// (c) 2024-2024 Fair Isaac Corporation /** * An example that demonstrates how to model a piecewise linear cost function. A * piecewise linear cost function f(x) assigns a different linear cost function * for different intervals of the domain of its argument x. This situation * occurs in real-world problems if there are price discounts available starting * from a certain quantity of sold goods. * * - Example discussed in mipformref whitepaper - */ #include <iostream>
#include <xpress.hpp>

using namespace xpress;
using namespace xpress::objects;

int main(void) {
  std::cout << "Formulating the piecewise linear example problem" << std::endl;

  XpressProblem prob;
  Variable x = prob.addVariable("x");
  Variable fx = prob.addVariable("fx");
  Expression objective = fx;

  std::vector<double> BREAKPOINT_X{0,   50,  50,
                                   120, 120, 200}; // the breakpoints x values
  std::vector<double> BREAKPOINT_Y{0,   50,  75,
                                   180, 240, 400}; // the breakpoints y values

  // Create the break points from the x,y data
  std::vector<PwlBreakpoint> breakpoints(BREAKPOINT_X.size()); for (unsigned i = 0; i < breakpoints.size(); ++i) breakpoints[i] = PwlBreakpoint(BREAKPOINT_X[i], BREAKPOINT_Y[i]); // add the piecewise linear constraints with the breakpoints prob.addConstraint(fx.pwlOf(x, breakpoints, "pwl_with_breakpoints")); // ! Add a lower bound on x to get a somewhat more meaningful model // x >= 150 x.setLB(150); // set objective function with a minimization sense prob.setObjective(objective, ObjSense::Minimize); // write the problem in LP format for manual inspection std::cout << "Writing the problem to 'PiecewiseLinear.lp'" << std::endl; prob.writeProb("PiecewiseLinear.lp", "l"); // Solve the problem std::cout << "Solving the problem" << std::endl; prob.optimize(); // check the solution status std::cout << "Problem finished with SolStatus " << to_string(prob.attributes.getSolStatus()) << std::endl; if (prob.attributes.getSolStatus() != SolStatus::Optimal) { throw std::runtime_error("Problem not solved to optimality"); } // print the optimal solution of the problem to the console std::cout << "Solution has objective value (profit) of " << prob.attributes.getObjVal() << std::endl; std::cout << std::endl; std::cout << "*** Solution ***" << std::endl; auto sol = prob.getSolution(); std::cout << "x = " << x.getValue(sol) << ", fx = " << fx.getValue(sol) << std::endl; return 0; }