clique merge

Former-commit-id: 2a315a6

Author: h-g-s

examples/clique_merge.py

@@ -0,0 +1,60 @@
+"""Example with clique merge: a formulation of a knapsack problem
+with conflicting items where clique merge can improve it"""
+
+from mip import Model, xsum, maximize, BINARY
+
+I = set(range(1, 7))
+
+# weigths
+w = {1: -4, 2: 4, 3: 5, 4: 6, 5: 7, 6: 10}
+
+# profits
+p = {1: -2, 2: 8, 3: 10, 4: 12, 5: 13, 6: 13}
+
+# capacity
+c = 6
+
+# conflicting items
+C = ((2, 3), (2, 4), (3, 4), (2, 5))
+
+m = Model()
+
+x = {i: m.add_var("x({})".format(i), var_type=BINARY) for i in I}
+
+m.objective = maximize(xsum(p[i] * x[i] for i in I))
+
+m += xsum(w[i] * x[i] for i in I) <= c
+
+for (i, j) in C:
+    m += x[i] + x[j] <= 1
+
+m.verbose = 0
+m.write("b.lp")
+m.optimize(relax=True)
+
+print(
+    "constraints before clique merging: {}. lower bound:"
+    "{}.".format(len(m.constrs), m.objective_value)
+)
+
+m.clique_merge()
+
+m.optimize(relax=True)
+
+print(
+    "constraints after clique merging: {}. lower bound:"
+    "{}.".format(len(m.constrs), m.objective_value)
+)
+
+m.optimize()
+
+print("optimal: {}".format(m.objective_value))
+
+
+# sanity tests
+from mip import OptimizationStatus
+
+assert m.status == OptimizationStatus.OPTIMAL
+if m.solver_name.upper() == "CBC":
+    assert m.num_rows == 2
+assert abs(m.objective_value - 12) <= 1e-4

mip/cbc.py

@@ -933,6 +933,15 @@ def generate_cuts(
         OsiCuts_delete(osi_cuts)
         return cp
 
+    def clique_merge(self, constrs: Optional[List["mip.Constr"]] = None):
+        if constrs is None:
+            cbclib.Cbc_strengthenPacking(self._model)
+        else:
+            nr = len(constrs)
+            idxr = ffi.new("int[]", [c.idx for c in constrs])
+            strengthenPacking = cbclib.Cbc_strengthenPackingRows
+            strengthenPacking(self._model, nr, idxr)
+
     def optimize(self, relax: bool = False) -> OptimizationStatus:
         # get name indexes from an osi problem
         def cbc_get_osi_name_indexes(osi_solver) -> Dict[str, int]:

mip/model.py

@@ -473,6 +473,35 @@ def var_by_name(self: "Model", name: str) -> Optional["mip.Var"]:
             return None
         return self.vars[v]
 
+    def clique_merge(self, constrs: Optional[List["mip.Constr"]] = None):
+        r"""This procedure searches for constraints with conflicting variables
+        and attempts to group these constraints in larger constraints with all
+        conflicts merged.
+
+        For example, if your model has the following constraints:
+
+        .. math::
+
+            x_1 + x_2   \leq 1
+
+            x_2 + x_3   \leq 1
+
+            x_1 + x_3   \leq 1
+
+        Then they can all be removed and replaced by the stronger inequality:
+
+        .. math::
+
+            x_1 + x_2 + x_3 \leq 1
+
+        Args:
+            constrs (Optional[List[Constrs]]): constraints that should be checked for
+                merging. If nor informed, all constraints will be checked.
+
+        """
+        self.solver.clique_merge(constrs)
+        self.constrs.update_constrs(self.solver.num_rows())
+
     def generate_cuts(
         self: "Model",
         cut_types: Optional[List["mip.CutType"]] = None,

mip/solver.py

@@ -65,6 +65,9 @@ def generate_cuts(
     ) -> "mip.CutPool":
         pass
 
+    def clique_merge(self, constrs: Optional[List["mip.Constr"]] = None):
+        pass
+
     def optimize(self: "Solver", relax: bool = False,) -> "mip.OptimizationStatus":
         pass