如何使用 Java CPLEX 求解 p 中值？

Question

这是与 CPLEX Studio/opl/examples/opl/pmedian 附带的示例等效的模型，但使用 OPL 编写。这是 Java 中的等效内容：

import ilog.concert.IloConstraint;
import ilog.concert.IloException;
import ilog.concert.IloLinearNumExpr;
import ilog.concert.IloNumVar;
import ilog.concert.IloRange;
import ilog.cplex.IloCplex;


public class P_Median {

    public static void main(String args[]) {
        solveMe();
    }

    public static void solveMe() {

        int p = 2;

        int n = 4; //costumers
        int m = 3; //warehouses
        String[] costumers = {"Albert", "Bob", "Chris", "Daniel"};
        String[] warehouses = {"Santa Clara", "San Jose", "Berkeley"};
        double[] demand = {100.0,   80.0,   80.0,   70.0};
        double[][] distance = { {2.0,   10.0,   50.0},
                                {2.0,   10.0,   52.0}, 
                                {50.0,  60.0,   3.0},
                                {40.0,  60.0,   1.0}};

        double[][]cost = new double [n][m];
        for (int c = 0; c < n; c++) {
            for (int w = 0; w < m; w++) {
                cost[c][w] = demand[c]*distance[c][w];
            }
        }
        System.out.println("cost   = [");
        for (int c = 0; c < n; c++) {
            for (int w = 0; w < m; w++) {
                System.out.print(cost[c][w] + "\t");
            }
            System.out.print("\n\r");
        }
        System.out.println("]");

        IloCplex cplex = null;

        try {
            // define new model
            cplex  = new IloCplex();
            //cplex.setParam(IloCplex.Param.Simplex.Display, 0);

            //variables
            IloNumVar[] openWarehouse = new IloNumVar[m];
            for (int w = 0 ; w < m; w++) {
                openWarehouse[w] = cplex.boolVar("openWarehouse"+"_"+w);
            }

            IloNumVar[][] shipToCustomer = new IloNumVar[n][m];
            for (int c = 0; c < n; c++) {
                for (int w = 0; w < m; w++) {
                    shipToCustomer[c][w] = cplex.boolVar("shipToCustomer"+"_"+c+"_"+w);
                }
            }

            //objective
            IloLinearNumExpr objective = cplex.linearNumExpr();
            for (int c = 0; c < n; c++) {
                for (int w = 0; w < m; w++) {
                    objective.addTerm(cost[c][w],shipToCustomer[c][w]);
                }
            }
            cplex.addMinimize(objective);

            // constraints
            IloConstraint[] shipConstraints = new IloConstraint[n];
            IloLinearNumExpr[] shipConstraintExpression = new IloLinearNumExpr[n];
            for (int c=0; c<n; c++) {
                shipConstraintExpression[c] = cplex.linearNumExpr();
                for (int w=0; w<m; w++) {
                    shipConstraintExpression[c].addTerm(1.0, shipToCustomer[c][w]);
                }
                IloRange shipConstraint = cplex.addEq(shipConstraintExpression[c], 1);
                shipConstraint.setName("shipConstraint"+c);
                shipConstraints[c]=shipConstraint;
            }

            IloLinearNumExpr openConstraintExpression = cplex.linearNumExpr();
            for (int w=0; w<m; w++) {
                openConstraintExpression.addTerm(1.0, openWarehouse[w]);
            }
            IloRange openConstraint = cplex.addEq(openConstraintExpression, p);
            openConstraint.setName("openConstraint");

            IloConstraint[][] shipOpenConstraints = new IloConstraint[n][m];
            IloLinearNumExpr[][] shipOpenExpression = new IloLinearNumExpr[n][m];
            for (int c = 0; c < n; c++) {
                for (int w = 0; w < m; w++) {
                    shipOpenExpression[c][w] = cplex.linearNumExpr();
                    shipOpenExpression[c][w].addTerm(1.0, shipToCustomer[c][w]);
                    IloConstraint shipOpenConstraint = cplex.addLe(shipOpenExpression[c][w], openWarehouse[w]);
                    shipOpenConstraint.setName("shipOpenConstraint"+c+w);
                    shipOpenConstraints[c][w]=shipOpenConstraint;
                }
            }

            // solve model
            if (cplex.solve()) {

                System.out.println("\nSolution status = "+ cplex.getStatus()+"\n");
                System.out.println("obj = "+cplex.getObjValue());

                System.out.println("openWarehouse   = [");
                for (int w = 0 ; w < m; w++) {
                    System.out.print(cplex.getValue(openWarehouse[w]) + "\t");
                }
                System.out.println("]");


                System.out.println("shipToCustomer   = [");
                for (int c = 0; c < n; c++) {
                    for (int w = 0; w < m; w++) {
                        System.out.print(cplex.getValue(shipToCustomer[c][w]) + "\t");
                    }
                    System.out.print("\n\r");
                }
                System.out.println("]");

                System.out.println("------ ship Constraints -----");
                for (int c=0;c<shipConstraints.length;c++) {
                    System.out.print(((IloRange) shipConstraints[c])+" -> "+"\t");
                    System.out.print("slack constraint "+(c+1)+" = "+cplex.getSlack((IloRange) shipConstraints[c])+"\n");
                }

                System.out.println("------ open Constraint -----");
                System.out.print(((IloRange) openConstraint)+" -> "+"\t");
                System.out.print("slack constraint  = "+cplex.getSlack((IloRange) openConstraint)+"\n");

                System.out.println("------ ship Open Constraints -----");
                for (int c = 0; c < n; c++) {
                    for (int w = 0; w < m; w++) {
                        System.out.print(((IloRange) shipOpenConstraints[c][w])+" -> "+"\t");
                        System.out.print("slack constraint "+(c+1)+""+(w+1)+" = "+cplex.getSlack((IloRange) shipOpenConstraints[c][w])+"\n");
                    }
                }


            } else {
                System.out.println("problem not solved");
            }

        } catch (IloException exc) {
            exc.printStackTrace();
        } finally {
            if(cplex!=null) cplex.end();
        }

    }

}

请哪位大佬分析一下这个解决方案是否可以？

整数规划问题是一种数学优化或可行性程序，其中部分或全部变量被限制为整数。在许多设置中，该术语指的是整数线性规划 (ILP)，其中目标函数和约束（整数约束除外）是线性的。

整数规划是 NP 完全的。特别是，0-1整数线性规划的特殊情况，其中未知数是二元的，并且仅必须满足限制，是卡普的21个NP完全问题之一。

如果某些决策变量不是离散的，则该问题称为混合整数规划问题。

Answer 1

您可以在 https://www.youtube.com/watch?v=XUFd0gLTrXk

观看有关 pmedian 与 CPLEX 的精彩视频

如果我运行 OPL 模型，我会得到

// solution (optimal) with objective 670
670

我明白了

在有问题的浏览器中。

这可以帮助您检查您的价值观是否正确。

顺便说一句，在java中，你不需要再次编写你的OPL模型，你可以从java调用你的OPL模型。

请参阅 CPLEX_Studio2211\opl xamples\opl_interfaces\java 中的示例