采用C++实现置换流水车间调度问题数学模型并通过算例验证代码的正确性

置换流水车间调度问题是一个NP难问题，需要采用一些启发式算法或元启发式算法来求解。其中，最常用的启发式算法是遗传算法和禁忌搜索算法。下面是一个采用遗传算法求解置换流水车间调度问题的C++代码示例：

#include <iostream>
#include <algorithm>
#include <vector>
#include <random>
#include <chrono>
using namespace std;

// 定义工件类
class Job {
public:
    int id;         // 工件编号
    int process[3]; // 该工件在三台机器上的加工时间
    Job(int id, int p1, int p2, int p3) {
        this->id = id;
        this->process[0] = p1;
        this->process[1] = p2;
        this->process[2] = p3;
    }
};

// 定义车间类
class Workshop {
public:
    vector<Job> jobs; // 所有工件
    int n;            // 工件数量
    Workshop(vector<Job>& jobs) {
        this->jobs = jobs;
        this->n = jobs.size();
    }
    // 计算某个解的目标函数值
    int objectiveFunction(vector<int>& solution) {
        int makespan = 0;
        vector<int> finishTime(n);
        for (int i = 0; i < n; i++) {
            int job = solution[i]; // 第i个工件的编号
            for (int j = 0; j < 3; j++) {
                int machine = j + 1; // 第j台机器的编号
                int processingTime = jobs[job].process[j];
                int startTime = (i == 0) ? 0 : finishTime[solution[i - 1]]; // 开始时间
                finishTime[job] = startTime + processingTime;
                makespan = max(makespan, finishTime[job]);
            }
        }
        return makespan;
    }
};

// 定义遗传算法类
class GeneticAlgorithm {
public:
    Workshop* workshop; // 车间
    int populationSize; // 种群大小
    double crossoverRate; // 交叉率
    double mutationRate; // 变异率
    int maxGeneration; // 最大迭代次数
    GeneticAlgorithm(Workshop* workshop, int populationSize, double crossoverRate, double mutationRate, int maxGeneration) {
        this->workshop = workshop;
        this->populationSize = populationSize;
        this->crossoverRate = crossoverRate;
        this->mutationRate = mutationRate;
        this->maxGeneration = maxGeneration;
    }
    // 初始化种群
    vector<vector<int>> initializePopulation() {
        vector<vector<int>> population;
        for (int i = 0; i < populationSize; i++) {
            vector<int> solution(workshop->n);
            for (int j = 0; j < workshop->n; j++) {
                solution[j] = j;
            }
            shuffle(solution.begin(), solution.end(), default_random_engine(chrono::system_clock::now().time_since_epoch().count()));
            population.push_back(solution);
        }
        return population;
    }
    // 选择操作
    vector<vector<int>> selection(vector<vector<int>>& population) {
        vector<vector<int>> parents;
        for (int i = 0; i < populationSize; i++) {
            int a = rand() % populationSize;
            int b = rand() % populationSize;
            if (workshop->objectiveFunction(population[a]) < workshop->objectiveFunction(population[b])) {
                parents.push_back(population[a]);
            }
            else {
                parents.push_back(population[b]);
            }
        }
        return parents;
    }
    // 交叉操作
    vector<vector<int>> crossover(vector<vector<int>>& parents) {
        vector<vector<int>> offspring;
        for (int i = 0; i < populationSize; i += 2) {
            if (rand() < crossoverRate * RAND_MAX) {
                int r1 = rand() % workshop->n;
                int r2 = rand() % workshop->n;
                while (r2 == r1) {
                    r2 = rand() % workshop->n;
                }
                if (r1 > r2) {
                    swap(r1, r2);
                }
                vector<int> p1 = parents[i];
                vector<int> p2 = parents[i + 1];
                vector<int> o1(workshop->n), o2(workshop->n);
                for (int j = r1; j <= r2; j++) {
                    o1[j] = p1[j];
                    o2[j] = p2[j];
                }
                int k1 = r2 + 1, k2 = r2 + 1;
                for (int j = 0; j < workshop->n; j++) {
                    if (find(o1.begin(), o1.end(), p2[j]) == o1.end()) {
                        o1[k1++] = p2[j];
                    }
                    if (find(o2.begin(), o2.end(), p1[j]) == o2.end()) {
                        o2[k2++] = p1[j];
                    }
                }
                offspring.push_back(o1);
                offspring.push_back(o2);
            }
            else {
                offspring.push_back(parents[i]);
                offspring.push_back(parents[i + 1]);
            }
        }
        return offspring;
    }
    // 变异操作
    void mutation(vector<vector<int>>& offspring) {
        for (int i = 0; i < populationSize; i++) {
            if (rand() < mutationRate * RAND_MAX) {
                int r1 = rand() % workshop->n;
                int r2 = rand() % workshop->n;
                swap(offspring[i][r1], offspring[i][r2]);
            }
        }
    }
    // 更新种群
    void updatePopulation(vector<vector<int>>& population, vector<vector<int>>& offspring) {
        population.insert(population.end(), offspring.begin(), offspring.end());
        sort(population.begin(), population.end(), [&](const vector<int>& a, const vector<int>& b) {
            return workshop->objectiveFunction(a) < workshop->objectiveFunction(b);
        });
        population.resize(populationSize);
    }
    // 求解
    vector<int> solve() {
        vector<vector<int>> population = initializePopulation();
        for (int i = 0; i < maxGeneration; i++) {
            vector<vector<int>> parents = selection(population);
            vector<vector<int>> offspring = crossover(parents);
            mutation(offspring);
            updatePopulation(population, offspring);
        }
        return population.front();
    }
};

int main() {
    vector<Job> jobs = {
        Job(0, 2, 4, 3),
        Job(1, 2, 3, 1),
        Job(2, 3, 5, 2),
        Job(3, 1, 4, 2),
        Job(4, 3, 2, 1)
    };
    Workshop workshop(jobs);
    GeneticAlgorithm ga(&workshop, 100, 0.8, 0.1, 1000);
    vector<int> solution = ga.solve();
    cout << "Solution: ";
    for (int i : solution) {
        cout << i << " ";
    }
    cout << endl;
    cout << "Makespan: " << workshop.objectiveFunction(solution) << endl;
    return 0;
}

上述代码采用遗传算法求解置换流水车间调度问题。其中，`Job`类表示工件，`Workshop`类表示车间，`GeneticAlgorithm`类表示遗传算法类。在`GeneticAlgorithm`类中，`initializePopulation()`方法用于初始化种群，`selection()`方法用于选择操作，`crossover()`方法用于交叉操作，`mutation()`方法用于变异操作，`updatePopulation()`方法用于更新种群，`solve()`方法用于求解。在主函数中，我们定义了一个包含5个工件的车间，并使用遗传算法求解最优调度方案。