Knapsack: add fix_w and w_jitter

docs/problems.md

@@ -86,6 +86,12 @@ $$
 $$
 
 where $K$, the correlation coefficient, and $u_j$, the correlation multiplier, are sampled
-from the provided probability distributions `K` and `u`. Note that $K$ is only sample once for the entire instance.
+from the provided probability distributions `K` and `u`. Note that $K$ is only sample once for each generated instance.
 
-This random generation procedure was developed by A. Freville and G. Plateau (*An efficient preprocessing procedure for the multidimensional knapsack problem*, Discrete Applied Mathematics 49 (1994) 189–212).
+If `fix_w=True` is provided, then $w_{ij}$ are kept the same in all generated instances. This also implies that $n$ and $m$ are kept fixed. Although the prices and capacities are derived from $w_{ij}$, as long as `u` and `K` are not constants, the generated instances will still not be completely identical.
+
+
+If a probability distribution `w_jitter` is provided, then item weights will be set to $w_{ij} + \gamma_{ij}$ where $\gamma_{ij}$ is sampled from `w_jitter`. When combined with `fix_w=True`, this argument may be used to generate instances where the weight of each item is roughly the same, but not exactly identical, across all instances. The prices of the items and the capacities of the knapsacks will be calculated as above, but using these perturbed weights instead.
+
+!!! note
+    Random generator based on *A. Freville and G. Plateau, **An efficient preprocessing procedure for the multidimensional knapsack problem**, Discrete Applied Mathematics 49 (1994) 189–212*.

miplearn/problems/knapsack.py

@@ -72,6 +72,8 @@ class MultiKnapsackGenerator:
                  K=randint(low=500, high=500),
                  u=uniform(loc=0.0, scale=1.0),
                  alpha=uniform(loc=0.25, scale=0.0),
+                 fix_w=False,
+                 w_jitter=randint(low=0, high=1),
                 ):
         """Initialize the problem generator.
         
@@ -93,6 +95,19 @@ class MultiKnapsackGenerator:
         from the provided probability distributions. Note that `K` is only sample once for the
         entire instance.
         
+        If fix_w=True is provided, then w[i,j] are kept the same in all generated instances. This
+        also implies that n and m are kept fixed. Although the prices and capacities are derived
+        from w[i,j], as long as u and K are not constants, the generated instances will still not
+        be completely identical.
+
+
+        If a probability distribution w_jitter is provided, then item weights will be set to
+        w[i,j] + gamma[i,j] where gamma[i,j] is sampled from w_jitter. When combined with 
+        fix_w=True, this argument may be used to generate instances where the weight of each item
+        is roughly the same, but not exactly identical, across all instances. The prices of the
+        items and the capacities of the knapsacks will be calculated as above, but using these
+        perturbed weights instead.
+        
         Parameters
         ----------
         n: rv_discrete
@@ -107,6 +122,10 @@ class MultiKnapsackGenerator:
             Probability distribution for the profit multiplier
         alpha: rv_continuous
             Probability distribution for the tightness ratio
+        fix_w: boolean
+            If true, weights are kept the same (minus the noise from w_jitter) in all instances
+        w_jitter: rv_continuous
+            Probability distribution for random noise added to the weights
         """
         assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
         assert isinstance(m, rv_frozen), "m should be a SciPy probability distribution"
@@ -114,24 +133,44 @@ class MultiKnapsackGenerator:
         assert isinstance(K, rv_frozen), "K should be a SciPy probability distribution"
         assert isinstance(u, rv_frozen), "u should be a SciPy probability distribution"
         assert isinstance(alpha, rv_frozen), "alpha should be a SciPy probability distribution"
+        assert isinstance(fix_w, bool), "fix_w should be boolean"
+        assert isinstance(w_jitter, rv_frozen), \
+                "w_jitter should be a SciPy probability distribution"
+        
         self.n = n
         self.m = m
         self.w = w
         self.K = K
         self.u = u
         self.alpha = alpha
+        self.w_jitter = w_jitter
+        
+        if fix_w:
+            self.fix_n = self.n.rvs()
+            self.fix_m = self.m.rvs()
+            self.fix_w = np.array([self.w.rvs(self.fix_n) for _ in range(self.fix_m)])
+        else:
+            self.fix_n = None
+            self.fix_m = None
+            self.fix_w = None
     
     def generate(self, n_samples):
         def _sample():
+            if self.fix_w is not None:
+                n = self.fix_n
+                m = self.fix_m
+                w = self.fix_w
+            else:
                 n = self.n.rvs()
                 m = self.m.rvs()
+                w = np.array([self.w.rvs(n) for _ in range(m)])
+            w = w + np.array([self.w_jitter.rvs(n) for _ in range(m)])
             K = self.K.rvs()
             u = self.u.rvs(n)
             alpha = self.alpha.rvs(m)
-            weights = np.array([self.w.rvs(n) for _ in range(m)])
-            prices = np.array([weights[:,j].sum() / m + K * u[j] for j in range(n)])
-            capacities = np.array([weights[i,:].sum() * alpha[i] for i in range(m)])
-            return MultiKnapsackInstance(prices, capacities, weights)
+            p = np.array([w[:,j].sum() / m + K * u[j] for j in range(n)])
+            b = np.array([w[i,:].sum() * alpha[i] for i in range(m)])
+            return MultiKnapsackInstance(p, b, w)
         return [_sample() for _ in range(n_samples)]
     
     

miplearn/problems/tests/test_knapsack.py

@@ -42,3 +42,31 @@ def test_knapsack_instance():
     solver = LearningSolver()
     results = solver.solve(instance)
     assert results["Problem"][0]["Lower bound"] == 30.0
+    
+def test_knapsack_fixed_weights_jitter():
+    gen = MultiKnapsackGenerator(n=randint(low=50, high=51),
+                                 m=randint(low=10, high=11),
+                                 w=randint(low=0, high=1000),
+                                 K=randint(low=500, high=501),
+                                 u=uniform(loc=1.0, scale=0.0),
+                                 alpha=uniform(loc=0.50, scale=0.0),
+                                 fix_w=True,
+                                 w_jitter=randint(low=0, high=1),
+                                )
+    instances = gen.generate(100)
+    w = [instance.weights[0,0] for instance in instances]
+    assert np.std(w) == 0.
+    
+    gen = MultiKnapsackGenerator(n=randint(low=1, high=2),
+                                 m=randint(low=10, high=11),
+                                 w=randint(low=1000, high=1001),
+                                 K=randint(low=500, high=501),
+                                 u=uniform(loc=1.0, scale=0.0),
+                                 alpha=uniform(loc=0.50, scale=0.0),
+                                 fix_w=True,
+                                 w_jitter=randint(low=0, high=1001),
+                                )
+    instances = gen.generate(1_000)
+    w = [instance.weights[0,0] for instance in instances]
+    assert round(np.std(w), -1) == 290.
+    assert round(np.mean(w), -2) == 1500.