cplex 使用遗传算法求解多目标规划模型代码

遗传算法是一种常用的优化算法，可以用于多目标规划模型的求解。而Cplex是一种商业化的数学优化软件，可以用于求解各种复杂的数学规划问题。下面是使用Cplex和遗传算法求解多目标规划模型的代码示例：

#include <ilcplex/ilocplex.h>
#include <ilcplex/cplex.h>
#include <iostream>
#include <fstream>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <ctime>

ILOSTLBEGIN

int main(int argc, char **argv) {
    // 遗传算法相关参数
    const int POP_SIZE = 50; // 种群大小
    const int MAX_GEN = 100; // 最大迭代次数
    const double CROSSOVER_RATE = 0.8; // 交叉概率
    const double MUTATION_RATE = 0.1; // 变异概率
    const int TOURNAMENT_SIZE = 5; // 锦标赛选择的大小

    // 多目标规划模型相关参数
    const int NUM_VAR = 2; // 决策变量个数
    const int NUM_OBJ = 2; // 目标函数个数

    // 初始化随机数生成器
    srand((unsigned) time(NULL));

    // 初始化Cplex环境
    IloEnv env;
    try {
        // 定义决策变量
        IloNumVarArray x(env, NUM_VAR, 0, 1, ILOBOOL);

        // 定义目标函数
        IloObjective obj(env);
        obj.setSense(IloObjective::Minimize);
        obj.setExpr(0.5 * x[0] + 0.5 * x[1]);

        // 定义约束条件
        IloRangeArray range(env);
        range.add(x[0] + x[1] <= 1);

        // 定义Cplex模型
        IloModel model(env);
        model.add(obj);
        model.add(range);

        // 定义Cplex求解器
        IloCplex cplex(model);

        // 定义遗传算法种群
        std::vector<std::vector<int>> population;
        for (int i = 0; i < POP_SIZE; i++) {
            std::vector<int> chromosome;
            for (int j = 0; j < NUM_VAR; j++) {
                chromosome.push_back(rand() % 2);
            }
            population.push_back(chromosome);
        }

        // 迭代优化
        for (int gen = 0; gen < MAX_GEN; gen++) {
            // 计算适应度
            std::vector<double> fitness;
            for (int i = 0; i < POP_SIZE; i++) {
                double obj1 = 0.5 * population[i][0] + 0.5 * population[i][1];
                double obj2 = 1 - obj1;
                fitness.push_back(obj1);
                fitness.push_back(obj2);
            }

            // 选择操作
            std::vector<std::vector<int>> newPopulation;
            for (int i = 0; i < POP_SIZE; i++) {
                std::vector<int> parent1, parent2;
                for (int j = 0; j < TOURNAMENT_SIZE; j++) {
                    int index = rand() % POP_SIZE;
                    if (j == 0 || fitness[index * NUM_OBJ] > fitness[parent1[0] * NUM_OBJ]) {
                        parent1.clear();
                        parent1.push_back(index);
                    } else if (fitness[index * NUM_OBJ] == fitness[parent1[0] * NUM_OBJ]) {
                        parent1.push_back(index);
                    }
                    if (j == 0 || fitness[index * NUM_OBJ] > fitness[parent2[0] * NUM_OBJ]) {
                        parent2.clear();
                        parent2.push_back(index);
                    } else if (fitness[index * NUM_OBJ] == fitness[parent2[0] * NUM_OBJ]) {
                        parent2.push_back(index);
                    }
                }
                int crossoverPoint = rand() % (NUM_VAR - 1) + 1;
                std::vector<int> offspring1, offspring2;
                if ((double) rand() / RAND_MAX < CROSSOVER_RATE) {
                    for (int j = 0; j < crossoverPoint; j++) {
                        offspring1.push_back(population[parent1[rand() % parent1.size()]][j]);
                        offspring2.push_back(population[parent2[rand() % parent2.size()]][j]);
                    }
                    for (int j = crossoverPoint; j < NUM_VAR; j++) {
                        offspring1.push_back(population[parent2[rand() % parent2.size()]][j]);
                        offspring2.push_back(population[parent1[rand() % parent1.size()]][j]);
                    }
                } else {
                    offspring1 = population[parent1[rand() % parent1.size()]];
                    offspring2 = population[parent2[rand() % parent2.size()]];
                }
                if ((double) rand() / RAND_MAX < MUTATION_RATE) {
                    int mutationPoint = rand() % NUM_VAR;
                    offspring1[mutationPoint] = 1 - offspring1[mutationPoint];
                }
                if ((double) rand() / RAND_MAX < MUTATION_RATE) {
                    int mutationPoint = rand() % NUM_VAR;
                    offspring2[mutationPoint] = 1 - offspring2[mutationPoint];
                }
                newPopulation.push_back(offspring1);
                newPopulation.push_back(offspring2);
            }

            // 更新种群
            population = newPopulation;

            // 输出迭代结果
            std::cout << "Generation " << gen + 1 << ":" << std::endl;
            for (int i = 0; i < POP_SIZE; i++) {
                std::cout << "    ";
                for (int j = 0; j < NUM_VAR; j++) {
                    std::cout << population[i][j] << " ";
                }
                std::cout << "-> ";
                cplex.setParam(IloCplex::Param::Emphasis::Objective, 1);
                cplex.setOut(env.getNullStream());
                cplex.solve();
                std::cout << "Obj1 = " << cplex.getObjValue() << ", Obj2 = " << 1 - cplex.getObjValue() << std::endl;
            }
        }

        // 释放Cplex资源
        cplex.end();
        model.end();
        range.end();
        obj.end();
        x.end();
    } catch (IloException &e) {
        std::cerr << "Concert exception caught: " << e << std::endl;
    } catch (...) {
        std::cerr << "Unknown exception caught" << std::endl;
    }

    // 释放Cplex环境
    env.end();

    return 0;
}

注：以上代码仅为示例，可能存在语法错误或逻辑错误，仅供参考和学习。