Add possibility for nonlinear objective function (#781)

* addPiecewiseLinearCons method and test

* Update CHANGELOG

* Fix recommendations

* Add possibility for nonlinear objective

* Add nonlinear objective test

* Modify other tests

* Update CHANGELOG

* Add untested changes to fix test and assert

* Move to recipes folder

* Update CHANGELOG

* Fix segfault

* Reset locale to standard

* Fix test

* Small refactoring

---------

Co-authored-by: Mark Turner <[email protected]>
Co-authored-by: Mohammed Ghannam <[email protected]>

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Unreleased
 ### Added
+- Added recipe for nonlinear objective functions
 - Added method for adding piecewise linear constraints
 - Add SCIP function SCIPgetTreesizeEstimation and wrapper getTreesizeEstimation
 - New test for model setLogFile

src/pyscipopt/recipes/nonlinear.py

@@ -0,0 +1,18 @@
+from pyscipopt import Model
+
+def set_nonlinear_objective(model: Model, expr, sense="minimize"):
+        """
+        Takes a nonlinear expression and performs an epigraph reformulation.
+        """
+
+        assert expr.degree() > 1, "For linear objectives, please use the setObjective method."
+        new_obj = model.addVar(lb=-float("inf"),obj=1)
+        if sense == "minimize":
+            model.addCons(expr <= new_obj)
+            model.setMinimize()
+        elif sense == "maximize":
+            model.addCons(expr >= new_obj)
+            model.setMaximize()
+        else:
+            raise Warning("unrecognized optimization sense: %s" % sense)
+

src/pyscipopt/scip.pxi

@@ -1315,24 +1315,26 @@ cdef class Model:
         """returns current limit on objective function."""
         return SCIPgetObjlimit(self._scip)
 
-    def setObjective(self, coeffs, sense = 'minimize', clear = 'true'):
+    def setObjective(self, expr, sense = 'minimize', clear = 'true'):
         """Establish the objective function as a linear expression.
 
-        :param coeffs: the coefficients
+        :param expr: the objective function SCIP Expr, or constant value
         :param sense: the objective sense (Default value = 'minimize')
         :param clear: set all other variables objective coefficient to zero (Default value = 'true')
 
         """
+
         cdef SCIP_VAR** _vars
         cdef int _nvars
 
         # turn the constant value into an Expr instance for further processing
-        if not isinstance(coeffs, Expr):
-            assert(_is_number(coeffs)), "given coefficients are neither Expr or number but %s" % coeffs.__class__.__name__
-            coeffs = Expr() + coeffs
+        if not isinstance(expr, Expr):
+            print(expr)
+            assert(_is_number(expr)), "given coefficients are neither Expr or number but %s" % expr.__class__.__name__
+            expr = Expr() + expr
 
-        if coeffs.degree() > 1:
-            raise ValueError("Nonlinear objective functions are not supported!")
+        if expr.degree() > 1:
+            raise ValueError("SCIP does not support nonlinear objective functions. Consider using set_nonlinear_objective in the pyscipopt.recipe.nonlinear")
 
         if clear:
             # clear existing objective function
@@ -1342,10 +1344,10 @@ cdef class Model:
             for i in range(_nvars):
                 PY_SCIP_CALL(SCIPchgVarObj(self._scip, _vars[i], 0.0))
 
-        if coeffs[CONST] != 0.0:
-            self.addObjoffset(coeffs[CONST])
+        if expr[CONST] != 0.0:
+            self.addObjoffset(expr[CONST])
 
-        for term, coef in coeffs.terms.items():
+        for term, coef in expr.terms.items():
             # avoid CONST term of Expr
             if term != CONST:
                 assert len(term) == 1

tests/test_cons.py

@@ -152,7 +152,6 @@ def test_printCons():
 
     m.printCons(c)
 
-
 @pytest.mark.skip(reason="TODO: test getValsLinear()")
 def test_getValsLinear():
     assert True

tests/test_linexpr.py

@@ -215,9 +215,4 @@ def test_objective(model):
 
     # setting affine objective
     m.setObjective(x + y + 1)
-    assert m.getObjoffset() == 1
-
-    # setting nonlinear objective
-    with pytest.raises(ValueError):
-        m.setObjective(x ** 2 - y * z)
-
+    assert m.getObjoffset() == 1

tests/test_model.py

@@ -288,6 +288,14 @@ def test_getStage():
     assert m.getStage() == SCIP_STAGE.SOLVED
     assert m.getStageName() == "SOLVED"
 
+def test_getObjective():
+    m = Model()
+    m.addVar(obj=2, name="x1")
+    m.addVar(obj=3, name="x2")
+
+    assert str(m.getObjective()) == "Expr({Term(x1): 2.0, Term(x2): 3.0})"
+
+
 def test_getTreesizeEstimation():
     m = Model()
 
@@ -349,3 +357,5 @@ def test_locale():
 
     with open("model.cip") as file:
         assert "1,1" not in file.read()
+
+    locale.setlocale(locale.LC_NUMERIC,"")

tests/test_nonlinear.py

@@ -1,6 +1,7 @@
 import pytest
+import random
 
-from pyscipopt import Model, quicksum, sqrt
+from pyscipopt import Model, quicksum, sqrt, exp, log, sin
 
 # test string with polynomial formulation (uses only Expr)
 def test_string_poly():

tests/test_recipe_nonlinear.py

@@ -0,0 +1,52 @@
+from pyscipopt import Model, exp, log, sqrt, sin
+from pyscipopt.recipes.nonlinear import set_nonlinear_objective
+
+def test_nonlinear_objective():
+    model = Model()
+
+    v = model.addVar()
+    w = model.addVar()
+    x = model.addVar()
+    y = model.addVar()
+    z = model.addVar()
+
+    obj = 0
+    obj += exp(v)
+    obj += log(w)
+    obj += sqrt(x)
+    obj += sin(y)
+    obj += z**3 * y
+
+    model.addCons(v + w + x + y + z <= 1)
+    set_nonlinear_objective(model, obj, sense='maximize')
+
+    model2 = Model()
+
+    a = model2.addVar()
+    b = model2.addVar()
+    c = model2.addVar()
+    d = model2.addVar()
+    e = model2.addVar()
+
+    obj2 = 0
+    obj2 += exp(a)
+    obj2 += log(b)
+    obj2 += sqrt(c)
+    obj2 += sin(d)
+    obj2 += e**3 * d
+
+    model2.addCons(a + b + c + d + e <= 1)
+
+    t = model2.addVar(lb=-float("inf"),obj=1)
+    model2.addCons(t <= obj2)
+    model2.setMaximize()
+
+    obj_expr = model.getObjective()
+    assert obj_expr.degree() == 1
+
+    model.setParam("numerics/epsilon", 10**(-5)) # bigger eps due to nonlinearities
+    model2.setParam("numerics/epsilon", 10**(-5)) 
+
+    model.optimize()
+    model2.optimize()
+    assert model.isEQ(model.getObjVal(), model2.getObjVal())

tests/test_piecewise.py → tests/test_recipe_piecewise.py

@@ -14,7 +14,6 @@ def test_add_piecewise_linear_cons():
     m.optimize()
     assert m.isEQ(m.getObjVal(), -2)
 
-
 def test_add_piecewise_linear_cons2():
     m = Model()