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GCPWLFunc.java
/* Copyright 2024, Gurobi Optimization, LLC This example considers the following nonconvex nonlinear problem maximize 2 x + y subject to exp(x) + 4 sqrt(y) <= 9 x, y >= 0 We show you two approaches to solve this: 1) Use a piecewise-linear approach to handle general function constraints (such as exp and sqrt). a) Add two variables u = exp(x) v = sqrt(y) b) Compute points (x, u) of u = exp(x) for some step length (e.g., x = 0, 1e-3, 2e-3, ..., xmax) and points (y, v) of v = sqrt(y) for some step length (e.g., y = 0, 1e-3, 2e-3, ..., ymax). We need to compute xmax and ymax (which is easy for this example, but this does not hold in general). c) Use the points to add two general constraints of type piecewise-linear. 2) Use the Gurobis built-in general function constraints directly (EXP and POW). Here, we do not need to compute the points and the maximal possible values, which will be done internally by Gurobi. In this approach, we show how to "zoom in" on the optimal solution and tighten tolerances to improve the solution quality. */ import com.gurobi.gurobi.*; public class GCPWLFunc { private static double f(double u) { return Math.exp(u); } private static double g(double u) { return Math.sqrt(u); } private static void printsol(GRBModel m, GRBVar x, GRBVar y, GRBVar u, GRBVar v) throws GRBException { assert(m.get(GRB.IntAttr.Status) == GRB.OPTIMAL); System.out.println("x = " + x.get(GRB.DoubleAttr.X) + ", u = " + u.get(GRB.DoubleAttr.X)); System.out.println("y = " + y.get(GRB.DoubleAttr.X) + ", v = " + v.get(GRB.DoubleAttr.X)); System.out.println("Obj = " + m.get(GRB.DoubleAttr.ObjVal)); // Calculate violation of exp(x) + 4 sqrt(y) <= 9 double vio = f(x.get(GRB.DoubleAttr.X)) + 4 * g(y.get(GRB.DoubleAttr.X)) - 9; if (vio < 0.0) vio = 0.0; System.out.println("Vio = " + vio); } public static void main(String[] args) { try { // Create environment GRBEnv env = new GRBEnv(); // Create a new m GRBModel m = new GRBModel(env); double lb = 0.0, ub = GRB.INFINITY; GRBVar x = m.addVar(lb, ub, 0.0, GRB.CONTINUOUS, "x"); GRBVar y = m.addVar(lb, ub, 0.0, GRB.CONTINUOUS, "y"); GRBVar u = m.addVar(lb, ub, 0.0, GRB.CONTINUOUS, "u"); GRBVar v = m.addVar(lb, ub, 0.0, GRB.CONTINUOUS, "v"); // Set objective GRBLinExpr obj = new GRBLinExpr(); obj.addTerm(2.0, x); obj.addTerm(1.0, y); m.setObjective(obj, GRB.MAXIMIZE); // Add linear constraint GRBLinExpr expr = new GRBLinExpr(); expr.addTerm(1.0, u); expr.addTerm(4.0, v); m.addConstr(expr, GRB.LESS_EQUAL, 9.0, "l1"); // Approach 1) PWL constraint approach double intv = 1e-3; double xmax = Math.log(9.0); int len = (int) Math.ceil(xmax/intv) + 1; double[] xpts = new double[len]; double[] upts = new double[len]; for (int i = 0; i < len; i++) { xpts[i] = i*intv; upts[i] = f(i*intv); } GRBGenConstr gc1 = m.addGenConstrPWL(x, u, xpts, upts, "gc1"); double ymax = (9.0/4.0)*(9.0/4.0); len = (int) Math.ceil(ymax/intv) + 1; double[] ypts = new double[len]; double[] vpts = new double[len]; for (int i = 0; i < len; i++) { ypts[i] = i*intv; vpts[i] = g(i*intv); } GRBGenConstr gc2 = m.addGenConstrPWL(y, v, ypts, vpts, "gc2"); // Optimize the model and print solution m.optimize(); printsol(m, x, y, u, v); // Approach 2) General function constraint approach with auto PWL // translation by Gurobi // restore unsolved state and get rid of PWL constraints m.reset(); m.remove(gc1); m.remove(gc2); m.update(); GRBGenConstr gcf1 = m.addGenConstrExp(x, u, "gcf1", null); GRBGenConstr gcf2 = m.addGenConstrPow(y, v, 0.5, "gcf2", ""); // Use the equal piece length approach with the length = 1e-3 m.set(GRB.IntParam.FuncPieces, 1); m.set(GRB.DoubleParam.FuncPieceLength, 1e-3); // Optimize the model and print solution m.optimize(); printsol(m, x, y, u, v); // Zoom in, use optimal solution to reduce the ranges and use a smaller // pclen=1e-5 to solve it double xval = x.get(GRB.DoubleAttr.X); double yval = y.get(GRB.DoubleAttr.X); x.set(GRB.DoubleAttr.LB, Math.max(x.get(GRB.DoubleAttr.LB), xval-0.01)); x.set(GRB.DoubleAttr.UB, Math.min(x.get(GRB.DoubleAttr.UB), xval+0.01)); y.set(GRB.DoubleAttr.LB, Math.max(y.get(GRB.DoubleAttr.LB), yval-0.01)); y.set(GRB.DoubleAttr.UB, Math.min(y.get(GRB.DoubleAttr.UB), yval+0.01)); m.update(); m.reset(); m.set(GRB.DoubleParam.FuncPieceLength, 1e-5); // Optimize the model and print solution m.optimize(); printsol(m, x, y, u, v); // Dispose of model and environment m.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } } }