highs: support optimize(relax=True)

Author: rschwarz

mip/highs.py

@@ -382,8 +382,7 @@ def get_objective_const(self: "SolverHighs") -> numbers.Real:
         check(self._lib.Highs_getObjectiveOffset(self._model, offset))
         return offset[0]
 
-    def relax(self: "SolverHighs"):
-        # change integrality of all columns
+    def _all_cols_continuous(self: "SolverHighs"):
         n = self.num_cols()
         integrality = ffi.new(
             "int[]", [self._lib.kHighsVarTypeContinuous for i in range(n)]
@@ -393,6 +392,24 @@ def relax(self: "SolverHighs"):
                 self._model, 0, n - 1, integrality
             )
         )
+
+    def _reset_var_types(self: "SolverHighs"):
+        var_type_map = {
+            mip.CONTINUOUS: self._lib.kHighsVarTypeContinuous,
+            mip.BINARY: self._lib.kHighsVarTypeInteger,
+            mip.INTEGER: self._lib.kHighsVarTypeInteger,
+        }
+        integrality = ffi.new("int[]", [var_type_map[vt] for vt in self._var_type])
+        n = self.num_cols()
+        check(
+            self._lib.Highs_changeColsIntegralityByRange(
+                self._model, 0, n - 1, integrality
+            )
+        )
+
+    def relax(self: "SolverHighs"):
+        # change integrality of all columns
+        self._all_cols_continuous()
         self._var_type = [mip.CONTINUOUS] * len(self._var_type)
 
     def generate_cuts(
@@ -413,8 +430,10 @@ def optimize(
         relax: bool = False,
     ) -> "mip.OptimizationStatus":
         if relax:
-            # TODO: handle relax (need to remember and reset integrality?!
-            raise NotImplementedError()
+            # Temporarily change variable types. Original types are still stored
+            # in self._var_type.
+            self._all_cols_continuous()
+
         check(self._lib.Highs_run(self._model))
 
         # store solution values for later access
@@ -440,6 +459,10 @@ def optimize(
             if self._has_dual_solution():
                 self._pi = [row_dual[i] for i in range(m)]
 
+        if relax:
+            # Undo the temporary changes.
+            self._reset_var_types()
+
         return opt_status
 
     def get_objective_value(self: "SolverHighs") -> numbers.Real:

test/test_model.py

@@ -1360,3 +1360,31 @@ def test_change_objective_sense(solver):
     status = m.optimize()
     assert status == OptimizationStatus.OPTIMAL
     assert x.x == pytest.approx(10.0)
+
+@pytest.mark.parametrize("solver", SOLVERS)
+def test_solve_relaxation(solver):
+    m = Model(solver_name=solver)
+    x = m.add_var("x", var_type=CONTINUOUS)
+    y = m.add_var("y", var_type=INTEGER)
+    z = m.add_var("z", var_type=BINARY)
+
+    m.add_constr(x <= 10 * z)
+    m.add_constr(x <= 9.5)
+    m.add_constr(x + y <= 20)
+    m.objective = mip.maximize(4*x + y - z)
+
+    # first solve proper MIP
+    status = m.optimize()
+    assert status == OptimizationStatus.OPTIMAL
+    assert x.x == pytest.approx(9.5)
+    assert y.x == pytest.approx(10.0)
+    assert z.x == pytest.approx(1.0)
+
+    # then compare LP relaxation
+    # (seems to fail for CBC?!)
+    if solver == HIGHS:
+        status = m.optimize(relax=True)
+        assert status == OptimizationStatus.OPTIMAL
+        assert x.x == pytest.approx(9.5)
+        assert y.x == pytest.approx(10.5)
+        assert z.x == pytest.approx(0.95)