332,13564.0,13564.0,0.0,1,exact,1.0,1.0,4.222470132021685,,1.0
70,ml-exact,20,27.741767644882202,13567.699999999997,13569.0,9.581579781414025e-05,1,exact,0.9999041933819734,1.0,15.852514244896831,inf,1.0
71,ml-exact,21,5.77320122718811,13566.0,13566.0,0.0,1,exact,1.0,1.0,5.91045215839762,,1.0
72,ml-exact,22,3.9558210372924805,13563.871192621193,13565.0,8.32216232944913e-05,1,exact,0.9999167853019678,1.0,5.41113907141357,inf,1.0
73,ml-exact,23,23.586190462112427,13578.64814814815,13580.0,9.955717514005507e-05,1,exact,0.9999004527355044,1.0,14.390891817144492,inf,1.0
74,ml-exact,24,4.234185695648193,13543.0,13543.0,0.0,1,exact,1.0,1.0,5.2958290206504826,,1.0
75,ml-exact,25,4.053018093109131,13541.0,13542.0,7.384978952809984e-05,1,exact,0.9999999999999999,1.0,3.0932697924001986,1.0000000000018192,1.0
76,ml-exact,26,4.456820011138916,13532.0,13532.0,0.0,1,exact,1.0,1.0,4.9386013486451725,,1.0
77,ml-exact,27,6.604680299758911,13520.892857142859,13522.0,8.188385699369056e-05,1,exact,0.9999920758185681,1.0,3.827631755843238,1.10715163041169,1.0
78,ml-exact,28,4.3237597942352295,13569.666666666666,13571.0,9.825837038497186e-05,1,exact,0.9999017512833738,1.0,3.3373739087612315,inf,1.0
79,ml-exact,29,4.937336444854736,13593.833333333334,13595.0,8.582322866981795e-05,1,exact,0.9999141841363247,1.0,3.7036873425140273,inf,1.0
80,ml-exact,30,7.1004478931427,13575.670776255707,13577.0,9.791219647266045e-05,1,exact,0.9999757495768788,1.0,4.087105351928353,1.3292559793128385,1.0
81,ml-exact,31,4.129274129867554,13582.0,13582.0,0.0,1,exact,1.0,1.0,5.3827155697676625,,1.0
82,ml-exact,32,4.985649824142456,13522.750000000002,13524.0,9.243681943378239e-05,1,exact,0.9999815129778896,1.0,3.1675128987275314,1.2500231092030394,1.0
83,ml-exact,33,26.542813777923584,13546.649999999996,13548.0,9.9655634419137e-05,1,exact,0.9999741640215545,1.0,19.29659718442664,1.350034879473593,1.0
84,ml-exact,34,5.016777992248535,13557.0,13557.0,0.0,1,exact,1.0,1.0,4.053624007009211,,1.0
85,ml-exact,35,35.91903018951416,13566.666666666662,13568.0,9.828009828041115e-05,1,exact,0.9999017295597481,1.0,22.657799180648382,inf,1.0
86,ml-exact,36,7.446932315826416,13552.654459753448,13554.0,9.928241368119515e-05,1,exact,0.9999745045195491,1.0,4.1310098938875015,1.345574552621238,1.0
87,ml-exact,37,7.494789361953735,13530.666666666668,13532.0,9.854158454858992e-05,1,exact,0.9999014681249385,1.0,9.612292131450713,inf,1.0
88,ml-exact,38,5.067941904067993,13512.8,13514.0,8.880468888762712e-05,1,exact,1.0,1.0,5.59009989154572,1.0,1.0
89,ml-exact,39,6.453751564025879,13536.75,13538.0,9.234121927345928e-05,1,exact,0.99990766730684,1.0,8.249633979390692,inf,1.0
90,ml-exact,40,5.8958964347839355,13578.0,13578.0,0.0,1,exact,1.0,1.0,8.354213476977858,,1.0
91,ml-exact,41,4.61811900138855,13524.9455782313,13526.0,7.79612577811263e-05,1,exact,0.9999220448197028,1.0,2.5000022586733377,inf,1.0
92,ml-exact,42,7.025639057159424,13527.725,13529.0,9.425088106090537e-05,1,exact,0.9999057580013305,1.0,4.654599027527176,inf,1.0
93,ml-exact,43,10.472574234008789,13563.657608695652,13565.0,9.89697132643173e-05,1,exact,0.9999747573500186,1.0,5.188350921887166,1.3424251907171998,1.0
94,ml-exact,44,4.061512231826782,13551.75,13553.0,9.223900972199163e-05,1,exact,0.9999907761841074,1.0,5.485301125832847,1.1111213598899692,1.0
95,ml-exact,45,4.208792209625244,13521.0,13521.0,0.0,1,exact,1.0,1.0,5.435817738123648,,1.0
96,ml-exact,46,4.613062381744385,13541.897435897436,13543.0,8.141873085242141e-05,1,exact,0.9999185878976177,1.0,3.664252312908731,inf,1.0
97,ml-exact,47,4.933764457702637,13564.0,13564.0,0.0,1,exact,1.0,1.0,7.091505494332267,,1.0
98,ml-exact,48,4.755006313323975,13550.955555555562,13552.0,7.707533540025109e-05,1,exact,0.9999229306047492,1.0,6.582191661014823,inf,1.0
99,ml-exact,49,5.486748695373535,13522.728991596638,13524.0,9.3990525444403e-05,1,exact,0.9999060183079442,1.0,4.102243916490891,inf,1.0
100,ml-heuristic,0,2.11967134475708,13538.833333333334,13540.0,8.61718759616949e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
101,ml-heuristic,1,0.9772210121154785,13567.0,13567.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
102,ml-heuristic,2,1.4947700500488281,13561.736842105263,13563.0,9.314130700537644e-05,1,heuristic,1.0,1.000073735437251,1.0,1.0104527831741152,1.0
103,ml-heuristic,3,0.9660820960998535,13522.0,13522.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
104,ml-heuristic,4,1.8247687816619873,13533.000000000002,13534.0,7.38934456512363e-05,1,heuristic,0.9999261120141866,1.0,1.0,inf,1.0
105,ml-heuristic,5,1.2372217178344727,13530.666666666668,13532.0,9.854158454858992e-05,1,heuristic,0.9999975364664555,1.0,1.0,1.0256435523465277,1.0
106,ml-heuristic,6,1.438443660736084,13535.0,13535.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
107,ml-heuristic,7,1.5224583148956299,13613.0,13613.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
108,ml-heuristic,8,1.8233003616333008,13578.666666666666,13580.0,9.819324430483649e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
109,ml-heuristic,9,1.5888559818267822,13584.0,13584.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
110,ml-heuristic,10,1.8794469833374023,13578.0,13578.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
111,ml-heuristic,11,0.8336913585662842,13574.0,13575.0,7.367025195226167e-05,1,heuristic,0.999926335174954,1.0,1.0,inf,1.0
112,ml-heuristic,12,1.5068776607513428,13544.0,13544.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
113,ml-heuristic,13,1.353994369506836,13534.0,13534.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
114,ml-heuristic,14,1.4777379035949707,13551.0,13551.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
115,ml-heuristic,15,1.8219943046569824,13594.0,13594.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
116,ml-heuristic,16,2.5624449253082275,13593.0,13594.0,7.356727727506805e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
117,ml-heuristic,17,1.6540775299072266,13543.0,13544.0,7.383888355608063e-05,1,heuristic,1.0,1.0000738388835562,1.0,1.0,1.0
118,ml-heuristic,18,0.8923168182373047,13525.0,13525.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
119,ml-heuristic,19,1.3496067523956299,13563.0,13564.0,7.37300007373e-05,1,heuristic,0.9999262754349749,1.0,1.0,inf,1.0
120,ml-heuristic,20,1.7499916553497314,13569.0,13569.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
121,ml-heuristic,21,0.9767782688140869,13566.0,13566.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
122,ml-heuristic,22,0.7310514450073242,13565.0,13565.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
123,ml-heuristic,23,1.6389665603637695,13580.0,13580.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
124,ml-heuristic,24,0.7995321750640869,13543.0,13543.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
125,ml-heuristic,25,1.310269832611084,13541.000000000002,13542.0,7.38497895279655e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
126,ml-heuristic,26,0.9024457931518555,13532.0,13532.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
127,ml-heuristic,27,1.7255265712738037,13521.0,13522.0,7.395902669920864e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
128,ml-heuristic,28,1.2955574989318848,13571.0,13571.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
129,ml-heuristic,29,1.3330867290496826,13595.0,13595.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
130,ml-heuristic,30,1.7372803688049316,13576.0,13577.0,7.365939893930465e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
131,ml-heuristic,31,0.7671358585357666,13582.0,13582.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
132,ml-heuristic,32,1.5739951133728027,13522.999999999998,13524.0,7.39480884420483e-05,1,heuristic,0.9999999999999999,1.0,1.0,1.0000000000018192,1.0
133,ml-heuristic,33,1.3755178451538086,13546.999999999998,13548.0,7.381708127274076e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
134,ml-heuristic,34,1.2376031875610352,13557.0,13557.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
135,ml-heuristic,35,1.5852832794189453,13568.0,13568.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
136,ml-heuristic,36,1.8026905059814453,13553.0,13554.0,7.378440197742197e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
137,ml-heuristic,37,0.7797088623046875,13532.0,13532.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
138,ml-heuristic,38,0.9065923690795898,13512.75,13514.0,9.250522654529981e-05,1,heuristic,0.9999962998046298,1.0,1.0,1.0416705210504744,1.0
139,ml-heuristic,39,0.7823076248168945,13538.0,13538.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
140,ml-heuristic,40,0.7057392597198486,13576.75,13578.0,9.206916235476089e-05,1,heuristic,0.9999079393135956,1.0,1.0,inf,1.0
141,ml-heuristic,41,1.8472459316253662,13526.0,13526.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
142,ml-heuristic,42,1.509397268295288,13529.0,13529.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
143,ml-heuristic,43,2.0184783935546875,13564.0,13565.0,7.372456502506635e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
144,ml-heuristic,44,0.7404356002807617,13551.875,13553.0,8.301434303371305e-05,1,heuristic,1.0,1.0,1.0,1.0,1.0
145,ml-heuristic,45,0.7742702960968018,13520.0,13521.0,7.396449704142012e-05,1,heuristic,0.9999260409733008,1.0,1.0,inf,1.0
146,ml-heuristic,46,1.258936882019043,13543.0,13543.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
147,ml-heuristic,47,0.6957287788391113,13564.0,13564.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
148,ml-heuristic,48,0.7224047183990479,13552.0,13552.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
149,ml-heuristic,49,1.3374993801116943,13524.0,13524.0,0.0,1,heuristic,1.0,1.0,1.0,,1.0
1 Solver Instance Wallclock Time Lower Bound Upper Bound Gap Nodes Mode Relative Lower Bound Relative Upper Bound Relative Wallclock Time Relative Gap Relative Nodes
2 0 baseline 0 88.44052076339722 13538.699999999995 13540.0 9.602103599333102e-05 1 exact 0.999990151785604 1.0 41.72369503515307 1.1142966881214733 1.0
3 1 baseline 1 74.86838150024414 13565.666666666664 13567.0 9.828734304744377e-05 1 exact 0.9999017223164048 1.0 76.61356087521061 inf 1.0
4 2 baseline 2 113.96127772331238 13560.699999999995 13562.0 9.586525769340156e-05 1 exact 0.9999235465104994 1.0 76.24000609297043 1.0400038346080955 1.0
5 3 baseline 3 91.72307801246643 13520.666666666664 13522.0 9.861446674231594e-05 1 exact 0.9999013952571116 1.0 94.94335769471294 inf 1.0
6 4 baseline 4 75.70191454887392 13532.98571428571 13534.0 7.49491454216524e-05 1 exact 0.9999250564715317 1.0 41.48575715983321 inf 1.0
7 5 baseline 5 148.34671473503113 13530.670398009952 13532.0 9.82657880901199e-05 1 exact 0.9999978122351358 1.0 119.90309626530366 1.0227729991614376 1.0
8 6 baseline 6 128.75406980514526 13533.647058823528 13535.0 9.99687054488398e-05 1 exact 0.9999000412872943 1.0 89.50928932403158 inf 1.0
9 7 baseline 7 89.82294702529906 13611.833333333336 13613.0 8.570973785060009e-05 1 exact 0.9999142976076791 1.0 58.998624886131445 inf 1.0
10 8 baseline 8 163.10344243049622 13578.666666666664 13580.0 9.819324430497046e-05 1 exact 0.9999999999999999 1.0 89.45505955167431 1.0000000000013642 1.0
11 9 baseline 9 110.7302086353302 13582.666666666664 13584.0 9.816432708371644e-05 1 exact 0.9999018453082056 1.0 69.69178446747482 inf 1.0
12 10 baseline 10 969.3387920856476 13576.642857142857 13578.0 9.996159370362496e-05 1 exact 0.9999000483976179 1.0 515.7574545488682 inf 1.0
13 11 baseline 11 74.61696720123291 13575.0 13575.0 0.0 1 exact 1.0 1.0 89.50190791176391 1.0
14 12 baseline 12 83.92108988761902 13542.649999999998 13544.0 9.968506902284139e-05 1 exact 0.9999003248670997 1.0 55.69203928988848 inf 1.0
15 13 baseline 13 71.3746600151062 13532.75 13534.0 9.236851342114499e-05 1 exact 0.9999076400177331 1.0 52.71414831739878 inf 1.0
16 14 baseline 14 95.41746068000792 13549.66666666667 13551.0 9.840340475758086e-05 1 exact 0.9999016062775197 1.0 64.56994873575405 inf 1.0
17 15 baseline 15 119.16796040534972 13592.724074074076 13594.0 9.386830181858343e-05 1 exact 0.9999061405086124 1.0 65.40523211338186 inf 1.0
18 16 baseline 16 236.61669611930847 13592.65 13594.0 9.931838162539048e-05 1 exact 0.9999742514529537 1.0 92.34020750352192 1.3500347614339328 1.0
19 17 baseline 17 151.28878140449527 13542.65 13544.0 9.968506902270708e-05 1 exact 0.9999741563907554 1.0000738388835562 91.4641415949715 1.350034889774522 1.0
20 18 baseline 18 85.78852319717406 13523.833333333332 13525.0 8.62674537545725e-05 1 exact 0.9999137399876771 1.0 96.1413272100395 inf 1.0
21 19 baseline 19 101.29387998580931 13562.666666666662 13564.0 9.830908375965231e-05 1 exact 0.9999017005799663 1.0 75.05436661902205 inf 1.0
22 20 baseline 20 158.05654454231262 13567.666666666664 13569.0 9.827285458078812e-05 1 exact 0.999901736802024 1.0 90.31845612470958 inf 1.0
23 21 baseline 21 142.13706088066098 13564.750000000002 13566.0 9.215061095841657e-05 1 exact 0.9999078578799943 1.0 145.5161989355379 inf 1.0
24 22 baseline 22 75.7931275367737 13563.714285714286 13565.0 9.479072314785627e-05 1 exact 0.9999052182612816 1.0 103.67687261190537 inf 1.0
25 23 baseline 23 125.0184965133667 13578.651041666662 13580.0 9.934406070221867e-05 1 exact 0.9999006658075599 1.0 76.27885738292231 inf 1.0
26 24 baseline 24 110.1647527217865 13541.666666666664 13543.0 9.846153846158324e-05 1 exact 0.9999015481552583 1.0 137.78651586217427 inf 1.0
27 25 baseline 25 107.13047480583192 13540.75 13542.0 9.231394125140777e-05 1 exact 0.9999815375526179 1.0 81.76214710854182 1.2500230784875868 1.0
28 26 baseline 26 86.15372657775879 13530.672413793101 13532.0 9.811679466463352e-05 1 exact 0.9999018928312963 1.0 95.4669269129848 inf 1.0
29 27 baseline 27 94.40602779388428 13520.7 13522.0 9.614886803192679e-05 1 exact 0.9999778122919903 1.0 54.71143091363273 1.3000288446596822 1.0
30 28 baseline 28 65.10137605667114 13569.749999999998 13571.0 9.21166565339685e-05 1 exact 0.9999078918281629 1.0 50.24970031074932 inf 1.0
31 29 baseline 29 62.560155391693115 13593.777777777776 13595.0 8.991041653046851e-05 1 exact 0.9999100976666256 1.0 46.92879617539241 inf 1.0
32 30 baseline 30 123.58262610435486 13575.666666666668 13577.0 9.821494340354953e-05 1 exact 0.9999754468670203 1.0 71.13568329179179 1.3333660716465885 1.0
33 31 baseline 31 77.88054895401002 13580.75 13582.0 9.20420448060674e-05 1 exact 0.9999079664261522 1.0 101.52119482807224 inf 1.0
34 32 baseline 32 91.31177544593812 13523.0 13524.0 7.394808844191378e-05 1 exact 1.0 1.0 58.01274392159489 1.0 1.0
35 33 baseline 33 125.20542597770692 13546.724137931033 13548.0 9.418233190376748e-05 1 exact 0.9999796366672351 1.0 91.02421056827991 1.275888050298017 1.0
36 34 baseline 34 93.4059066772461 13555.999999999995 13557.0 7.376807317819698e-05 1 exact 0.9999262373681489 1.0 75.47322729615996 inf 1.0
37 35 baseline 35 133.77592086791992 13566.671171171172 13568.0 9.794803839953082e-05 1 exact 0.9999020615544791 1.0 84.38612997732044 inf 1.0
38 36 baseline 36 105.60492086410522 13552.674418604644 13554.0 9.780958019141684e-05 1 exact 0.9999759771714486 1.0 58.58183671223716 1.3256132403342726 1.0
39 37 baseline 37 106.68410634994508 13530.666666666664 13532.0 9.854158454872437e-05 1 exact 0.9999014681249382 1.0 136.8255659357326 inf 1.0
40 38 baseline 38 76.45212483406067 13512.666666666664 13514.0 9.867285016532191e-05 1 exact 0.9999901328123457 1.0 84.32910693002859 1.1111220747609611 1.0
41 39 baseline 39 66.65553593635559 13536.666666666664 13538.0 9.849790691952276e-05 1 exact 0.9999015117939625 1.0 85.20374060262657 inf 1.0
42 40 baseline 40 72.2125403881073 13578.0 13578.0 0.0 1 exact 1.0 1.0 102.32184109577935 1.0
43 41 baseline 41 68.3276731967926 13526.0 13526.0 0.0 1 exact 1.0 1.0 36.988942309740004 1.0
44 42 baseline 42 91.24437737464905 13527.7 13529.0 9.609911514886287e-05 1 exact 0.9999039101190037 1.0 60.45086955649546 inf 1.0
45 43 baseline 43 197.3597583770752 13563.651515151521 13565.0 9.941901315984781e-05 1 exact 0.9999743081061281 1.0 97.77650283861117 1.3485194945001757 1.0
46 44 baseline 44 68.33869886398314 13551.749999999995 13553.0 9.223900972239434e-05 1 exact 0.9999907761841069 1.0 92.29526354225831 1.1111213598948202 1.0
47 45 baseline 45 88.19205832481384 13519.66666666667 13521.0 9.862176089131646e-05 1 exact 0.9999013879644013 1.0 113.90345047382237 inf 1.0
48 46 baseline 46 85.30370616912842 13541.745070422534 13543.0 9.267118609455138e-05 1 exact 0.9999073374010584 1.0 67.75852498047483 inf 1.0
49 47 baseline 47 80.86965203285217 13562.678333333333 13564.0 9.744879545055802e-05 1 exact 0.9999025606998919 1.0 116.23732479169651 inf 1.0
50 48 baseline 48 88.52302312850952 13550.6875 13552.0 9.685855422464728e-05 1 exact 0.9999031508264463 1.0 122.53937560747 inf 1.0
51 49 baseline 49 130.87233448028564 13523.000000000002 13524.0 7.394808844177925e-05 1 exact 0.9999260573794737 1.0 97.84851972743084 inf 1.0
52 50 ml-exact 0 9.014199018478394 13538.699999999999 13540.0 9.602103599319664e-05 1 exact 0.9999901517856042 1.0 4.252639939099353 1.114296688119914 1.0
53 51 ml-exact 1 5.4113500118255615 13565.709677419356 13567.0 9.511648202170943e-05 1 exact 0.999904892564263 1.0 5.537488392836666 inf 1.0
54 52 ml-exact 2 7.311800241470337 13560.749999999995 13562.0 9.217779252662703e-05 1 exact 0.9999272333539017 1.0 4.891588670265028 1.0 1.0
55 53 ml-exact 3 22.324601411819458 13520.72222222222 13522.0 9.450514231252222e-05 1 exact 0.9999055037880654 1.0 23.108389547788498 inf 1.0
56 54 ml-exact 4 7.276817560195923 13534.0 13534.0 0.0 1 exact 1.0 1.0 3.987802527818481 1.0
57 55 ml-exact 5 6.725529432296753 13530.699999999999 13532.0 9.607780824355662e-05 1 exact 1.0 1.0 5.435993674657236 1.0 1.0
58 56 ml-exact 6 8.695855855941772 13533.665041782733 13535.0 9.863981509409236e-05 1 exact 0.9999013699137593 1.0 6.045322519960155 inf 1.0
59 57 ml-exact 7 6.677775144577026 13612.0 13613.0 7.346459006758743e-05 1 exact 0.9999265408065819 1.0 4.386179299125712 inf 1.0
60 58 ml-exact 8 11.08420991897583 13578.642857142859 13580.0 9.994687034775287e-05 1 exact 0.999998246549209 1.0 6.079201294649372 1.0178589276210523 1.0
61 59 ml-exact 9 16.643534421920776 13582.66666666667 13584.0 9.816432708331462e-05 1 exact 0.9999018453082059 1.0 10.475168682554177 inf 1.0
62 60 ml-exact 10 16.841771364212036 13576.691176470587 13578.0 9.640224649735783e-05 1 exact 0.999903607046 1.0 8.961024978903895 inf 1.0
63 61 ml-exact 11 4.076904058456421 13573.75 13575.0 9.208951100469657e-05 1 exact 0.9999079189686925 1.0 4.89018389907214 inf 1.0
64 62 ml-exact 12 6.3809661865234375 13542.750000000002 13544.0 9.230030828289534e-05 1 exact 0.9999077082102777 1.0 4.234561539217345 inf 1.0
65 63 ml-exact 13 4.139940500259399 13532.999999999998 13534.0 7.389344565150514e-05 1 exact 0.9999261120141864 1.0 3.0575758610926025 inf 1.0
66 64 ml-exact 14 7.238400936126709 13549.66666666667 13551.0 9.840340475758086e-05 1 exact 0.9999016062775197 1.0 4.898298215480208 inf 1.0
67 65 ml-exact 15 7.4390175342559814 13592.6875 13594.0 9.655927129936593e-05 1 exact 0.9999034500514933 1.0 4.082898346741258 inf 1.0
68 66 ml-exact 16 45.386595487594604 13592.666666666664 13594.0 9.809210849005043e-05 1 exact 0.9999754775742414 1.0 17.712222822558893 1.3333660307052555 1.0
69 67 ml-exact 17 7.782220363616943 13541.750000000002 13543.0 9.230712426371635e-05 1 exact 0.9999077013955551 1.0 4.704870372100049 1.2501153839035106 1.0
70 68 ml-exact 18 3.7182631492614746 13525.0 13525.0 0.0 1 exact 1.0 1.0 4.166976429522626 1.0
71 69 ml-exact 19 5.698674201965332 13564.0 13564.0 0.0 1 exact 1.0 1.0 4.222470132021685 1.0
72 70 ml-exact 20 27.741767644882202 13567.699999999997 13569.0 9.581579781414025e-05 1 exact 0.9999041933819734 1.0 15.852514244896831 inf 1.0
73 71 ml-exact 21 5.77320122718811 13566.0 13566.0 0.0 1 exact 1.0 1.0 5.91045215839762 1.0
74 72 ml-exact 22 3.9558210372924805 13563.871192621193 13565.0 8.32216232944913e-05 1 exact 0.9999167853019678 1.0 5.41113907141357 inf 1.0
75 73 ml-exact 23 23.586190462112427 13578.64814814815 13580.0 9.955717514005507e-05 1 exact 0.9999004527355044 1.0 14.390891817144492 inf 1.0
76 74 ml-exact 24 4.234185695648193 13543.0 13543.0 0.0 1 exact 1.0 1.0 5.2958290206504826 1.0
77 75 ml-exact 25 4.053018093109131 13541.0 13542.0 7.384978952809984e-05 1 exact 0.9999999999999999 1.0 3.0932697924001986 1.0000000000018192 1.0
78 76 ml-exact 26 4.456820011138916 13532.0 13532.0 0.0 1 exact 1.0 1.0 4.9386013486451725 1.0
79 77 ml-exact 27 6.604680299758911 13520.892857142859 13522.0 8.188385699369056e-05 1 exact 0.9999920758185681 1.0 3.827631755843238 1.10715163041169 1.0
80 78 ml-exact 28 4.3237597942352295 13569.666666666666 13571.0 9.825837038497186e-05 1 exact 0.9999017512833738 1.0 3.3373739087612315 inf 1.0
81 79 ml-exact 29 4.937336444854736 13593.833333333334 13595.0 8.582322866981795e-05 1 exact 0.9999141841363247 1.0 3.7036873425140273 inf 1.0
82 80 ml-exact 30 7.1004478931427 13575.670776255707 13577.0 9.791219647266045e-05 1 exact 0.9999757495768788 1.0 4.087105351928353 1.3292559793128385 1.0
83 81 ml-exact 31 4.129274129867554 13582.0 13582.0 0.0 1 exact 1.0 1.0 5.3827155697676625 1.0
84 82 ml-exact 32 4.985649824142456 13522.750000000002 13524.0 9.243681943378239e-05 1 exact 0.9999815129778896 1.0 3.1675128987275314 1.2500231092030394 1.0
85 83 ml-exact 33 26.542813777923584 13546.649999999996 13548.0 9.9655634419137e-05 1 exact 0.9999741640215545 1.0 19.29659718442664 1.350034879473593 1.0
86 84 ml-exact 34 5.016777992248535 13557.0 13557.0 0.0 1 exact 1.0 1.0 4.053624007009211 1.0
87 85 ml-exact 35 35.91903018951416 13566.666666666662 13568.0 9.828009828041115e-05 1 exact 0.9999017295597481 1.0 22.657799180648382 inf 1.0
88 86 ml-exact 36 7.446932315826416 13552.654459753448 13554.0 9.928241368119515e-05 1 exact 0.9999745045195491 1.0 4.1310098938875015 1.345574552621238 1.0
89 87 ml-exact 37 7.494789361953735 13530.666666666668 13532.0 9.854158454858992e-05 1 exact 0.9999014681249385 1.0 9.612292131450713 inf 1.0
90 88 ml-exact 38 5.067941904067993 13512.8 13514.0 8.880468888762712e-05 1 exact 1.0 1.0 5.59009989154572 1.0 1.0
91 89 ml-exact 39 6.453751564025879 13536.75 13538.0 9.234121927345928e-05 1 exact 0.99990766730684 1.0 8.249633979390692 inf 1.0
92 90 ml-exact 40 5.8958964347839355 13578.0 13578.0 0.0 1 exact 1.0 1.0 8.354213476977858 1.0
93 91 ml-exact 41 4.61811900138855 13524.9455782313 13526.0 7.79612577811263e-05 1 exact 0.9999220448197028 1.0 2.5000022586733377 inf 1.0
94 92 ml-exact 42 7.025639057159424 13527.725 13529.0 9.425088106090537e-05 1 exact 0.9999057580013305 1.0 4.654599027527176 inf 1.0
95 93 ml-exact 43 10.472574234008789 13563.657608695652 13565.0 9.89697132643173e-05 1 exact 0.9999747573500186 1.0 5.188350921887166 1.3424251907171998 1.0
96 94 ml-exact 44 4.061512231826782 13551.75 13553.0 9.223900972199163e-05 1 exact 0.9999907761841074 1.0 5.485301125832847 1.1111213598899692 1.0
97 95 ml-exact 45 4.208792209625244 13521.0 13521.0 0.0 1 exact 1.0 1.0 5.435817738123648 1.0
98 96 ml-exact 46 4.613062381744385 13541.897435897436 13543.0 8.141873085242141e-05 1 exact 0.9999185878976177 1.0 3.664252312908731 inf 1.0
99 97 ml-exact 47 4.933764457702637 13564.0 13564.0 0.0 1 exact 1.0 1.0 7.091505494332267 1.0
100 98 ml-exact 48 4.755006313323975 13550.955555555562 13552.0 7.707533540025109e-05 1 exact 0.9999229306047492 1.0 6.582191661014823 inf 1.0
101 99 ml-exact 49 5.486748695373535 13522.728991596638 13524.0 9.3990525444403e-05 1 exact 0.9999060183079442 1.0 4.102243916490891 inf 1.0
102 100 ml-heuristic 0 2.11967134475708 13538.833333333334 13540.0 8.61718759616949e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
103 101 ml-heuristic 1 0.9772210121154785 13567.0 13567.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
104 102 ml-heuristic 2 1.4947700500488281 13561.736842105263 13563.0 9.314130700537644e-05 1 heuristic 1.0 1.000073735437251 1.0 1.0104527831741152 1.0
105 103 ml-heuristic 3 0.9660820960998535 13522.0 13522.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
106 104 ml-heuristic 4 1.8247687816619873 13533.000000000002 13534.0 7.38934456512363e-05 1 heuristic 0.9999261120141866 1.0 1.0 inf 1.0
107 105 ml-heuristic 5 1.2372217178344727 13530.666666666668 13532.0 9.854158454858992e-05 1 heuristic 0.9999975364664555 1.0 1.0 1.0256435523465277 1.0
108 106 ml-heuristic 6 1.438443660736084 13535.0 13535.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
109 107 ml-heuristic 7 1.5224583148956299 13613.0 13613.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
110 108 ml-heuristic 8 1.8233003616333008 13578.666666666666 13580.0 9.819324430483649e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
111 109 ml-heuristic 9 1.5888559818267822 13584.0 13584.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
112 110 ml-heuristic 10 1.8794469833374023 13578.0 13578.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
113 111 ml-heuristic 11 0.8336913585662842 13574.0 13575.0 7.367025195226167e-05 1 heuristic 0.999926335174954 1.0 1.0 inf 1.0
114 112 ml-heuristic 12 1.5068776607513428 13544.0 13544.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
115 113 ml-heuristic 13 1.353994369506836 13534.0 13534.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
116 114 ml-heuristic 14 1.4777379035949707 13551.0 13551.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
117 115 ml-heuristic 15 1.8219943046569824 13594.0 13594.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
118 116 ml-heuristic 16 2.5624449253082275 13593.0 13594.0 7.356727727506805e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
119 117 ml-heuristic 17 1.6540775299072266 13543.0 13544.0 7.383888355608063e-05 1 heuristic 1.0 1.0000738388835562 1.0 1.0 1.0
120 118 ml-heuristic 18 0.8923168182373047 13525.0 13525.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
121 119 ml-heuristic 19 1.3496067523956299 13563.0 13564.0 7.37300007373e-05 1 heuristic 0.9999262754349749 1.0 1.0 inf 1.0
122 120 ml-heuristic 20 1.7499916553497314 13569.0 13569.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
123 121 ml-heuristic 21 0.9767782688140869 13566.0 13566.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
124 122 ml-heuristic 22 0.7310514450073242 13565.0 13565.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
125 123 ml-heuristic 23 1.6389665603637695 13580.0 13580.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
126 124 ml-heuristic 24 0.7995321750640869 13543.0 13543.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
127 125 ml-heuristic 25 1.310269832611084 13541.000000000002 13542.0 7.38497895279655e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
128 126 ml-heuristic 26 0.9024457931518555 13532.0 13532.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
129 127 ml-heuristic 27 1.7255265712738037 13521.0 13522.0 7.395902669920864e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
130 128 ml-heuristic 28 1.2955574989318848 13571.0 13571.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
131 129 ml-heuristic 29 1.3330867290496826 13595.0 13595.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
132 130 ml-heuristic 30 1.7372803688049316 13576.0 13577.0 7.365939893930465e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
133 131 ml-heuristic 31 0.7671358585357666 13582.0 13582.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
134 132 ml-heuristic 32 1.5739951133728027 13522.999999999998 13524.0 7.39480884420483e-05 1 heuristic 0.9999999999999999 1.0 1.0 1.0000000000018192 1.0
135 133 ml-heuristic 33 1.3755178451538086 13546.999999999998 13548.0 7.381708127274076e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
136 134 ml-heuristic 34 1.2376031875610352 13557.0 13557.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
137 135 ml-heuristic 35 1.5852832794189453 13568.0 13568.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
138 136 ml-heuristic 36 1.8026905059814453 13553.0 13554.0 7.378440197742197e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
139 137 ml-heuristic 37 0.7797088623046875 13532.0 13532.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
140 138 ml-heuristic 38 0.9065923690795898 13512.75 13514.0 9.250522654529981e-05 1 heuristic 0.9999962998046298 1.0 1.0 1.0416705210504744 1.0
141 139 ml-heuristic 39 0.7823076248168945 13538.0 13538.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
142 140 ml-heuristic 40 0.7057392597198486 13576.75 13578.0 9.206916235476089e-05 1 heuristic 0.9999079393135956 1.0 1.0 inf 1.0
143 141 ml-heuristic 41 1.8472459316253662 13526.0 13526.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
144 142 ml-heuristic 42 1.509397268295288 13529.0 13529.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
145 143 ml-heuristic 43 2.0184783935546875 13564.0 13565.0 7.372456502506635e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
146 144 ml-heuristic 44 0.7404356002807617 13551.875 13553.0 8.301434303371305e-05 1 heuristic 1.0 1.0 1.0 1.0 1.0
147 145 ml-heuristic 45 0.7742702960968018 13520.0 13521.0 7.396449704142012e-05 1 heuristic 0.9999260409733008 1.0 1.0 inf 1.0
148 146 ml-heuristic 46 1.258936882019043 13543.0 13543.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
149 147 ml-heuristic 47 0.6957287788391113 13564.0 13564.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
150 148 ml-heuristic 48 0.7224047183990479 13552.0 13552.0 0.0 1 heuristic 1.0 1.0 1.0 1.0
151 149 ml-heuristic 49 1.3374993801116943 13524.0 13524.0 0.0 1 heuristic 1.0 1.0 1.0 1.0

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@ -20,6 +20,8 @@ To illustrate the performance of `LearningSolver`, and to set a baseline for new
All experiments presented here were performed on a Linux server (Ubuntu Linux 18.04 LTS) with Intel Xeon Gold 6230s (2 processors, 40 cores, 80 threads) and 256 GB RAM (DDR4, 2933 MHz). All solvers were restricted to use 4 threads, with no time limits, and 10 instances were solved simultaneously at a time. All experiments presented here were performed on a Linux server (Ubuntu Linux 18.04 LTS) with Intel Xeon Gold 6230s (2 processors, 40 cores, 80 threads) and 256 GB RAM (DDR4, 2933 MHz). All solvers were restricted to use 4 threads, with no time limits, and 10 instances were solved simultaneously at a time.
## Maximum Weight Stable Set Problem ## Maximum Weight Stable Set Problem
### Problem definition ### Problem definition
@ -45,6 +47,53 @@ MaxWeightStableSetGenerator(w=uniform(loc=100., scale=50.),
![alt](figures/benchmark_stab_a.png) ![alt](figures/benchmark_stab_a.png)
## Traveling Salesman Problem
### Problem definition
Given a list of cities and the distance between each pair of cities, the problem asks for the
shortest route starting at the first city, visiting each other city exactly once, then returning
to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's
21 NP-complete problems.
### Random problem generator
The class `TravelingSalesmanGenerator` can be used to generate random instances of this
problem. Initially, the generator creates $n$ cities $(x_1,y_1),\ldots,(x_n,y_n) \in \mathbb{R}^2$,
where $n, x_i$ and $y_i$ are sampled independently from the provided probability distributions `n`,
`x` and `y`. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:
$$
d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}
$$
where $\gamma_{i,j}$ is sampled from the distribution `gamma`.
If `fix_cities=True` is provided, the list of cities is kept the same for all generated instances.
The $gamma$ values, and therefore also the distances, are still different.
By default, all distances $d_{i,j}$ are rounded to the nearest integer. If `round=False`
is provided, this rounding will be disabled.
### Challenge A
* Fixed list of 350 cities in the $[0, 1000]^2$ square
* $\gamma_{i,j} \sim U(0.95, 1.05)$
* 500 training instances, 50 test instances
```python
TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=350, high=351),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True,
round=True,
)
```
![alt](figures/benchmark_tsp_a.png)
## Multidimensional 0-1 Knapsack Problem ## Multidimensional 0-1 Knapsack Problem
### Problem definition ### Problem definition
@ -115,3 +164,4 @@ MultiKnapsackGenerator(n=randint(low=250, high=251),
``` ```
![alt](figures/benchmark_knapsack_a.png) ![alt](figures/benchmark_knapsack_a.png)

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@ -35,16 +35,16 @@ Instances to be solved by `LearningSolver` must derive from the abstract class `
* `instance.to_model()`, which returns a concrete Pyomo model corresponding to the instance; * `instance.to_model()`, which returns a concrete Pyomo model corresponding to the instance;
* `instance.get_instance_features()`, which returns a 1-dimensional Numpy array of (numerical) features describing the entire instance; * `instance.get_instance_features()`, which returns a 1-dimensional Numpy array of (numerical) features describing the entire instance;
* `instance.get_variable_features(var, index)`, which returns a 1-dimensional array of (numerical) features describing a particular decision variable. * `instance.get_variable_features(var_name, index)`, which returns a 1-dimensional array of (numerical) features describing a particular decision variable.
The first method is used by `LearningSolver` to construct a concrete Pyomo model, which will be provided to the internal MIP solver. The user should keep a reference to this Pyomo model, in order to retrieve, for example, the optimal variable values. The first method is used by `LearningSolver` to construct a concrete Pyomo model, which will be provided to the internal MIP solver. The user should keep a reference to this Pyomo model, in order to retrieve, for example, the optimal variable values.
The second and third methods provide an encoding of the instance, which can be used by the ML models to make predictions. In the knapsack problem, for example, an implementation may decide to provide as instance features the average weights, average prices, number of items and the size of the knapsack. The weight and the price of each individual item could be provided as variable features. See `miplearn/problems/knapsack.py` for a concrete example. The second and third methods provide an encoding of the instance, which can be used by the ML models to make predictions. In the knapsack problem, for example, an implementation may decide to provide as instance features the average weights, average prices, number of items and the size of the knapsack. The weight and the price of each individual item could be provided as variable features. See `miplearn/problems/knapsack.py` for a concrete example.
An optional method which can be implemented is `instance.get_variable_category(var, index)`, which returns a category (a string, an integer or any hashable type) for each decision variable. If two variables have the same category, `LearningSolver` will use the same internal ML model to predict the values of both variables. By default, all variables belong to the `"default"` category, and therefore only one ML model is used for all variables. If the returned category is `None`, ML predictors will ignore the variable. An optional method which can be implemented is `instance.get_variable_category(var_name, index)`, which returns a category (a string, an integer or any hashable type) for each decision variable. If two variables have the same category, `LearningSolver` will use the same internal ML model to predict the values of both variables. By default, all variables belong to the `"default"` category, and therefore only one ML model is used for all variables. If the returned category is `None`, ML predictors will ignore the variable.
It is not necessary to have a one-to-one correspondence between features and problem instances. One important (and deliberate) limitation of MIPLearn, however, is that `get_instance_features()` must always return arrays of same length for all relevant instances of the problem. Similarly, `get_variable_features(var, index)` must also always return arrays of same length for all variables in each category. It is up to the user to decide how to encode variable-length characteristics of the problem into fixed-length vectors. In graph problems, for example, graph embeddings can be used to reduce the (variable-length) lists of nodes and edges into a fixed-length structure that still preserves some properties of the graph. Different instance encodings may have significant impact on performance. It is not necessary to have a one-to-one correspondence between features and problem instances. One important (and deliberate) limitation of MIPLearn, however, is that `get_instance_features()` must always return arrays of same length for all relevant instances of the problem. Similarly, `get_variable_features(var_name, index)` must also always return arrays of same length for all variables in each category. It is up to the user to decide how to encode variable-length characteristics of the problem into fixed-length vectors. In graph problems, for example, graph embeddings can be used to reduce the (variable-length) lists of nodes and edges into a fixed-length structure that still preserves some properties of the graph. Different instance encodings may have significant impact on performance.
### Obtaining heuristic solutions ### Obtaining heuristic solutions

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@ -32,15 +32,6 @@
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@ -142,9 +133,10 @@
<hr> <hr>
<p> <p>
<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.<br></small> <small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
<small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</p></small> <small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</small>
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@ -32,15 +32,6 @@
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<script>
WebFont.load({
google: {
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@ -200,9 +191,10 @@ POSSIBILITY OF SUCH DAMAGE.
<hr> <hr>
<p> <p>
<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.<br></small> <small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
<small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</p></small> <small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</small>
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@ -32,15 +32,6 @@
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<![endif]--> <![endif]-->
<script src="//ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
<script>
WebFont.load({
google: {
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}
});
</script>
@ -209,9 +200,10 @@ benchmark.parallel_solve(test_instances)
<hr> <hr>
<p> <p>
<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.<br></small> <small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
<small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</p></small> <small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</small>
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@ -32,15 +32,6 @@
<script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
<![endif]--> <![endif]-->
<script src="//ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
<script>
WebFont.load({
google: {
families: ['Open Sans', 'PT Sans']
}
});
</script>
@ -162,9 +153,10 @@ solver = LearningSolver(solver=&quot;cplex&quot;,
<hr> <hr>
<p> <p>
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@ -32,15 +32,6 @@
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<![endif]--> <![endif]-->
<script src="//ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
<script>
WebFont.load({
google: {
families: ['Open Sans', 'PT Sans']
}
});
</script>
@ -188,9 +179,10 @@
<hr> <hr>
<p> <p>
<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.<br></small> <small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
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@ -276,6 +268,6 @@
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@ -1,88 +1,78 @@
function getSearchTerm() function getSearchTerm() {
{
var sPageURL = window.location.search.substring(1); var sPageURL = window.location.search.substring(1);
var sURLVariables = sPageURL.split('&'); var sURLVariables = sPageURL.split('&');
for (var i = 0; i < sURLVariables.length; i++) for (var i = 0; i < sURLVariables.length; i++) {
{
var sParameterName = sURLVariables[i].split('='); var sParameterName = sURLVariables[i].split('=');
if (sParameterName[0] == 'q') if (sParameterName[0] == 'q') {
{
return sParameterName[1]; return sParameterName[1];
} }
} }
} }
$(document).ready(function() { $(document).ready(function() {
/**
* ------------------------------------------------------------------------
* Cinder theme specific
* ------------------------------------------------------------------------
*/
hljs.initHighlightingOnLoad();
/** /**
* ------------------------------------------------------------------------ * ------------------------------------------------------------------------
* Taken from themes/mkdocs/js/base.js * Taken from themes/mkdocs/js/base.js
* ------------------------------------------------------------------------ * ------------------------------------------------------------------------
*/ */
var search_term = getSearchTerm(), var search_term = getSearchTerm(),
$search_modal = $('#mkdocs_search_modal'), $search_modal = $('#mkdocs_search_modal'),
$keyboard_modal = $('#mkdocs_keyboard_modal'); $keyboard_modal = $('#mkdocs_keyboard_modal');
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$search_modal.modal(); $search_modal.modal();
} }
// make sure search input gets autofocus everytime modal opens. // make sure search input gets autofocus everytime modal opens.
$search_modal.on('shown.bs.modal', function () { $search_modal.on('shown.bs.modal', function() {
$search_modal.find('#mkdocs-search-query').focus(); $search_modal.find('#mkdocs-search-query').focus();
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// Close search modal when result is selected // Close search modal when result is selected
// The links get added later so listen to parent // The links get added later so listen to parent
$('#mkdocs-search-results').click(function(e) { $('#mkdocs-search-results').click(function(e) {
if ($(e.target).is('a')) { if ($(e.target).is('a')) {
$search_modal.modal('hide'); $search_modal.modal('hide');
} }
}); });
if (typeof shortcuts !== 'undefined') { if (typeof shortcuts !== 'undefined') {
// Populate keyboard modal with proper Keys // Populate keyboard modal with proper Keys
$keyboard_modal.find('.help.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.help]; $keyboard_modal.find('.help.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.help];
$keyboard_modal.find('.prev.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.previous]; $keyboard_modal.find('.prev.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.previous];
$keyboard_modal.find('.next.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.next]; $keyboard_modal.find('.next.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.next];
$keyboard_modal.find('.search.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.search]; $keyboard_modal.find('.search.shortcut kbd')[0].innerHTML = keyCodes[shortcuts.search];
// Keyboard navigation // Keyboard navigation
document.addEventListener("keydown", function(e) { document.addEventListener("keydown", function(e) {
if ($(e.target).is(':input')) return true; if ($(e.target).is(':input')) return true;
var key = e.which || e.key || window.event && window.event.key; var key = e.which || e.key || window.event && window.event.key;
var page; var page;
switch (key) { switch (key) {
case shortcuts.next: case shortcuts.next:
page = $('.navbar a[rel="next"]:first').prop('href'); page = $('.navbar a[rel="next"]:first').prop('href');
break; break;
case shortcuts.previous: case shortcuts.previous:
page = $('.navbar a[rel="prev"]:first').prop('href'); page = $('.navbar a[rel="prev"]:first').prop('href');
break; break;
case shortcuts.search: case shortcuts.search:
e.preventDefault(); e.preventDefault();
$keyboard_modal.modal('hide'); $keyboard_modal.modal('hide');
$search_modal.modal('show'); $search_modal.modal('show');
$search_modal.find('#mkdocs-search-query').focus(); $search_modal.find('#mkdocs-search-query').focus();
break; break;
case shortcuts.help: case shortcuts.help:
$search_modal.modal('hide'); $search_modal.modal('hide');
$keyboard_modal.modal('show'); $keyboard_modal.modal('show');
break; break;
default: break; default:
} break;
if (page) { }
$keyboard_modal.modal('hide'); if (page) {
window.location.href = page; $keyboard_modal.modal('hide');
} window.location.href = page;
}); }
});
} }
$('table').addClass('table table-striped table-hover'); $('table').addClass('table table-striped table-hover');
@ -121,115 +111,115 @@ $("li.disabled a").click(function() {
// See https://www.cambiaresearch.com/articles/15/javascript-char-codes-key-codes // See https://www.cambiaresearch.com/articles/15/javascript-char-codes-key-codes
// We only list common keys below. Obscure keys are omited and their use is discouraged. // We only list common keys below. Obscure keys are omited and their use is discouraged.
var keyCodes = { var keyCodes = {
8: 'backspace', 8: 'backspace',
9: 'tab', 9: 'tab',
13: 'enter', 13: 'enter',
16: 'shift', 16: 'shift',
17: 'ctrl', 17: 'ctrl',
18: 'alt', 18: 'alt',
19: 'pause/break', 19: 'pause/break',
20: 'caps lock', 20: 'caps lock',
27: 'escape', 27: 'escape',
32: 'spacebar', 32: 'spacebar',
33: 'page up', 33: 'page up',
34: 'page down', 34: 'page down',
35: 'end', 35: 'end',
36: 'home', 36: 'home',
37: '&larr;', 37: '&larr;',
38: '&uarr;', 38: '&uarr;',
39: '&rarr;', 39: '&rarr;',
40: '&darr;', 40: '&darr;',
45: 'insert', 45: 'insert',
46: 'delete', 46: 'delete',
48: '0', 48: '0',
49: '1', 49: '1',
50: '2', 50: '2',
51: '3', 51: '3',
52: '4', 52: '4',
53: '5', 53: '5',
54: '6', 54: '6',
55: '7', 55: '7',
56: '8', 56: '8',
57: '9', 57: '9',
65: 'a', 65: 'a',
66: 'b', 66: 'b',
67: 'c', 67: 'c',
68: 'd', 68: 'd',
69: 'e', 69: 'e',
70: 'f', 70: 'f',
71: 'g', 71: 'g',
72: 'h', 72: 'h',
73: 'i', 73: 'i',
74: 'j', 74: 'j',
75: 'k', 75: 'k',
76: 'l', 76: 'l',
77: 'm', 77: 'm',
78: 'n', 78: 'n',
79: 'o', 79: 'o',
80: 'p', 80: 'p',
81: 'q', 81: 'q',
82: 'r', 82: 'r',
83: 's', 83: 's',
84: 't', 84: 't',
85: 'u', 85: 'u',
86: 'v', 86: 'v',
87: 'w', 87: 'w',
88: 'x', 88: 'x',
89: 'y', 89: 'y',
90: 'z', 90: 'z',
91: 'Left Windows Key / Left ⌘', 91: 'Left Windows Key / Left ⌘',
92: 'Right Windows Key', 92: 'Right Windows Key',
93: 'Windows Menu / Right ⌘', 93: 'Windows Menu / Right ⌘',
96: 'numpad 0', 96: 'numpad 0',
97: 'numpad 1', 97: 'numpad 1',
98: 'numpad 2', 98: 'numpad 2',
99: 'numpad 3', 99: 'numpad 3',
100: 'numpad 4', 100: 'numpad 4',
101: 'numpad 5', 101: 'numpad 5',
102: 'numpad 6', 102: 'numpad 6',
103: 'numpad 7', 103: 'numpad 7',
104: 'numpad 8', 104: 'numpad 8',
105: 'numpad 9', 105: 'numpad 9',
106: 'multiply', 106: 'multiply',
107: 'add', 107: 'add',
109: 'subtract', 109: 'subtract',
110: 'decimal point', 110: 'decimal point',
111: 'divide', 111: 'divide',
112: 'f1', 112: 'f1',
113: 'f2', 113: 'f2',
114: 'f3', 114: 'f3',
115: 'f4', 115: 'f4',
116: 'f5', 116: 'f5',
117: 'f6', 117: 'f6',
118: 'f7', 118: 'f7',
119: 'f8', 119: 'f8',
120: 'f9', 120: 'f9',
121: 'f10', 121: 'f10',
122: 'f11', 122: 'f11',
123: 'f12', 123: 'f12',
124: 'f13', 124: 'f13',
125: 'f14', 125: 'f14',
126: 'f15', 126: 'f15',
127: 'f16', 127: 'f16',
128: 'f17', 128: 'f17',
129: 'f18', 129: 'f18',
130: 'f19', 130: 'f19',
131: 'f20', 131: 'f20',
132: 'f21', 132: 'f21',
133: 'f22', 133: 'f22',
134: 'f23', 134: 'f23',
135: 'f24', 135: 'f24',
144: 'num lock', 144: 'num lock',
145: 'scroll lock', 145: 'scroll lock',
186: '&semi;', 186: '&semi;',
187: '&equals;', 187: '&equals;',
188: '&comma;', 188: '&comma;',
189: '&hyphen;', 189: '&hyphen;',
190: '&period;', 190: '&period;',
191: '&quest;', 191: '&quest;',
192: '&grave;', 192: '&grave;',
219: '&lsqb;', 219: '&lsqb;',
220: '&bsol;', 220: '&bsol;',
221: '&rsqb;', 221: '&rsqb;',
222: '&apos;', 222: '&apos;',
}; };

62
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@ -32,15 +32,6 @@
<script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
<![endif]--> <![endif]-->
<script src="//ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
<script>
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families: ['Open Sans', 'PT Sans']
}
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@ -149,11 +140,16 @@
<li class="third-level"><a href="#problem-definition">Problem definition</a></li> <li class="third-level"><a href="#problem-definition">Problem definition</a></li>
<li class="third-level"><a href="#random-instance-generator">Random instance generator</a></li> <li class="third-level"><a href="#random-instance-generator">Random instance generator</a></li>
<li class="third-level"><a href="#challenge-a">Challenge A</a></li> <li class="third-level"><a href="#challenge-a">Challenge A</a></li>
<li class="second-level"><a href="#multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</a></li> <li class="second-level"><a href="#traveling-salesman-problem">Traveling Salesman Problem</a></li>
<li class="third-level"><a href="#problem-definition_1">Problem definition</a></li> <li class="third-level"><a href="#problem-definition_1">Problem definition</a></li>
<li class="third-level"><a href="#random-instance-generator_1">Random instance generator</a></li> <li class="third-level"><a href="#random-problem-generator">Random problem generator</a></li>
<li class="third-level"><a href="#challenge-a_1">Challenge A</a></li> <li class="third-level"><a href="#challenge-a_1">Challenge A</a></li>
<li class="second-level"><a href="#multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</a></li>
<li class="third-level"><a href="#problem-definition_2">Problem definition</a></li>
<li class="third-level"><a href="#random-instance-generator_1">Random instance generator</a></li>
<li class="third-level"><a href="#challenge-a_2">Challenge A</a></li>
</ul> </ul>
</div></div> </div></div>
<div class="col-md-9" role="main"> <div class="col-md-9" role="main">
@ -190,8 +186,43 @@
</code></pre> </code></pre>
<p><img alt="alt" src="../figures/benchmark_stab_a.png" /></p> <p><img alt="alt" src="../figures/benchmark_stab_a.png" /></p>
<h2 id="multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</h2> <h2 id="traveling-salesman-problem">Traveling Salesman Problem</h2>
<h3 id="problem-definition_1">Problem definition</h3> <h3 id="problem-definition_1">Problem definition</h3>
<p>Given a list of cities and the distance between each pair of cities, the problem asks for the
shortest route starting at the first city, visiting each other city exactly once, then returning
to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's
21 NP-complete problems.</p>
<h3 id="random-problem-generator">Random problem generator</h3>
<p>The class <code>TravelingSalesmanGenerator</code> can be used to generate random instances of this
problem. Initially, the generator creates $n$ cities $(x_1,y_1),\ldots,(x_n,y_n) \in \mathbb{R}^2$,
where $n, x_i$ and $y_i$ are sampled independently from the provided probability distributions <code>n</code>,
<code>x</code> and <code>y</code>. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:
<script type="math/tex; mode=display">
d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}
</script>
where $\gamma_{i,j}$ is sampled from the distribution <code>gamma</code>.</p>
<p>If <code>fix_cities=True</code> is provided, the list of cities is kept the same for all generated instances.
The $gamma$ values, and therefore also the distances, are still different.</p>
<p>By default, all distances $d_{i,j}$ are rounded to the nearest integer. If <code>round=False</code>
is provided, this rounding will be disabled.</p>
<h3 id="challenge-a_1">Challenge A</h3>
<ul>
<li>Fixed list of 350 cities in the $[0, 1000]^2$ square</li>
<li>$\gamma_{i,j} \sim U(0.95, 1.05)$</li>
<li>500 training instances, 50 test instances</li>
</ul>
<pre><code class="python">TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=350, high=351),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True,
round=True,
)
</code></pre>
<p><img alt="alt" src="../figures/benchmark_tsp_a.png" /></p>
<h2 id="multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</h2>
<h3 id="problem-definition_2">Problem definition</h3>
<p>Given a set of $n$ items and $m$ types of resources (also called <em>knapsacks</em>), the problem is to find a subset of items that maximizes profit without consuming more resources than it is available. More precisely, the problem is:</p> <p>Given a set of $n$ items and $m$ types of resources (also called <em>knapsacks</em>), the problem is to find a subset of items that maximizes profit without consuming more resources than it is available. More precisely, the problem is:</p>
<p> <p>
<script type="math/tex; mode=display">\begin{align*} <script type="math/tex; mode=display">\begin{align*}
@ -233,7 +264,7 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
<li>Fréville, Arnaud. <em>The multidimensional 0–1 knapsack problem: An overview.</em> European Journal of Operational Research 155.1 (2004): 1-21.</li> <li>Fréville, Arnaud. <em>The multidimensional 0–1 knapsack problem: An overview.</em> European Journal of Operational Research 155.1 (2004): 1-21.</li>
</ul> </ul>
</div> </div>
<h3 id="challenge-a_1">Challenge A</h3> <h3 id="challenge-a_2">Challenge A</h3>
<ul> <ul>
<li>250 variables, 10 constraints, fixed weights</li> <li>250 variables, 10 constraints, fixed weights</li>
<li>$w \sim U(0, 1000), \gamma \sim U(0.95, 1.05)$</li> <li>$w \sim U(0, 1000), \gamma \sim U(0.95, 1.05)$</li>
@ -260,9 +291,10 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
<hr> <hr>
<p> <p>
<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.<br></small> <small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
<small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</p></small> <small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</small>
</p>

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<?xml version="1.0" encoding="UTF-8"?> <?xml version="1.0" encoding="UTF-8"?>
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"> <urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"><url>
<url>
<loc>None</loc> <loc>None</loc>
<lastmod>2020-02-24</lastmod> <lastmod>2020-02-25</lastmod>
<changefreq>daily</changefreq> <changefreq>daily</changefreq>
</url> </url><url>
<url>
<loc>None</loc> <loc>None</loc>
<lastmod>2020-02-24</lastmod> <lastmod>2020-02-25</lastmod>
<changefreq>daily</changefreq> <changefreq>daily</changefreq>
</url> </url><url>
<url>
<loc>None</loc> <loc>None</loc>
<lastmod>2020-02-24</lastmod> <lastmod>2020-02-25</lastmod>
<changefreq>daily</changefreq> <changefreq>daily</changefreq>
</url> </url><url>
<url>
<loc>None</loc> <loc>None</loc>
<lastmod>2020-02-24</lastmod> <lastmod>2020-02-25</lastmod>
<changefreq>daily</changefreq> <changefreq>daily</changefreq>
</url> </url><url>
<url>
<loc>None</loc> <loc>None</loc>
<lastmod>2020-02-24</lastmod> <lastmod>2020-02-25</lastmod>
<changefreq>daily</changefreq> <changefreq>daily</changefreq>
</url> </url><url>
<url>
<loc>None</loc> <loc>None</loc>
<lastmod>2020-02-24</lastmod> <lastmod>2020-02-25</lastmod>
<changefreq>daily</changefreq> <changefreq>daily</changefreq>
</url> </url>
</urlset> </urlset>

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docs/usage/index.html
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@ -32,15 +32,6 @@
<script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script> <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
<![endif]--> <![endif]-->
<script src="//ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
<script>
WebFont.load({
google: {
families: ['Open Sans', 'PT Sans']
}
});
</script>
@ -182,12 +173,12 @@ for instance in all_instances:
<ul> <ul>
<li><code>instance.to_model()</code>, which returns a concrete Pyomo model corresponding to the instance;</li> <li><code>instance.to_model()</code>, which returns a concrete Pyomo model corresponding to the instance;</li>
<li><code>instance.get_instance_features()</code>, which returns a 1-dimensional Numpy array of (numerical) features describing the entire instance;</li> <li><code>instance.get_instance_features()</code>, which returns a 1-dimensional Numpy array of (numerical) features describing the entire instance;</li>
<li><code>instance.get_variable_features(var, index)</code>, which returns a 1-dimensional array of (numerical) features describing a particular decision variable.</li> <li><code>instance.get_variable_features(var_name, index)</code>, which returns a 1-dimensional array of (numerical) features describing a particular decision variable.</li>
</ul> </ul>
<p>The first method is used by <code>LearningSolver</code> to construct a concrete Pyomo model, which will be provided to the internal MIP solver. The user should keep a reference to this Pyomo model, in order to retrieve, for example, the optimal variable values.</p> <p>The first method is used by <code>LearningSolver</code> to construct a concrete Pyomo model, which will be provided to the internal MIP solver. The user should keep a reference to this Pyomo model, in order to retrieve, for example, the optimal variable values.</p>
<p>The second and third methods provide an encoding of the instance, which can be used by the ML models to make predictions. In the knapsack problem, for example, an implementation may decide to provide as instance features the average weights, average prices, number of items and the size of the knapsack. The weight and the price of each individual item could be provided as variable features. See <code>miplearn/problems/knapsack.py</code> for a concrete example.</p> <p>The second and third methods provide an encoding of the instance, which can be used by the ML models to make predictions. In the knapsack problem, for example, an implementation may decide to provide as instance features the average weights, average prices, number of items and the size of the knapsack. The weight and the price of each individual item could be provided as variable features. See <code>miplearn/problems/knapsack.py</code> for a concrete example.</p>
<p>An optional method which can be implemented is <code>instance.get_variable_category(var, index)</code>, which returns a category (a string, an integer or any hashable type) for each decision variable. If two variables have the same category, <code>LearningSolver</code> will use the same internal ML model to predict the values of both variables. By default, all variables belong to the <code>"default"</code> category, and therefore only one ML model is used for all variables. If the returned category is <code>None</code>, ML predictors will ignore the variable.</p> <p>An optional method which can be implemented is <code>instance.get_variable_category(var_name, index)</code>, which returns a category (a string, an integer or any hashable type) for each decision variable. If two variables have the same category, <code>LearningSolver</code> will use the same internal ML model to predict the values of both variables. By default, all variables belong to the <code>"default"</code> category, and therefore only one ML model is used for all variables. If the returned category is <code>None</code>, ML predictors will ignore the variable.</p>
<p>It is not necessary to have a one-to-one correspondence between features and problem instances. One important (and deliberate) limitation of MIPLearn, however, is that <code>get_instance_features()</code> must always return arrays of same length for all relevant instances of the problem. Similarly, <code>get_variable_features(var, index)</code> must also always return arrays of same length for all variables in each category. It is up to the user to decide how to encode variable-length characteristics of the problem into fixed-length vectors. In graph problems, for example, graph embeddings can be used to reduce the (variable-length) lists of nodes and edges into a fixed-length structure that still preserves some properties of the graph. Different instance encodings may have significant impact on performance.</p> <p>It is not necessary to have a one-to-one correspondence between features and problem instances. One important (and deliberate) limitation of MIPLearn, however, is that <code>get_instance_features()</code> must always return arrays of same length for all relevant instances of the problem. Similarly, <code>get_variable_features(var_name, index)</code> must also always return arrays of same length for all variables in each category. It is up to the user to decide how to encode variable-length characteristics of the problem into fixed-length vectors. In graph problems, for example, graph embeddings can be used to reduce the (variable-length) lists of nodes and edges into a fixed-length structure that still preserves some properties of the graph. Different instance encodings may have significant impact on performance.</p>
<h3 id="obtaining-heuristic-solutions">Obtaining heuristic solutions</h3> <h3 id="obtaining-heuristic-solutions">Obtaining heuristic solutions</h3>
<p>By default, <code>LearningSolver</code> uses Machine Learning to accelerate the MIP solution process, while maintaining all optimality guarantees provided by the MIP solver. In the default mode of operation, for example, predicted optimal solutions are used only as MIP starts.</p> <p>By default, <code>LearningSolver</code> uses Machine Learning to accelerate the MIP solution process, while maintaining all optimality guarantees provided by the MIP solver. In the default mode of operation, for example, predicted optimal solutions are used only as MIP starts.</p>
<p>For more significant performance benefits, <code>LearningSolver</code> can also be configured to place additional trust in the Machine Learning predictors, by using the <code>mode="heuristic"</code> constructor argument. When operating in this mode, if a ML model is statistically shown (through <em>stratified k-fold cross validation</em>) to have exceptionally high accuracy, the solver may decide to restrict the search space based on its predictions. The parts of the solution which the ML models cannot predict accurately will still be explored using traditional (branch-and-bound) methods. For particular applications, this mode has been shown to quickly produce optimal or near-optimal solutions (see <a href="../about/#references">references</a> and <a href="../benchmark/">benchmark results</a>).</p> <p>For more significant performance benefits, <code>LearningSolver</code> can also be configured to place additional trust in the Machine Learning predictors, by using the <code>mode="heuristic"</code> constructor argument. When operating in this mode, if a ML model is statistically shown (through <em>stratified k-fold cross validation</em>) to have exceptionally high accuracy, the solver may decide to restrict the search space based on its predictions. The parts of the solution which the ML models cannot predict accurately will still be explored using traditional (branch-and-bound) methods. For particular applications, this mode has been shown to quickly produce optimal or near-optimal solutions (see <a href="../about/#references">references</a> and <a href="../benchmark/">benchmark results</a>).</p>
@ -245,9 +236,10 @@ solver.solve(test_instance)
<hr> <hr>
<p> <p>
<small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.<br></small> <small>Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.</small><br>
<small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</p></small> <small>Documentation built with <a href="http://www.mkdocs.org/">MkDocs</a>.</small>
</p>

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miplearn/__init__.py
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@ -3,13 +3,13 @@
# Released under the modified BSD license. See COPYING.md for more details. # Released under the modified BSD license. See COPYING.md for more details.
from .extractors import (SolutionExtractor, from .extractors import (SolutionExtractor,
CombinedExtractor,
InstanceFeaturesExtractor, InstanceFeaturesExtractor,
ObjectiveValueExtractor, ObjectiveValueExtractor,
VariableFeaturesExtractor, VariableFeaturesExtractor,
) )
from .components.component import Component from .components.component import Component
from .components.objective import ObjectiveValueComponent from .components.objective import ObjectiveValueComponent
from .components.lazy import LazyConstraintsComponent
from .components.primal import (PrimalSolutionComponent, from .components.primal import (PrimalSolutionComponent,
AdaptivePredictor, AdaptivePredictor,
) )

4
miplearn/components/component.py
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@ -18,10 +18,6 @@ class Component(ABC):
def after_solve(self, solver, instance, model): def after_solve(self, solver, instance, model):
pass pass
@abstractmethod
def merge(self, other):
pass
@abstractmethod @abstractmethod
def fit(self, training_instances): def fit(self, training_instances):
pass pass

57
miplearn/components/lazy.py
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@ -0,0 +1,57 @@
# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
from .component import Component
from ..extractors import *
from abc import ABC, abstractmethod
from copy import deepcopy
import numpy as np
from sklearn.pipeline import make_pipeline
from sklearn.linear_model import LogisticRegression
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import cross_val_score
from sklearn.metrics import roc_curve
from sklearn.neighbors import KNeighborsClassifier
from tqdm.auto import tqdm
import pyomo.environ as pe
import logging
logger = logging.getLogger(__name__)
class LazyConstraintsComponent(Component):
"""
A component that predicts which lazy constraints to enforce.
"""
def __init__(self):
self.violations = set()
self.count = {}
self.n_samples = 0
def before_solve(self, solver, instance, model):
logger.info("Enforcing %d lazy constraints" % len(self.violations))
for v in self.violations:
if self.count[v] < self.n_samples * 0.05:
continue
cut = instance.build_lazy_constraint(model, v)
solver.internal_solver.add_constraint(cut)
def after_solve(self, solver, instance, model):
pass
def fit(self, training_instances):
logger.debug("Fitting...")
self.n_samples = len(training_instances)
for instance in training_instances:
if not hasattr(instance, "found_violations"):
continue
for v in instance.found_violations:
self.violations.add(v)
if v not in self.count.keys():
self.count[v] = 0
self.count[v] += 1
def predict(self, instance, model=None):
return self.violations

6
miplearn/components/objective.py
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@ -30,16 +30,16 @@ class ObjectiveValueComponent(Component):
def after_solve(self, solver, instance, model): def after_solve(self, solver, instance, model):
pass pass
def merge(self, other):
pass
def fit(self, training_instances): def fit(self, training_instances):
logger.debug("Extracting features...")
features = InstanceFeaturesExtractor().extract(training_instances) features = InstanceFeaturesExtractor().extract(training_instances)
ub = ObjectiveValueExtractor(kind="upper bound").extract(training_instances) ub = ObjectiveValueExtractor(kind="upper bound").extract(training_instances)
lb = ObjectiveValueExtractor(kind="lower bound").extract(training_instances) lb = ObjectiveValueExtractor(kind="lower bound").extract(training_instances)
self.ub_regressor = deepcopy(self.regressor_prototype) self.ub_regressor = deepcopy(self.regressor_prototype)
self.lb_regressor = deepcopy(self.regressor_prototype) self.lb_regressor = deepcopy(self.regressor_prototype)
logger.debug("Fitting ub_regressor...")
self.ub_regressor.fit(features, ub) self.ub_regressor.fit(features, ub)
logger.debug("Fitting ub_regressor...")
self.lb_regressor.fit(features, lb) self.lb_regressor.fit(features, lb)
def predict(self, instances): def predict(self, instances):

14
miplearn/components/primal.py
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@ -129,7 +129,7 @@ class PrimalSolutionComponent(Component):
self.dynamic_thresholds = dynamic_thresholds self.dynamic_thresholds = dynamic_thresholds
def before_solve(self, solver, instance, model): def before_solve(self, solver, instance, model):
solution = self.predict(instance, model) solution = self.predict(instance)
if self.mode == "heuristic": if self.mode == "heuristic":
solver.internal_solver.fix(solution) solver.internal_solver.fix(solution)
else: else:
@ -139,6 +139,7 @@ class PrimalSolutionComponent(Component):
pass pass
def fit(self, training_instances): def fit(self, training_instances):
logger.debug("Extracting features...")
features = VariableFeaturesExtractor().extract(training_instances) features = VariableFeaturesExtractor().extract(training_instances)
solutions = SolutionExtractor().extract(training_instances) solutions = SolutionExtractor().extract(training_instances)
@ -180,12 +181,10 @@ class PrimalSolutionComponent(Component):
self.thresholds[category, label] = thresholds[k] self.thresholds[category, label] = thresholds[k]
def predict(self, instance, model=None): def predict(self, instance):
if model is None: x_test = VariableFeaturesExtractor().extract([instance])
model = instance.to_model()
x_test = VariableFeaturesExtractor().extract([instance], [model])
solution = {} solution = {}
var_split = Extractor.split_variables(instance, model) var_split = Extractor.split_variables(instance)
for category in var_split.keys(): for category in var_split.keys():
for (i, (var, index)) in enumerate(var_split[category]): for (i, (var, index)) in enumerate(var_split[category]):
if var not in solution.keys(): if var not in solution.keys():
@ -200,6 +199,3 @@ class PrimalSolutionComponent(Component):
if ws[i, 1] >= self.thresholds[category, label]: if ws[i, 1] >= self.thresholds[category, label]:
solution[var][index] = label solution[var][index] = label
return solution return solution
def merge(self, other_components):
pass

28
miplearn/components/tests/test_primal.py
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@ -27,29 +27,7 @@ def test_predict():
instances, models = _get_instances() instances, models = _get_instances()
comp = PrimalSolutionComponent() comp = PrimalSolutionComponent()
comp.fit(instances) comp.fit(instances)
solution = comp.predict(instances[0], models[0]) solution = comp.predict(instances[0])
assert models[0].x in solution.keys() assert "x" in solution
for idx in range(4): for idx in range(4):
assert idx in solution[models[0].x].keys() assert idx in solution["x"]
# def test_warm_start_save_load():
# state_file = tempfile.NamedTemporaryFile(mode="r")
# solver = LearningSolver(components={"warm-start": WarmStartComponent()})
# solver.parallel_solve(_get_instances(), n_jobs=2)
# solver.fit()
# comp = solver.components["warm-start"]
# assert comp.x_train["default"].shape == (8, 6)
# assert comp.y_train["default"].shape == (8, 2)
# assert ("default", 0) in comp.predictors.keys()
# assert ("default", 1) in comp.predictors.keys()
# solver.save_state(state_file.name)
# solver.solve(_get_instances()[0])
# solver = LearningSolver(components={"warm-start": WarmStartComponent()})
# solver.load_state(state_file.name)
# comp = solver.components["warm-start"]
# assert comp.x_train["default"].shape == (8, 6)
# assert comp.y_train["default"].shape == (8, 2)
# assert ("default", 0) in comp.predictors.keys()
# assert ("default", 1) in comp.predictors.keys()

98
miplearn/extractors.py
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@ -5,6 +5,10 @@
import numpy as np import numpy as np
from abc import ABC, abstractmethod from abc import ABC, abstractmethod
from pyomo.core import Var from pyomo.core import Var
from tqdm.auto import tqdm, trange
from p_tqdm import p_map
import logging
logger = logging.getLogger(__name__)
class Extractor(ABC): class Extractor(ABC):
@ -13,59 +17,39 @@ class Extractor(ABC):
pass pass
@staticmethod @staticmethod
def split_variables(instance, model): def split_variables(instance):
assert hasattr(instance, "lp_solution")
result = {} result = {}
for var in model.component_objects(Var): for var_name in instance.lp_solution:
for index in var: for index in instance.lp_solution[var_name]:
category = instance.get_variable_category(var, index) category = instance.get_variable_category(var_name, index)
if category is None: if category is None:
continue continue
if category not in result.keys(): if category not in result:
result[category] = [] result[category] = []
result[category] += [(var, index)] result[category] += [(var_name, index)]
return result return result
@staticmethod
def merge(partial_results, vertical=False):
results = {}
all_categories = set()
for pr in partial_results:
all_categories |= pr.keys()
for category in all_categories:
results[category] = []
for pr in partial_results:
if category in pr.keys():
results[category] += [pr[category]]
if vertical:
results[category] = np.vstack(results[category])
else:
results[category] = np.hstack(results[category])
return results
class VariableFeaturesExtractor(Extractor): class VariableFeaturesExtractor(Extractor):
def extract(self, def extract(self, instances):
instances,
models=None,
):
result = {} result = {}
if models is None: for instance in tqdm(instances,
models = [instance.to_model() for instance in instances] desc="Extract var features",
for (index, instance) in enumerate(instances): disable=len(instances) < 5):
model = models[index]
instance_features = instance.get_instance_features() instance_features = instance.get_instance_features()
var_split = self.split_variables(instance, model) var_split = self.split_variables(instance)
for (category, var_index_pairs) in var_split.items(): for (category, var_index_pairs) in var_split.items():
if category not in result.keys(): if category not in result:
result[category] = [] result[category] = []
for (var, index) in var_index_pairs: for (var_name, index) in var_index_pairs:
result[category] += [np.hstack([ result[category] += [
instance_features, instance_features.tolist() + \
instance.get_variable_features(var, index), instance.get_variable_features(var_name, index).tolist() + \
instance.lp_solution[str(var)][index], [instance.lp_solution[var_name][index]]
])] ]
for category in result.keys(): for category in result:
result[category] = np.vstack(result[category]) result[category] = np.array(result[category])
return result return result
@ -73,39 +57,29 @@ class SolutionExtractor(Extractor):
def __init__(self, relaxation=False): def __init__(self, relaxation=False):
self.relaxation = relaxation self.relaxation = relaxation
def extract(self, instances, models=None): def extract(self, instances):
result = {} result = {}
if models is None: for instance in tqdm(instances,
models = [instance.to_model() for instance in instances] desc="Extract solution",
for (index, instance) in enumerate(instances): disable=len(instances) < 5):
model = models[index] var_split = self.split_variables(instance)
var_split = self.split_variables(instance, model)
for (category, var_index_pairs) in var_split.items(): for (category, var_index_pairs) in var_split.items():
if category not in result.keys(): if category not in result:
result[category] = [] result[category] = []
for (var, index) in var_index_pairs: for (var_name, index) in var_index_pairs:
if self.relaxation: if self.relaxation:
v = instance.lp_solution[str(var)][index] v = instance.lp_solution[var_name][index]
else: else:
v = instance.solution[str(var)][index] v = instance.solution[var_name][index]
if v is None: if v is None:
result[category] += [[0, 0]] result[category] += [[0, 0]]
else: else:
result[category] += [[1 - v, v]] result[category] += [[1 - v, v]]
for category in result.keys(): for category in result:
result[category] = np.vstack(result[category]) result[category] = np.array(result[category])
return result return result
class CombinedExtractor(Extractor):
def __init__(self, extractors):
self.extractors = extractors
def extract(self, instances, models):
return self.merge([ex.extract(instances, models)
for ex in self.extractors])
class InstanceFeaturesExtractor(Extractor): class InstanceFeaturesExtractor(Extractor):
def extract(self, instances, models=None): def extract(self, instances, models=None):
return np.vstack([ return np.vstack([

46
miplearn/instance.py
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@ -65,12 +65,50 @@ class Instance(ABC):
def get_variable_category(self, var, index): def get_variable_category(self, var, index):
""" """
Returns a category (a string, an integer or any hashable type) for each decision variable. Returns the category (a string, an integer or any hashable type) for each decision
variable.
If two variables have the same category, LearningSolver will use the same internal ML model If two variables have the same category, LearningSolver will use the same internal ML
to predict the values of both variables. By default, all variables belong to the "default" model to predict the values of both variables. By default, all variables belong to the
category, and therefore only one ML model is used for all variables. "default" category, and therefore only one ML model is used for all variables.
If the returned category is None, ML models will ignore the variable. If the returned category is None, ML models will ignore the variable.
""" """
return "default" return "default"
def find_violations(self, model):
"""
Returns lazy constraint violations found for the current solution.
After solving a model, LearningSolver will ask the instance to identify which lazy
constraints are violated by the current solution. For each identified violation,
LearningSolver will then call the build_lazy_constraint, add the generated Pyomo
constraint to the model, then resolve the problem. The process repeats until no further
lazy constraint violations are found.
Each "violation" is simply a string, a tuple or any other hashable type which allows the
instance to identify unambiguously which lazy constraint should be generated. In the
Traveling Salesman Problem, for example, a subtour violation could be a frozen set
containing the cities in the subtour.
For a concrete example, see TravelingSalesmanInstance.
"""
return []
def build_lazy_constraint(self, model, violation):
"""
Returns a Pyomo constraint which fixes a given violation.
This method is typically called immediately after find_violations. The violation object
provided to this method is exactly the same object returned earlier by find_violations.
After some training, LearningSolver may decide to proactively build some lazy constraints
at the beginning of the optimization process, before a solution is even available. In this
case, build_lazy_constraints will be called without a corresponding call to
find_violations.
The implementation should not directly add the constraint to the model. The constraint
will be added by LearningSolver after the method returns.
For a concrete example, see TravelingSalesmanInstance.
"""
pass

68
miplearn/problems/tests/test_tsp.py
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@ -0,0 +1,68 @@
# MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
from miplearn import LearningSolver
from miplearn.problems.tsp import TravelingSalesmanGenerator, TravelingSalesmanInstance
import numpy as np
from numpy.linalg import norm
from scipy.spatial.distance import pdist, squareform
from scipy.stats import uniform, randint
def test_generator():
instances = TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=100, high=101),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True).generate(100)
assert len(instances) == 100
assert instances[0].n_cities == 100
assert norm(instances[0].distances - instances[0].distances.T) < 1e-6
d = [instance.distances[0,1] for instance in instances]
assert np.std(d) > 0
def test_instance():
n_cities = 4
distances = np.array([
[0., 1., 2., 1.],
[1., 0., 1., 2.],
[2., 1., 0., 1.],
[1., 2., 1., 0.],
])
instance = TravelingSalesmanInstance(n_cities, distances)
solver = LearningSolver()
solver.solve(instance)
x = instance.solution["x"]
assert x[0,1] == 1.0
assert x[0,2] == 0.0
assert x[0,3] == 1.0
assert x[1,2] == 1.0
assert x[1,3] == 0.0
assert x[2,3] == 1.0
assert instance.lower_bound == 4.0
assert instance.upper_bound == 4.0
def test_subtour():
n_cities = 6
cities = np.array([
[0., 0.],
[1., 0.],
[2., 0.],
[3., 0.],
[0., 1.],
[3., 1.],
])
distances = squareform(pdist(cities))
instance = TravelingSalesmanInstance(n_cities, distances)
solver = LearningSolver()
solver.solve(instance)
x = instance.solution["x"]
assert x[0,1] == 1.0
assert x[0,4] == 1.0
assert x[1,2] == 1.0
assert x[2,3] == 1.0
assert x[3,5] == 1.0
assert x[4,5] == 1.0

169
miplearn/problems/tsp.py
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@ -0,0 +1,169 @@
# MIPLearn, an extensible framework for Learning-Enhanced Mixed-Integer Optimization
# Copyright (C) 2019-2020 Argonne National Laboratory. All rights reserved.
# Written by Alinson S. Xavier <axavier@anl.gov>
import numpy as np
import pyomo.environ as pe
from miplearn import Instance
from scipy.stats import uniform, randint
from scipy.spatial.distance import pdist, squareform
from scipy.stats.distributions import rv_frozen
import networkx as nx
import random
class ChallengeA:
def __init__(self,
seed=42,
n_training_instances=500,
n_test_instances=50,
):
np.random.seed(seed)
self.generator = TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=350, high=351),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True,
round=True,
)
np.random.seed(seed + 1)
self.training_instances = self.generator.generate(n_training_instances)
np.random.seed(seed + 2)
self.test_instances = self.generator.generate(n_test_instances)
class TravelingSalesmanGenerator:
"""Random generator for the Traveling Salesman Problem."""
def __init__(self,
x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=100, high=101),
gamma=uniform(loc=1.0, scale=0.0),
fix_cities=True,
round=True,
):
"""Initializes the problem generator.
Initially, the generator creates n cities (x_1,y_1),...,(x_n,y_n) where n, x_i and y_i are
sampled independently from the provided probability distributions `n`, `x` and `y`. For each
(unordered) pair of cities (i,j), the distance d[i,j] between them is set to:
d[i,j] = gamma[i,j] \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2}
where gamma is sampled from the provided probability distribution `gamma`.
If fix_cities=True, the list of cities is kept the same for all generated instances. The
gamma values, and therefore also the distances, are still different.
By default, all distances d[i,j] are rounded to the nearest integer. If `round=False`
is provided, this rounding will be disabled.
Arguments
---------
x: rv_continuous
Probability distribution for the x-coordinate of each city.
y: rv_continuous
Probability distribution for the y-coordinate of each city.
n: rv_discrete
Probability distribution for the number of cities.
fix_cities: bool
If False, cities will be resampled for every generated instance. Otherwise, list of
cities will be computed once, during the constructor.
round: bool
If True, distances are rounded to the nearest integer.
"""
assert isinstance(x, rv_frozen), "x should be a SciPy probability distribution"
assert isinstance(y, rv_frozen), "y should be a SciPy probability distribution"
assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
assert isinstance(gamma, rv_frozen), "gamma should be a SciPy probability distribution"
self.x = x
self.y = y
self.n = n
self.gamma = gamma
self.round = round
if fix_cities:
self.fixed_n, self.fixed_cities = self._generate_cities()
else:
self.fixed_n = None
self.fixed_cities = None
def generate(self, n_samples):
def _sample():
if self.fixed_cities is not None:
n, cities = self.fixed_n, self.fixed_cities
else:
n, cities = self._generate_cities()
distances = squareform(pdist(cities)) * self.gamma.rvs(size=(n, n))
distances = np.tril(distances) + np.triu(distances.T, 1)
if self.round:
distances = distances.round()
return TravelingSalesmanInstance(n, distances)
return [_sample() for _ in range(n_samples)]
def _generate_cities(self):
n = self.n.rvs()
cities = np.array([(self.x.rvs(), self.y.rvs()) for _ in range(n)])
return n, cities
class TravelingSalesmanInstance(Instance):
"""An instance ot the Traveling Salesman Problem.
Given a list of cities and the distance between each pair of cities, the problem asks for the
shortest route starting at the first city, visiting each other city exactly once, then
returning to the first city. This problem is a generalization of the Hamiltonian path problem,
one of Karp's 21 NP-complete problems.
"""
def __init__(self, n_cities, distances):
assert isinstance(distances, np.ndarray)
assert distances.shape == (n_cities, n_cities)
self.n_cities = n_cities
self.distances = distances
def to_model(self):
model = pe.ConcreteModel()
model.edges = edges = [(i,j)
for i in range(self.n_cities)
for j in range(i+1, self.n_cities)]
model.x = pe.Var(edges, domain=pe.Binary)
model.obj = pe.Objective(expr=sum(model.x[i,j] * self.distances[i,j]
for (i,j) in edges),
sense=pe.minimize)
model.eq_degree = pe.ConstraintList()
model.eq_subtour = pe.ConstraintList()
for i in range(self.n_cities):
model.eq_degree.add(sum(model.x[min(i,j), max(i,j)]
for j in range(self.n_cities) if i != j) == 2)
return model
def get_instance_features(self):
return np.array([1])
def get_variable_features(self, var_name, index):
return np.array([1])
def get_variable_category(self, var_name, index):
return index
def find_violations(self, model):
selected_edges = [e for e in model.edges if model.x[e].value > 0.5]
graph = nx.Graph()
graph.add_edges_from(selected_edges)
components = [frozenset(c) for c in list(nx.connected_components(graph))]
violations = []
for c in components:
if len(c) < self.n_cities:
violations += [c]
return violations
def build_lazy_constraint(self, model, component):
cut_edges = [e for e in model.edges
if (e[0] in component and e[1] not in component) or
(e[0] not in component and e[1] in component)]
return model.eq_subtour.add(sum(model.x[e] for e in cut_edges) >= 2)

151
miplearn/solvers.py
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@ -2,45 +2,66 @@
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved. # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details. # Released under the modified BSD license. See COPYING.md for more details.
from . import ObjectiveValueComponent, PrimalSolutionComponent from . import ObjectiveValueComponent, PrimalSolutionComponent, LazyConstraintsComponent
import pyomo.environ as pe import pyomo.environ as pe
from pyomo.core import Var from pyomo.core import Var
from copy import deepcopy from copy import deepcopy
import pickle import pickle
from scipy.stats import randint from scipy.stats import randint
from p_tqdm import p_map from p_tqdm import p_map
import numpy as np
import logging import logging
logger = logging.getLogger(__name__) logger = logging.getLogger(__name__)
# Global memory for multiprocessing
SOLVER = [None]
INSTANCES = [None]
def _parallel_solve(instance_idx):
solver = deepcopy(SOLVER[0])
instance = INSTANCES[0][instance_idx]
results = solver.solve(instance)
return {
"Results": results,
"Solution": instance.solution,
"LP solution": instance.lp_solution,
"LP value": instance.lp_value,
"Upper bound": instance.upper_bound,
"Lower bound": instance.lower_bound,
"Violations": instance.found_violations,
}
class InternalSolver: class InternalSolver:
def __init__(self): def __init__(self):
self.is_warm_start_available = False self.is_warm_start_available = False
self.model = None self.model = None
pass self.var_name_to_var = {}
def solve_lp(self, tee=False): def solve_lp(self, tee=False):
self.solver.set_instance(self.model)
# Relax domain # Relax domain
from pyomo.core.base.set_types import Reals from pyomo.core.base.set_types import Reals
original_domain = {} original_domains = []
for var in self.model.component_data_objects(Var): for (idx, var) in enumerate(self.model.component_data_objects(Var)):
original_domain[str(var)] = var.domain original_domains += [var.domain]
lb, ub = var.bounds lb, ub = var.bounds
var.setlb(lb) var.setlb(lb)
var.setub(ub) var.setub(ub)
var.domain = Reals var.domain = Reals
self.solver.update_var(var)
# Solve LP relaxation # Solve LP relaxation
self.solver.set_instance(self.model)
results = self.solver.solve(tee=tee) results = self.solver.solve(tee=tee)
# Restore domains # Restore domains
for var in self.model.component_data_objects(Var): for (idx, var) in enumerate(self.model.component_data_objects(Var)):
var.domain = original_domain[str(var)] var.domain = original_domains[idx]
self.solver.update_var(var)
# Reload original model
self.solver.set_instance(self.model)
return { return {
"Optimal value": results["Problem"][0]["Lower bound"], "Optimal value": results["Problem"][0]["Lower bound"],
} }
@ -58,36 +79,43 @@ class InternalSolver:
solution[str(var)][index] = var[index].value solution[str(var)][index] = var[index].value
return solution return solution
def set_warm_start(self, ws): def set_warm_start(self, solution):
self.is_warm_start_available = True self.is_warm_start_available = True
self.clear_values() self.clear_values()
count_total, count_fixed = 0, 0 count_total, count_fixed = 0, 0
for var in ws.keys(): for var_name in solution:
for index in var: var = self.var_name_to_var[var_name]
for index in solution[var_name]:
count_total += 1 count_total += 1
var[index].value = ws[var][index] var[index].value = solution[var_name][index]
if ws[var][index] is not None: if solution[var_name][index] is not None:
count_fixed += 1 count_fixed += 1
logger.info("Setting start values for %d variables (out of %d)" % logger.info("Setting start values for %d variables (out of %d)" %
(count_fixed, count_total)) (count_fixed, count_total))
def set_model(self, model): def set_model(self, model):
self.model = model self.model = model
self.solver.set_instance(model) self.solver.set_instance(model)
self.var_name_to_var = {}
for var in model.component_objects(Var):
self.var_name_to_var[var.name] = var
def fix(self, ws): def fix(self, solution):
count_total, count_fixed = 0, 0 count_total, count_fixed = 0, 0
for var in ws.keys(): for var_name in solution:
for index in var: for index in solution[var_name]:
var = self.var_name_to_var[var_name]
count_total += 1 count_total += 1
if ws[var][index] is None: if solution[var_name][index] is None:
continue continue
count_fixed += 1 count_fixed += 1
var[index].fix(ws[var][index]) var[index].fix(solution[var_name][index])
self.solver.update_var(var[index]) self.solver.update_var(var[index])
logger.info("Fixing values for %d variables (out of %d)" % logger.info("Fixing values for %d variables (out of %d)" %
(count_fixed, count_total)) (count_fixed, count_total))
def add_constraint(self, cut):
self.solver.add_constraint(cut)
class GurobiSolver(InternalSolver): class GurobiSolver(InternalSolver):
@ -198,6 +226,7 @@ class LearningSolver:
self.components = { self.components = {
"ObjectiveValue": ObjectiveValueComponent(), "ObjectiveValue": ObjectiveValueComponent(),
"PrimalSolution": PrimalSolutionComponent(), "PrimalSolution": PrimalSolutionComponent(),
"LazyConstraints": LazyConstraintsComponent(),
} }
assert self.mode in ["exact", "heuristic"] assert self.mode in ["exact", "heuristic"]
@ -231,27 +260,44 @@ class LearningSolver:
self.internal_solver = self._create_internal_solver() self.internal_solver = self._create_internal_solver()
self.internal_solver.set_model(model) self.internal_solver.set_model(model)
# Solve LP relaxation logger.debug("Solving LP relaxation...")
results = self.internal_solver.solve_lp(tee=tee) results = self.internal_solver.solve_lp(tee=tee)
instance.lp_solution = self.internal_solver.get_solution() instance.lp_solution = self.internal_solver.get_solution()
instance.lp_value = results["Optimal value"] instance.lp_value = results["Optimal value"]
# Invoke before_solve callbacks logger.debug("Running before_solve callbacks...")
for component in self.components.values(): for component in self.components.values():
component.before_solve(self, instance, model) component.before_solve(self, instance, model)
if relaxation_only: if relaxation_only:
return results return results
# Solver original MIP total_wallclock_time = 0
results = self.internal_solver.solve(tee=tee) instance.found_violations = []
while True:
logger.debug("Solving MIP...")
results = self.internal_solver.solve(tee=tee)
logger.debug(" %.2f s" % results["Wallclock time"])
total_wallclock_time += results["Wallclock time"]
if not hasattr(instance, "find_violations"):
break
logger.debug("Finding violated constraints...")
violations = instance.find_violations(model)
if len(violations) == 0:
break
instance.found_violations += violations
logger.debug(" %d violations found" % len(violations))
for v in violations:
cut = instance.build_lazy_constraint(model, v)
self.internal_solver.add_constraint(cut)
results["Wallclock time"] = total_wallclock_time
# Read MIP solution and bounds # Read MIP solution and bounds
instance.lower_bound = results["Lower bound"] instance.lower_bound = results["Lower bound"]
instance.upper_bound = results["Upper bound"] instance.upper_bound = results["Upper bound"]
instance.solution = self.internal_solver.get_solution() instance.solution = self.internal_solver.get_solution()
# Invoke after_solve callbacks logger.debug("Calling after_solve callbacks...")
for component in self.components.values(): for component in self.components.values():
component.after_solve(self, instance, model) component.after_solve(self, instance, model)
@ -266,40 +312,23 @@ class LearningSolver:
label="Solve", label="Solve",
collect_training_data=True, collect_training_data=True,
): ):
self.internal_solver = None
def _process(instance): self.internal_solver = None
solver = deepcopy(self) SOLVER[0] = self
results = solver.solve(instance) INSTANCES[0] = instances
solver.internal_solver = None p_map_results = p_map(_parallel_solve,
if not collect_training_data: list(range(len(instances))),
solver.components = {} num_cpus=n_jobs,
return { desc=label)
"Solver": solver,
"Results": results,
"Solution": instance.solution,
"LP solution": instance.lp_solution,
"LP value": instance.lp_value,
"Upper bound": instance.upper_bound,
"Lower bound": instance.lower_bound,
}
p_map_results = p_map(_process, instances, num_cpus=n_jobs, desc=label)
subsolvers = [p["Solver"] for p in p_map_results]
results = [p["Results"] for p in p_map_results] results = [p["Results"] for p in p_map_results]
for (idx, r) in enumerate(p_map_results): for (idx, r) in enumerate(p_map_results):
instances[idx].solution = r["Solution"] instances[idx].solution = r["Solution"]
instances[idx].lp_solution = r["LP solution"] instances[idx].lp_solution = r["LP solution"]
instances[idx].lp_value = r["LP value"] instances[idx].lp_value = r["LP value"]
instances[idx].lower_bound = r["Lower bound"] instances[idx].lower_bound = r["Lower bound"]
instances[idx].upper_bound = r["Upper bound"] instances[idx].upper_bound = r["Upper bound"]
instances[idx].found_violations = r["Violations"]
for (name, component) in self.components.items():
subcomponents = [subsolver.components[name]
for subsolver in subsolvers
if name in subsolver.components.keys()]
self.components[name].merge(subcomponents)
return results return results
@ -310,21 +339,3 @@ class LearningSolver:
return return
for component in self.components.values(): for component in self.components.values():
component.fit(training_instances) component.fit(training_instances)
def save_state(self, filename):
with open(filename, "wb") as file:
pickle.dump({
"version": 2,
"components": self.components,
}, file)
def load_state(self, filename):
with open(filename, "rb") as file:
data = pickle.load(file)
assert data["version"] == 2
for (component_name, component) in data["components"].items():
if component_name not in self.components.keys():
continue
else:
self.components[component_name].merge([component])

4
miplearn/tests/test_benchmark.py
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@ -18,8 +18,6 @@ def test_benchmark():
# Training phase... # Training phase...
training_solver = LearningSolver() training_solver = LearningSolver()
training_solver.parallel_solve(train_instances, n_jobs=10) training_solver.parallel_solve(train_instances, n_jobs=10)
training_solver.fit()
training_solver.save_state("data.bin")
# Test phase... # Test phase...
test_solvers = { test_solvers = {
@ -27,7 +25,7 @@ def test_benchmark():
"Strategy B": LearningSolver(), "Strategy B": LearningSolver(),
} }
benchmark = BenchmarkRunner(test_solvers) benchmark = BenchmarkRunner(test_solvers)
benchmark.load_state("data.bin") benchmark.fit(train_instances)
benchmark.parallel_solve(test_instances, n_jobs=2, n_trials=2) benchmark.parallel_solve(test_instances, n_jobs=2, n_trials=2)
assert benchmark.raw_results().values.shape == (12,13) assert benchmark.raw_results().values.shape == (12,13)

14
miplearn/tests/test_extractors.py
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@ -5,7 +5,6 @@
from miplearn.problems.knapsack import KnapsackInstance from miplearn.problems.knapsack import KnapsackInstance
from miplearn import (LearningSolver, from miplearn import (LearningSolver,
SolutionExtractor, SolutionExtractor,
CombinedExtractor,
InstanceFeaturesExtractor, InstanceFeaturesExtractor,
VariableFeaturesExtractor, VariableFeaturesExtractor,
) )
@ -33,7 +32,7 @@ def _get_instances():
def test_solution_extractor(): def test_solution_extractor():
instances, models = _get_instances() instances, models = _get_instances()
features = SolutionExtractor().extract(instances, models) features = SolutionExtractor().extract(instances)
assert isinstance(features, dict) assert isinstance(features, dict)
assert "default" in features.keys() assert "default" in features.keys()
assert isinstance(features["default"], np.ndarray) assert isinstance(features["default"], np.ndarray)
@ -48,17 +47,6 @@ def test_solution_extractor():
] ]
def test_combined_extractor():
instances, models = _get_instances()
extractor = CombinedExtractor(extractors=[VariableFeaturesExtractor(),
SolutionExtractor()])
features = extractor.extract(instances, models)
assert isinstance(features, dict)
assert "default" in features.keys()
assert isinstance(features["default"], np.ndarray)
assert features["default"].shape == (6, 7)
def test_instance_features_extractor(): def test_instance_features_extractor():
instances, models = _get_instances() instances, models = _get_instances()
features = InstanceFeaturesExtractor().extract(instances) features = InstanceFeaturesExtractor().extract(instances)

23
miplearn/tests/test_solver.py
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@ -41,29 +41,6 @@ def test_solver():
solver.fit() solver.fit()
solver.solve(instance) solver.solve(instance)
# def test_solve_save_load_state():
# instance = _get_instance()
# components_before = {
# "warm-start": WarmStartComponent(),
# }
# solver = LearningSolver(components=components_before)
# solver.solve(instance)
# solver.fit()
# solver.save_state("/tmp/knapsack_train.bin")
# prev_x_train_len = len(solver.components["warm-start"].x_train)
# prev_y_train_len = len(solver.components["warm-start"].y_train)
# components_after = {
# "warm-start": WarmStartComponent(),
# }
# solver = LearningSolver(components=components_after)
# solver.load_state("/tmp/knapsack_train.bin")
# assert len(solver.components.keys()) == 1
# assert len(solver.components["warm-start"].x_train) == prev_x_train_len
# assert len(solver.components["warm-start"].y_train) == prev_y_train_len
def test_parallel_solve(): def test_parallel_solve():
instances = [_get_instance() for _ in range(10)] instances = [_get_instance() for _ in range(10)]
solver = LearningSolver() solver = LearningSolver()

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