Finish TSP implementation; improve performance of Extractors

6 years ago · 0b04fa93da
parent b1f674fcc6
commit 0b04fa93da
33 changed files with 1345 additions and 677 deletions
--- a/benchmark/Makefile
+++ b/benchmark/Makefile
@ -5,7 +5,8 @@

 CHALLENGES := \
    stab/ChallengeA \
-    knapsack/ChallengeA
+    knapsack/ChallengeA \
+    tsp/ChallengeA

 main: $(addsuffix /performance.png, $(CHALLENGES))

--- a/benchmark/benchmark.py
+++ b/benchmark/benchmark.py
@ -20,9 +20,16 @@ from miplearn import (LearningSolver, BenchmarkRunner)
 from numpy import median
 import pyomo.environ as pe
 import pickle
-
 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('miplearn').setLevel(logging.INFO)
+logger = logging.getLogger("benchmark")

 n_jobs = 10
 time_limit = 900
@ -34,7 +41,7 @@ pathlib.Path(basepath).mkdir(parents=True, exist_ok=True)


 def save(obj, filename):
-    print("Writing %s..." % filename)
+    logger.info("Writing %s..." % filename)
    with open(filename, "wb") as file:
        pickle.dump(obj, file)
        
@ -55,7 +62,6 @@ def train():
                            solver=internal_solver,
                            components={})
    solver.parallel_solve(train_instances, n_jobs=n_jobs)
-    solver.fit(n_jobs=n_jobs)
    save(train_instances, "%s/train_instances.bin" % basepath)
    save(test_instances, "%s/test_instances.bin" % basepath)
    
@ -65,6 +71,7 @@ def test_baseline():
    solvers = {
        "baseline": LearningSolver(
            time_limit=time_limit,
+            solver=internal_solver,
            components={},
        ),
    }
@ -74,20 +81,26 @@ def test_baseline():
    
    
 def test_ml():
+    logger.info("Loading instances...")
    train_instances = load("%s/train_instances.bin" % basepath)
    test_instances = load("%s/test_instances.bin" % basepath)
    solvers = {
        "ml-exact": LearningSolver(
            time_limit=time_limit,
+            solver=internal_solver,
        ),
        "ml-heuristic": LearningSolver(
            time_limit=time_limit,
+            solver=internal_solver,
            mode="heuristic",
        ),
    }
    benchmark = BenchmarkRunner(solvers)
+    logger.info("Loading results...")
    benchmark.load_results("%s/benchmark_baseline.csv" % basepath)
+    logger.info("Fitting...")
    benchmark.fit(train_instances)
+    logger.info("Solving...")
    benchmark.parallel_solve(test_instances, n_jobs=n_jobs)
    benchmark.save_results("%s/benchmark_ml.csv" % basepath)

--- a/benchmark/tsp/ChallengeA/benchmark_baseline.csv
+++ b/benchmark/tsp/ChallengeA/benchmark_baseline.csv
@ -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
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--- a/benchmark/tsp/ChallengeA/benchmark_ml.csv
+++ b/benchmark/tsp/ChallengeA/benchmark_ml.csv
@ -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
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--- a/benchmark/tsp/ChallengeA/performance.png
+++ b/benchmark/tsp/ChallengeA/performance.png
--- a/docs-src/figures/benchmark_tsp_a.png
+++ b/docs-src/figures/benchmark_tsp_a.png
@ -0,0 +1 @@
+../../benchmark/tsp/ChallengeA/performance.png
--- a/docs-src/problems.md
+++ b/docs-src/problems.md
@ -48,6 +48,51 @@ MaxWeightStableSetGenerator(w=uniform(loc=100., scale=50.),
 ![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

@ -120,30 +165,3 @@ MultiKnapsackGenerator(n=randint(low=250, high=251),

 ![alt](figures/benchmark_knapsack_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.
--- a/docs-src/usage.md
+++ b/docs-src/usage.md
@ -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.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 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
--- a/docs/404.html
+++ b/docs/404.html
@ -14,14 +14,16 @@
    <title>MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
    <link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
    <link href="/css/bootstrap-custom.min.css" rel="stylesheet">
    <link href="/css/base.min.css" rel="stylesheet">
    <link href="/css/cinder.min.css" rel="stylesheet">
-    <link href="/css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="/css/custom.css" rel="stylesheet">

    <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@ -30,15 +32,6 @@
            <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
        <![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>
-
    

     
@ -140,17 +133,17 @@
        
        <hr>
        <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>

        
        
    </footer>
    <script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
    <script src="/js/bootstrap-3.0.3.min.js"></script>
-    <script src="/js/highlight.pack.js"></script>
-    <script>hljs.initHighlightingOnLoad();</script>
+    
    <script>var base_url = "/"</script>
    
    <script src="/js/base.js"></script>
@ -162,8 +155,11 @@
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-header">
+                <button type="button" class="close" data-dismiss="modal">
+                    <span aria-hidden="true">&times;</span>
+                    <span class="sr-only">Close</span>
+                </button>
                <h4 class="modal-title" id="searchModalLabel">Search</h4>
-                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
            </div>
            <div class="modal-body">
                <p>
--- a/docs/about/index.html
+++ b/docs/about/index.html
@ -14,14 +14,16 @@
    <title>About - MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
    <link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
    <link href="../css/bootstrap-custom.min.css" rel="stylesheet">
    <link href="../css/base.min.css" rel="stylesheet">
    <link href="../css/cinder.min.css" rel="stylesheet">
-    <link href="../css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="../css/custom.css" rel="stylesheet">

    <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@ -30,15 +32,6 @@
            <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
        <![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>
-
    

     
@ -198,17 +191,17 @@ POSSIBILITY OF SUCH DAMAGE.
        
        <hr>
        <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>

        
        
    </footer>
    <script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
    <script src="../js/bootstrap-3.0.3.min.js"></script>
-    <script src="../js/highlight.pack.js"></script>
-    <script>hljs.initHighlightingOnLoad();</script>
+    
    <script>var base_url = ".."</script>
    
    <script src="../js/base.js"></script>
@ -220,8 +213,11 @@ POSSIBILITY OF SUCH DAMAGE.
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-header">
+                <button type="button" class="close" data-dismiss="modal">
+                    <span aria-hidden="true">&times;</span>
+                    <span class="sr-only">Close</span>
+                </button>
                <h4 class="modal-title" id="searchModalLabel">Search</h4>
-                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
            </div>
            <div class="modal-body">
                <p>
--- a/docs/benchmark/index.html
+++ b/docs/benchmark/index.html
@ -14,14 +14,16 @@
    <title>Benchmark - MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
    <link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
    <link href="../css/bootstrap-custom.min.css" rel="stylesheet">
    <link href="../css/base.min.css" rel="stylesheet">
    <link href="../css/cinder.min.css" rel="stylesheet">
-    <link href="../css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="../css/custom.css" rel="stylesheet">

    <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@ -30,15 +32,6 @@
            <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
        <![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>
-
    

     
@ -207,17 +200,17 @@ benchmark.parallel_solve(test_instances)
        
        <hr>
        <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>

        
        
    </footer>
    <script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
    <script src="../js/bootstrap-3.0.3.min.js"></script>
-    <script src="../js/highlight.pack.js"></script>
-    <script>hljs.initHighlightingOnLoad();</script>
+    
    <script>var base_url = ".."</script>
    
    <script src="../js/base.js"></script>
@ -229,8 +222,11 @@ benchmark.parallel_solve(test_instances)
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-header">
+                <button type="button" class="close" data-dismiss="modal">
+                    <span aria-hidden="true">&times;</span>
+                    <span class="sr-only">Close</span>
+                </button>
                <h4 class="modal-title" id="searchModalLabel">Search</h4>
-                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
            </div>
            <div class="modal-body">
                <p>
--- a/docs/css/cinder.css
+++ b/docs/css/cinder.css
@ -10,23 +10,28 @@ body {
    color: #343838;
 }
 h1, h2, h3, h4, h5, h6 {
-    font-family:'PT Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;
+    font-family:'Inter', 'Helvetica Neue', Helvetica, Arial, sans-serif;
    color: #222;
 }
 h1 small, h2 small, h3 small, h4 small, h5 small, h6 small, .h1 small, .h2 small, .h3 small, .h4 small, .h5 small, .h6 small, h1 .small, h2 .small, h3 .small, h4 .small, h5 .small, h6 .small, .h1 .small, .h2 .small, .h3 .small, .h4 .small, .h5 .small, .h6 .small {
    color: #B1B7B9;
 }
+
+h2 {
+    margin-top: 35px;
+}
+
 h1, h2 {
    font-weight: 700;
 }
 h4 {
-    font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;
+    font-family: 'Inter', 'Helvetica Neue', Helvetica, Arial, sans-serif;
    font-weight: 300;
    margin-top: 20px;
    font-style: italic;
 }
 h5 {
-    font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;
+    font-family: 'Inter', 'Helvetica Neue', Helvetica, Arial, sans-serif;
    font-weight: 300;
    font-variant: small-caps;
 }
@ -41,7 +46,7 @@ pre {
    margin-bottom: 25px;
 }
 .lead {
-    font-family:"Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
+    font-family:"Inter", "Helvetica Neue", Helvetica, Arial, sans-serif;
    font-weight: 400;
    line-height: 1.4;
    letter-spacing: 0.0312em;
@ -54,7 +59,8 @@ pre {
 .bs-sidenav {
    background-image: url("../img/grid11.png");
    background-repeat: repeat;
-    font-size: 12px;
+    font-family: Inter,"Helvetica Neue",Helvetica,Arial,sans-serif;
+    font-size: 13px;
 }
 .well {
    background-color: #FCFDFF;
@ -71,7 +77,7 @@ pre {
    box-shadow: none;
 }
 #mkdocs-search-query {
-    font-family:"Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
+    font-family:"Inter", "Helvetica Neue", Helvetica, Arial, sans-serif;
    font-size: 20px;
    font-weight: 700;
    color: #343838;
--- a/docs/css/cinder.min.css
+++ b/docs/css/cinder.min.css
@ -1 +1 @@
-body{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;line-height:1.7;background-color:#FFF;color:#343838}h1,h2,h3,h4,h5,h6{font-family:'PT Sans','Helvetica Neue',Helvetica,Arial,sans-serif;color:#222}h1 small,h2 small,h3 small,h4 small,h5 small,h6 small,.h1 small,.h2 small,.h3 small,.h4 small,.h5 small,.h6 small,h1 .small,h2 .small,h3 .small,h4 .small,h5 .small,h6 .small,.h1 .small,.h2 .small,.h3 .small,.h4 .small,.h5 .small,.h6 .small{color:#b1b7b9}h1,h2{font-weight:700}h4{font-family:'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;margin-top:20px;font-style:italic}h5{font-family:'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;font-variant:small-caps}pre,code{background-color:#fcfdff}pre>code{font-size:13px}pre{margin-top:25px;margin-bottom:25px}.lead{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-weight:400;line-height:1.4;letter-spacing:.0312em;color:#b1b7b9}.navbar-default{background-color:#343838;border-bottom:8px #ebf2f2 solid}.bs-sidenav{background-image:url("../img/grid11.png");background-repeat:repeat;font-size:12px}.well{background-color:#fcfdff}.btn-default{background-color:#fcfdff}.table-striped>tbody>tr:nth-child(2n+1)>td,.table-striped>tbody>tr:nth-child(2n+1)>th{background-color:#fcfdff}#mkdocs-search-query:focus{outline:0;-webkit-box-shadow:none;box-shadow:none}#mkdocs-search-query{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:20px;font-weight:700;color:#343838;height:45px}footer>hr{width:35%}
+body{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;line-height:1.7;background-color:#FFF;color:#343838}h1,h2,h3,h4,h5,h6{font-family:'Inter','Helvetica Neue',Helvetica,Arial,sans-serif;color:#222}h1 small,h2 small,h3 small,h4 small,h5 small,h6 small,.h1 small,.h2 small,.h3 small,.h4 small,.h5 small,.h6 small,h1 .small,h2 .small,h3 .small,h4 .small,h5 .small,h6 .small,.h1 .small,.h2 .small,.h3 .small,.h4 .small,.h5 .small,.h6 .small{color:#b1b7b9}h2{margin-top:35px}h1,h2{font-weight:700}h4{font-family:'Inter','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;margin-top:20px;font-style:italic}h5{font-family:'Inter','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;font-variant:small-caps}pre,code{background-color:#fcfdff}pre>code{font-size:13px}pre{margin-top:25px;margin-bottom:25px}.lead{font-family:"Inter","Helvetica Neue",Helvetica,Arial,sans-serif;font-weight:400;line-height:1.4;letter-spacing:.0312em;color:#b1b7b9}.navbar-default{background-color:#343838;border-bottom:8px #ebf2f2 solid}.bs-sidenav{background-image:url("../img/grid11.png");background-repeat:repeat;font-family:Inter,"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px}.well{background-color:#fcfdff}.btn-default{background-color:#fcfdff}.table-striped>tbody>tr:nth-child(2n+1)>td,.table-striped>tbody>tr:nth-child(2n+1)>th{background-color:#fcfdff}#mkdocs-search-query:focus{outline:0;-webkit-box-shadow:none;box-shadow:none}#mkdocs-search-query{font-family:"Inter","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:20px;font-weight:700;color:#343838;height:45px}footer>hr{width:35%}
--- a/docs/customization/index.html
+++ b/docs/customization/index.html
@ -14,14 +14,16 @@
    <title>Customization - MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
    <link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
    <link href="../css/bootstrap-custom.min.css" rel="stylesheet">
    <link href="../css/base.min.css" rel="stylesheet">
    <link href="../css/cinder.min.css" rel="stylesheet">
-    <link href="../css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="../css/custom.css" rel="stylesheet">

    <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@ -30,15 +32,6 @@
            <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
        <![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>
-
    

     
@ -160,17 +153,17 @@ solver = LearningSolver(solver=&quot;cplex&quot;,
        
        <hr>
        <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>

        
        
    </footer>
    <script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
    <script src="../js/bootstrap-3.0.3.min.js"></script>
-    <script src="../js/highlight.pack.js"></script>
-    <script>hljs.initHighlightingOnLoad();</script>
+    
    <script>var base_url = ".."</script>
    
    <script src="../js/base.js"></script>
@ -182,8 +175,11 @@ solver = LearningSolver(solver=&quot;cplex&quot;,
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-header">
+                <button type="button" class="close" data-dismiss="modal">
+                    <span aria-hidden="true">&times;</span>
+                    <span class="sr-only">Close</span>
+                </button>
                <h4 class="modal-title" id="searchModalLabel">Search</h4>
-                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
            </div>
            <div class="modal-body">
                <p>
--- a/docs/figures/benchmark_tsp_a.png
+++ b/docs/figures/benchmark_tsp_a.png
--- a/docs/index.html
+++ b/docs/index.html
@ -14,14 +14,16 @@
    <title>Home - MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
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-    <link href="css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="css/custom.css" rel="stylesheet">

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-    <script src="//ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js"></script>
-    <script>
-    WebFont.load({
-        google: {
-            families: ['Open Sans', 'PT Sans']
-        }
-    });
-    </script>
-
    

     
@ -186,17 +179,17 @@
        
        <hr>
        <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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+    
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@ -208,8 +201,11 @@
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
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+                <button type="button" class="close" data-dismiss="modal">
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+                </button>
                <h4 class="modal-title" id="searchModalLabel">Search</h4>
-                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
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@ -272,6 +268,6 @@
 </html>

 <!--
-MkDocs version : 1.0.4
-Build Date UTC : 2020-02-25 04:02:08
+MkDocs version : 1.1
+Build Date UTC : 2020-02-26 04:29:16
 -->
--- a/docs/js/base.js
+++ b/docs/js/base.js
@ -1,26 +1,15 @@
-function getSearchTerm()
-{
+function getSearchTerm() {
    var sPageURL = window.location.search.substring(1);
    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('=');
-        if (sParameterName[0] == 'q')
-        {
+        if (sParameterName[0] == 'q') {
            return sParameterName[1];
        }
    }
 }

 $(document).ready(function() {
-    /**
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-     * Cinder theme specific
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-    hljs.initHighlightingOnLoad();
-
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     * Taken from themes/mkdocs/js/base.js
@ -30,12 +19,12 @@ $(document).ready(function() {
        $search_modal = $('#mkdocs_search_modal'),
        $keyboard_modal = $('#mkdocs_keyboard_modal');

-    if(search_term){
+    if (search_term) {
        $search_modal.modal();
    }

    // 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();
    });

@ -76,7 +65,8 @@ $(document).ready(function() {
                    $search_modal.modal('hide');
                    $keyboard_modal.modal('show');
                    break;
-              default: break;
+                default:
+                    break;
            }
            if (page) {
                $keyboard_modal.modal('hide');
--- a/docs/problems/index.html
+++ b/docs/problems/index.html
@ -14,14 +14,16 @@
    <title>Problems - MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
    <link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
    <link href="../css/bootstrap-custom.min.css" rel="stylesheet">
    <link href="../css/base.min.css" rel="stylesheet">
    <link href="../css/cinder.min.css" rel="stylesheet">
-    <link href="../css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="../css/custom.css" rel="stylesheet">

    <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@ -30,15 +32,6 @@
            <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
        <![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>
-
    

     
@ -147,15 +140,16 @@
                <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="#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="#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="second-level"><a href="#traveling-salesman-problem">Traveling Salesman Problem</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-problem-generator">Random problem generator</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>
 </div></div>
        <div class="col-md-9" role="main">
@ -192,8 +186,43 @@
 </code></pre>

 <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>
+<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>
 <script type="math/tex; mode=display">\begin{align*}
@ -235,7 +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>
 </ul>
 </div>
-<h3 id="challenge-a_1">Challenge A</h3>
+<h3 id="challenge-a_2">Challenge A</h3>
 <ul>
 <li>250 variables, 10 constraints, fixed weights</li>
 <li>$w \sim U(0, 1000), \gamma \sim U(0.95, 1.05)$</li>
@ -253,26 +282,7 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
                      )
 </code></pre>

-<p><img alt="alt" src="../figures/benchmark_knapsack_a.png" /></p>
-<h2 id="traveling-salesman-problem">Traveling Salesman Problem</h2>
-<h3 id="problem-definition_2">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></div>
+<p><img alt="alt" src="../figures/benchmark_knapsack_a.png" /></p></div>
        
        
    </div>
@ -281,17 +291,17 @@ is provided, this rounding will be disabled.</p></div>
        
        <hr>
        <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>

        
        
    </footer>
    <script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
    <script src="../js/bootstrap-3.0.3.min.js"></script>
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-    <script>hljs.initHighlightingOnLoad();</script>
+    
    <script>var base_url = ".."</script>
    
    <script src="../js/base.js"></script>
@ -303,8 +313,11 @@ is provided, this rounding will be disabled.</p></div>
    <div class="modal-dialog modal-lg">
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+                <button type="button" class="close" data-dismiss="modal">
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--- a/docs/search/lunr.js
+++ b/docs/search/lunr.js
--- a/docs/search/search_index.json
+++ b/docs/search/search_index.json
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@ -1,33 +1,27 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
-    <url>
+<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9"><url>
     <loc>None</loc>
-     <lastmod>2020-02-24</lastmod>
+     <lastmod>2020-02-25</lastmod>
     <changefreq>daily</changefreq>
-    </url>
-    <url>
+    </url><url>
     <loc>None</loc>
-     <lastmod>2020-02-24</lastmod>
+     <lastmod>2020-02-25</lastmod>
     <changefreq>daily</changefreq>
-    </url>
-    <url>
+    </url><url>
     <loc>None</loc>
-     <lastmod>2020-02-24</lastmod>
+     <lastmod>2020-02-25</lastmod>
     <changefreq>daily</changefreq>
-    </url>
-    <url>
+    </url><url>
     <loc>None</loc>
-     <lastmod>2020-02-24</lastmod>
+     <lastmod>2020-02-25</lastmod>
     <changefreq>daily</changefreq>
-    </url>
-    <url>
+    </url><url>
     <loc>None</loc>
-     <lastmod>2020-02-24</lastmod>
+     <lastmod>2020-02-25</lastmod>
     <changefreq>daily</changefreq>
-    </url>
-    <url>
+    </url><url>
     <loc>None</loc>
-     <lastmod>2020-02-24</lastmod>
+     <lastmod>2020-02-25</lastmod>
     <changefreq>daily</changefreq>
    </url>
 </urlset>
--- a/docs/sitemap.xml.gz
+++ b/docs/sitemap.xml.gz
--- a/docs/usage/index.html
+++ b/docs/usage/index.html
@ -14,14 +14,16 @@
    <title>Usage - MIPLearn</title>
    

-    <link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
+    <link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
    <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
-    <link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
+    <link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
    <link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
    <link href="../css/bootstrap-custom.min.css" rel="stylesheet">
    <link href="../css/base.min.css" rel="stylesheet">
    <link href="../css/cinder.min.css" rel="stylesheet">
-    <link href="../css/highlight.min.css" rel="stylesheet">
+
+    
    <link href="../css/custom.css" rel="stylesheet">

    <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@ -30,15 +32,6 @@
            <script src="https://cdn.jsdelivr.net/npm/respond.js@1.4.2/dest/respond.min.js"></script>
        <![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>
-
    

     
@ -180,12 +173,12 @@ for instance in all_instances:
 <ul>
 <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_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>
 <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>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>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>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_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>
 <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>
@ -243,17 +236,17 @@ solver.solve(test_instance)
        
        <hr>
        <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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    <script src="../js/bootstrap-3.0.3.min.js"></script>
-    <script src="../js/highlight.pack.js"></script>
-    <script>hljs.initHighlightingOnLoad();</script>
+    
    <script>var base_url = ".."</script>
    
    <script src="../js/base.js"></script>
@ -265,8 +258,11 @@ solver.solve(test_instance)
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-header">
+                <button type="button" class="close" data-dismiss="modal">
+                    <span aria-hidden="true">&times;</span>
+                    <span class="sr-only">Close</span>
+                </button>
                <h4 class="modal-title" id="searchModalLabel">Search</h4>
-                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
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                <p>
--- a/miplearn/init.py
+++ b/miplearn/init.py
@ -3,7 +3,6 @@
 #  Released under the modified BSD license. See COPYING.md for more details.

 from .extractors import (SolutionExtractor,
-                         CombinedExtractor,
                         InstanceFeaturesExtractor,
                         ObjectiveValueExtractor,
                         VariableFeaturesExtractor,
--- a/miplearn/components/lazy.py
+++ b/miplearn/components/lazy.py
@ -27,10 +27,14 @@ class LazyConstraintsComponent(Component):
    
    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)
        
@ -38,11 +42,16 @@ class LazyConstraintsComponent(Component):
        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
--- a/miplearn/components/objective.py
+++ b/miplearn/components/objective.py
@ -31,12 +31,15 @@ class ObjectiveValueComponent(Component):
        pass
    
    def fit(self, training_instances):
+        logger.debug("Extracting features...")
        features = InstanceFeaturesExtractor().extract(training_instances)
        ub = ObjectiveValueExtractor(kind="upper bound").extract(training_instances)
        lb = ObjectiveValueExtractor(kind="lower bound").extract(training_instances)
        self.ub_regressor = deepcopy(self.regressor_prototype)
        self.lb_regressor = deepcopy(self.regressor_prototype)
+        logger.debug("Fitting ub_regressor...")
        self.ub_regressor.fit(features, ub)
+        logger.debug("Fitting ub_regressor...")
        self.lb_regressor.fit(features, lb)
        
    def predict(self, instances):
--- a/miplearn/components/primal.py
+++ b/miplearn/components/primal.py
@ -129,7 +129,7 @@ class PrimalSolutionComponent(Component):
        self.dynamic_thresholds = dynamic_thresholds
    
    def before_solve(self, solver, instance, model):
-        solution = self.predict(instance, model)
+        solution = self.predict(instance)
        if self.mode == "heuristic":
            solver.internal_solver.fix(solution)
        else:
@ -139,6 +139,7 @@ class PrimalSolutionComponent(Component):
        pass
                
    def fit(self, training_instances):
+        logger.debug("Extracting features...")
        features = VariableFeaturesExtractor().extract(training_instances)
        solutions = SolutionExtractor().extract(training_instances)
        
@ -180,12 +181,10 @@ class PrimalSolutionComponent(Component):
                self.thresholds[category, label] = thresholds[k]
                
                
-    def predict(self, instance, model=None):
-        if model is None:
-            model = instance.to_model()
-        x_test = VariableFeaturesExtractor().extract([instance], [model])
+    def predict(self, instance):
+        x_test = VariableFeaturesExtractor().extract([instance])
        solution = {}
-        var_split = Extractor.split_variables(instance, model)
+        var_split = Extractor.split_variables(instance)
        for category in var_split.keys():
            for (i, (var, index)) in enumerate(var_split[category]):
                if var not in solution.keys():
--- a/miplearn/components/tests/test_primal.py
+++ b/miplearn/components/tests/test_primal.py
@ -27,29 +27,7 @@ def test_predict():
    instances, models = _get_instances()
    comp = PrimalSolutionComponent()
    comp.fit(instances)
-    solution = comp.predict(instances[0], models[0])
-    assert models[0].x in solution.keys()
+    solution = comp.predict(instances[0])
+    assert "x" in solution
    for idx in range(4):
-        assert idx in solution[models[0].x].keys()
-
-# 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()
+        assert idx in solution["x"]
--- a/miplearn/extractors.py
+++ b/miplearn/extractors.py
@ -5,6 +5,10 @@
 import numpy as np
 from abc import ABC, abstractmethod
 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):
@ -13,59 +17,39 @@ class Extractor(ABC):
        pass
    
    @staticmethod
-    def split_variables(instance, model):
+    def split_variables(instance):
+        assert hasattr(instance, "lp_solution")
        result = {}
-        for var in model.component_objects(Var):
-            for index in var:
-                category = instance.get_variable_category(var, index)
+        for var_name in instance.lp_solution:
+            for index in instance.lp_solution[var_name]:
+                category = instance.get_variable_category(var_name, index)
                if category is None:
                    continue
-                if category not in result.keys():
+                if category not in result:
                    result[category] = []
-                result[category] += [(var, index)]
+                result[category] += [(var_name, index)]
        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):
-    def extract(self,
-                instances,
-                models=None,
-               ):
+    def extract(self, instances):
        result = {}
-        if models is None:
-            models = [instance.to_model() for instance in instances]
-        for (index, instance) in enumerate(instances):
-            model = models[index]
+        for instance in tqdm(instances,
+                             desc="Extract var features",
+                             disable=len(instances) < 5):
            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():
-                if category not in result.keys():
+                if category not in result:
                    result[category] = []
-                for (var, index) in var_index_pairs:
-                    result[category] += [np.hstack([
-                        instance_features,
-                        instance.get_variable_features(var, index),
-                        instance.lp_solution[str(var)][index],
-                    ])]
-        for category in result.keys():
-            result[category] = np.vstack(result[category])
+                for (var_name, index) in var_index_pairs:
+                    result[category] += [
+                        instance_features.tolist() + \
+                        instance.get_variable_features(var_name, index).tolist() + \
+                        [instance.lp_solution[var_name][index]]
+                    ]
+        for category in result:
+            result[category] = np.array(result[category])
        return result


@ -73,39 +57,29 @@ class SolutionExtractor(Extractor):
    def __init__(self, relaxation=False):
        self.relaxation = relaxation
        
-    def extract(self, instances, models=None):
+    def extract(self, instances):
        result = {}
-        if models is None:
-            models = [instance.to_model() for instance in instances]
-        for (index, instance) in enumerate(instances):
-            model = models[index]
-            var_split = self.split_variables(instance, model)
+        for instance in tqdm(instances,
+                             desc="Extract solution",
+                             disable=len(instances) < 5):
+            var_split = self.split_variables(instance)
            for (category, var_index_pairs) in var_split.items():
-                if category not in result.keys():
+                if category not in result:
                    result[category] = []
-                for (var, index) in var_index_pairs:
+                for (var_name, index) in var_index_pairs:
                    if self.relaxation:
-                        v = instance.lp_solution[str(var)][index]
+                        v = instance.lp_solution[var_name][index]
                    else:
-                        v = instance.solution[str(var)][index]
+                        v = instance.solution[var_name][index]
                    if v is None:
                        result[category] += [[0, 0]]
                    else:
                        result[category] += [[1 - v, v]]
-        for category in result.keys():
-            result[category] = np.vstack(result[category])            
+        for category in result:
+            result[category] = np.array(result[category])            
        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):
    def extract(self, instances, models=None):
        return np.vstack([
--- a/miplearn/instance.py
+++ b/miplearn/instance.py
@ -65,11 +65,12 @@ class Instance(ABC):

    def get_variable_category(self, var, index):
        """
-        Returns the 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
-        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 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 models will ignore the variable.
        """
@ -99,10 +100,11 @@ class Instance(ABC):
        Returns a Pyomo constraint which fixes a given violation.
        
        This method is typically called immediately after find_violations. The violation object
-        provided by this method is exactly the same object returned earlier by find_violations.
+        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.
+        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.
--- a/miplearn/problems/tsp.py
+++ b/miplearn/problems/tsp.py
@ -25,6 +25,7 @@ class ChallengeA:
                                                    n=randint(low=350, high=351),
                                                    gamma=uniform(loc=0.95, scale=0.1),
                                                    fix_cities=True,
+                                                    round=True,
                                                   )

        np.random.seed(seed + 1)
@ -126,12 +127,12 @@ class TravelingSalesmanInstance(Instance):
        self.distances = distances
    
    def to_model(self):
-        self.model = model = pe.ConcreteModel()
-        self.edges = edges = [(i,j)
+        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(rule=lambda m : sum(m.x[i,j] * self.distances[i,j]
+        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()
@ -144,14 +145,14 @@ class TravelingSalesmanInstance(Instance):
    def get_instance_features(self):
        return np.array([1])
    
-    def get_variable_features(self, var, index):
+    def get_variable_features(self, var_name, index):
        return np.array([1])
    
-    def get_variable_category(self, var, index):
+    def get_variable_category(self, var_name, index):
        return index
    
    def find_violations(self, model):
-        selected_edges = [e for e in self.edges if model.x[e].value > 0.5]
+        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))]
@ -162,7 +163,7 @@ class TravelingSalesmanInstance(Instance):
        return violations
    
    def build_lazy_constraint(self, model, component):
-        cut_edges = [e for e in self.edges
+        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)
--- a/miplearn/solvers.py
+++ b/miplearn/solvers.py
@ -9,15 +9,36 @@ from copy import deepcopy
 import pickle
 from scipy.stats import randint
 from p_tqdm import p_map
+import numpy as np
 import logging
 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:
    def __init__(self):
        self.is_warm_start_available = False
        self.model = None
-        pass
+        self.var_name_to_var = {}
    
    def solve_lp(self, tee=False):
        self.solver.set_instance(self.model)
@ -58,33 +79,37 @@ class InternalSolver:
                solution[str(var)][index] = var[index].value
        return solution   
    
-    def set_warm_start(self, ws):
+    def set_warm_start(self, solution):
        self.is_warm_start_available = True
        self.clear_values()
        count_total, count_fixed = 0, 0
-        for var in ws.keys():
-            for index in var:
+        for var_name in solution:
+            var = self.var_name_to_var[var_name]
+            for index in solution[var_name]:
                count_total += 1
-                var[index].value = ws[var][index]
-                if ws[var][index] is not None:
+                var[index].value = solution[var_name][index]
+                if solution[var_name][index] is not None:
                    count_fixed += 1
        logger.info("Setting start values for %d variables (out of %d)" %
                    (count_fixed, count_total))
                
-                
    def set_model(self, model):
        self.model = 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
-        for var in ws.keys():
-            for index in var:
+        for var_name in solution:
+            for index in solution[var_name]:
+                var = self.var_name_to_var[var_name]
                count_total += 1
-                if ws[var][index] is None:
+                if solution[var_name][index] is None:
                    continue
                count_fixed += 1
-                var[index].fix(ws[var][index])
+                var[index].fix(solution[var_name][index])
                self.solver.update_var(var[index])        
        logger.info("Fixing values for %d variables (out of %d)" %
                    (count_fixed, count_total))
@ -287,29 +312,16 @@ class LearningSolver:
                       label="Solve",
                       collect_training_data=True,
                      ):
-        self.internal_solver = None
        
-        def _process(instance):
-            solver = deepcopy(self)
-            results = solver.solve(instance)
-            solver.internal_solver = None
-            if not collect_training_data:
-                solver.components = {}
-            return {
-                "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,
-                "Violations": instance.found_violations,
-            }
+        self.internal_solver = None
+        SOLVER[0] = self
+        INSTANCES[0] = instances
+        p_map_results = p_map(_parallel_solve,
+                              list(range(len(instances))),
+                              num_cpus=n_jobs,
+                              desc=label)

-        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]
-        
        for (idx, r) in enumerate(p_map_results):
            instances[idx].solution = r["Solution"]
            instances[idx].lp_solution = r["LP solution"]
--- a/miplearn/tests/test_extractors.py
+++ b/miplearn/tests/test_extractors.py
@ -5,7 +5,6 @@
 from miplearn.problems.knapsack import KnapsackInstance
 from miplearn import (LearningSolver,
                      SolutionExtractor,
-                      CombinedExtractor,
                      InstanceFeaturesExtractor,
                      VariableFeaturesExtractor,
                     )
@ -33,7 +32,7 @@ def _get_instances():

 def test_solution_extractor():
    instances, models = _get_instances()
-    features = SolutionExtractor().extract(instances, models)
+    features = SolutionExtractor().extract(instances)
    assert isinstance(features, dict)
    assert "default" in features.keys()
    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():
    instances, models = _get_instances()
    features = InstanceFeaturesExtractor().extract(instances)
				`@ -0,0 +1 @@`
				`../../benchmark/tsp/ChallengeA/performance.png`