CPLEX求解混合整數規劃模型

在CPLEX中，對於混合整數規劃模型的求解是其核心功能之一，因此我們對相關CPLEX的示例程序進行了深入的瞭解。如下：

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using ILOG.Concert;
using ILOG.CPLEX;

// MIPex3.cs - Entering and optimizing a MIP problem with SOS sets
//             and priority orders.  It is a modification of MIPex1.cs.
//             Note that the problem solved is slightly different than
//             MIPex1.cs so that the output is interesting.


namespace MiPex3
{
    class Program
    {

        static void Main(string[] args)
        {
            try
            {
                //create CPLEX optimizer/modeler and turn off presolve. 關閉MIP求解器的預處理模塊
                Cplex cplex = new Cplex();
                cplex.SetParam(Cplex.Param.Preprocessing.Presolve, false);

                //build the model
                INumVar[][] var = new INumVar[1][];
                IRange [][] rng = new IRange[1][];
                PopulateByRow(cplex, var, rng);

                //setup branch priorities,設置分支界定的優先級
                INumVar[] ordvar = { var[0][1], var[0][3] };
                int[] ordpri = { 8, 7 };
                cplex.SetPriorities(ordvar, ordpri);

                //setup branch directions.設置分直界定求解路線
                cplex.SetDirection(ordvar[0], Cplex.BranchDirection.Up);
                cplex.SetDirection(ordvar[1], Cplex.BranchDirection.Down);

                //write priority order to file
                cplex.WriteOrder("mipex3.ord");

                //optimize and output solution information
                if (cplex.Solve()) {
                    double[] x = cplex.GetValues(var[0]);
                    double[] slack = cplex.GetSlacks(rng[0]);

                    System.Console.WriteLine("Solution status = " + cplex.GetStatus());
                    System.Console.WriteLine("Solution value  = " + cplex.ObjValue);

                    for (int j = 0; j < x.Length; ++j) {
                        System.Console.WriteLine("Variable   " + j +
                                        ": Value = " + x[j]);
                    }

                    for (int i = 0; i < slack.Length; ++i)
                    {
                        System.Console.WriteLine("Constraint " + i +
                                                 ": Slack = " + slack[i]);
                    }
                }
                cplex.ExportModel("mipex3.lp");
                cplex.End();
                System.Console.ReadKey();

            }
            catch(ILOG.Concert.Exception e) {
                System.Console.WriteLine("Concert exception caught: " + e);
            }
        }
        internal static void PopulateByRow(IMPModeler model,
                                           INumVar[][] var,
                                           IRange[][] rng) {
            //Define the variables one-by-one
            INumVar[] x = new INumVar[4];
            x[0] = model.NumVar(0.0, 40.0, "x0");
            x[1] = model.IntVar(0, System.Int32.MaxValue, "x1");
            x[2] = model.IntVar(0, System.Int32.MaxValue, "x2");
            x[3] = model.IntVar(2, 3, "x3");
            var[0] = x;

            //objective function
            model.AddMaximize(model.Sum(model.Prod(1.0, x[0]),
                                        model.Prod(2.0, x[1]),
                                        model.Prod(3.0, x[2]),
                                        model.Prod(1.0, x[3])));
            //define three constraints one-by-one
            rng[0] = new IRange[3];
            rng[0][0] = model.AddLe(model.Sum(model.Prod(-1.0, x[0]),
                                            model.Prod(1.0, x[1]),
                                            model.Prod(1.0, x[2]),
                                            model.Prod(10.0, x[3])),
                                            20.0, "rng0");
            rng[0][1] = model.AddLe(model.Sum(model.Prod(1.0, x[0]),
                                        model.Prod(-3.0, x[1]),
                                        model.Prod(1.0, x[2])),
                              30.0, "rng1");
            rng[0][2] = model.AddEq(model.Sum(model.Prod(1.0, x[1]),
                                        model.Prod(-3.5, x[3])),
                              0, "rng2");
            // add special ordered set of type 1
            INumVar[] sosvars = { x[2], x[3] };
            double[] sosweights = { 25.0, 18.0 };
            model.AddSOS1(sosvars, sosweights);
        }
    }
}