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piecewise_c++.cpp
/* Copyright 2021, Gurobi Optimization, LLC */ /* This example considers the following separable, convex problem: minimize f(x) - y + g(z) subject to x + 2 y + 3 z <= 4 x + y >= 1 x, y, z <= 1 where f(u) = exp(-u) and g(u) = 2 u^2 - 4 u, for all real u. It formulates and solves a simpler LP model by approximating f and g with piecewise-linear functions. Then it transforms the model into a MIP by negating the approximation for f, which corresponds to a non-convex piecewise-linear function, and solves it again. */ #include "gurobi_c++.h" #include <cmath> using namespace std; double f(double u) { return exp(-u); } double g(double u) { return 2 * u * u - 4 * u; } int main(int argc, char *argv[]) { double *ptu = NULL; double *ptf = NULL; double *ptg = NULL; try { // Create environment GRBEnv env = GRBEnv(); // Create a new model GRBModel model = GRBModel(env); // Create variables double lb = 0.0, ub = 1.0; GRBVar x = model.addVar(lb, ub, 0.0, GRB_CONTINUOUS, "x"); GRBVar y = model.addVar(lb, ub, 0.0, GRB_CONTINUOUS, "y"); GRBVar z = model.addVar(lb, ub, 0.0, GRB_CONTINUOUS, "z"); // Set objective for y model.setObjective(-y); // Add piecewise-linear objective functions for x and z int npts = 101; ptu = new double[npts]; ptf = new double[npts]; ptg = new double[npts]; for (int i = 0; i < npts; i++) { ptu[i] = lb + (ub - lb) * i / (npts - 1); ptf[i] = f(ptu[i]); ptg[i] = g(ptu[i]); } model.setPWLObj(x, npts, ptu, ptf); model.setPWLObj(z, npts, ptu, ptg); // Add constraint: x + 2 y + 3 z <= 4 model.addConstr(x + 2 * y + 3 * z <= 4, "c0"); // Add constraint: x + y >= 1 model.addConstr(x + y >= 1, "c1"); // Optimize model as an LP model.optimize(); cout << "IsMIP: " << model.get(GRB_IntAttr_IsMIP) << endl; cout << x.get(GRB_StringAttr_VarName) << " " << x.get(GRB_DoubleAttr_X) << endl; cout << y.get(GRB_StringAttr_VarName) << " " << y.get(GRB_DoubleAttr_X) << endl; cout << z.get(GRB_StringAttr_VarName) << " " << z.get(GRB_DoubleAttr_X) << endl; cout << "Obj: " << model.get(GRB_DoubleAttr_ObjVal) << endl; cout << endl; // Negate piecewise-linear objective function for x for (int i = 0; i < npts; i++) { ptf[i] = -ptf[i]; } model.setPWLObj(x, npts, ptu, ptf); // Optimize model as a MIP model.optimize(); cout << "IsMIP: " << model.get(GRB_IntAttr_IsMIP) << endl; cout << x.get(GRB_StringAttr_VarName) << " " << x.get(GRB_DoubleAttr_X) << endl; cout << y.get(GRB_StringAttr_VarName) << " " << y.get(GRB_DoubleAttr_X) << endl; cout << z.get(GRB_StringAttr_VarName) << " " << z.get(GRB_DoubleAttr_X) << endl; cout << "Obj: " << model.get(GRB_DoubleAttr_ObjVal) << endl; } catch(GRBException e) { cout << "Error code = " << e.getErrorCode() << endl; cout << e.getMessage() << endl; } catch(...) { cout << "Exception during optimization" << endl; } delete[] ptu; delete[] ptf; delete[] ptg; return 0; }