用java代码实现一个旅行商问题

旅行商问题（Traveling Salesman Problem，TSP）是一个经典的组合优化问题，其目标是在给定的一组城市和每对城市之间的距离，找到一条经过每个城市一次且回到起点的最短路径。该问题属于 NP 难问题，没有多项式时间算法可以解决。

下面是一个用Java代码实现TSP的例子，采用了遗传算法来求解：

import java.util.Arrays;
import java.util.Random;

public class TSP {

    // 城市数量
    private static final int CITY_NUM = 20;

    // 迭代次数
    private static final int MAX_ITERATION = 1000;

    // 种群大小
    private static final int POPULATION_SIZE = 100;

    // 交叉概率
    private static final double CROSSOVER_RATE = 0.9;

    // 变异概率
    private static final double MUTATION_RATE = 0.1;

    // 交叉方式
    private static final int CROSSOVER_TYPE = 1;

    // 种群
    private int[][] population = new int[POPULATION_SIZE][CITY_NUM];

    // 适应度
    private double[] fitness = new double[POPULATION_SIZE];

    // 距离矩阵
    private double[][] distanceMatrix = new double[CITY_NUM][CITY_NUM];

    // 初始化距离矩阵
    private void initDistanceMatrix() {
        // 随机生成城市之间的距离
        Random random = new Random();
        for (int i = 0; i < CITY_NUM; i++) {
            for (int j = i; j < CITY_NUM; j++) {
                double distance = random.nextDouble() * 100;
                distanceMatrix[i][j] = distance;
                distanceMatrix[j][i] = distance;
            }
        }
    }

    // 计算一条路径的总距离
    private double calculateDistance(int[] path) {
        double distance = 0;
        for (int i = 0; i < CITY_NUM - 1; i++) {
            int city1 = path[i];
            int city2 = path[i + 1];
            distance += distanceMatrix[city1][city2];
        }
        distance += distanceMatrix[path[CITY_NUM - 1]][path[0]];
        return distance;
    }

    // 计算适应度
    private void calculateFitness() {
        double totalDistance = 0;
        for (int i = 0; i < POPULATION_SIZE; i++) {
            int[] path = population[i];
            double distance = calculateDistance(path);
            fitness[i] = 1.0 / distance;
            totalDistance += distance;
        }
        for (int i = 0; i < POPULATION_SIZE; i++) {
            fitness[i] /= totalDistance;
        }
    }

    // 选择
    private int select() {
        double r = Math.random();
        double sum = 0;
        for (int i = 0; i < POPULATION_SIZE; i++) {
            sum += fitness[i];
            if (r < sum) {
                return i;
            }
        }
        return 0;
    }

    // 交叉
    private int[] crossover(int[] parent1, int[] parent2) {
        int[] child = new int[CITY_NUM];
        if (CROSSOVER_TYPE == 1) {
            // 随机选择一个位置，将父代1的前半部分和父代2的后半部分拼接起来
            Random random = new Random();
            int pos = random.nextInt(CITY_NUM);
            for (int i = 0; i < pos; i++) {
                child[i] = parent1[i];
            }
            for (int i = pos; i < CITY_NUM; i++) {
                int city = parent2[i];
                while (contains(child, city)) {
                    city = parent2[++i % CITY_NUM];
                }
                child[i] = city;
            }
        } else if (CROSSOVER_TYPE == 2) {
            // 随机选择两个位置，将父代1这两个位置之间的城市和父代2这两个位置之间的城市交换
            Random random = new Random();
            int pos1 = random.nextInt(CITY_NUM);
            int pos2 = random.nextInt(CITY_NUM);
            if (pos2 < pos1) {
                int temp = pos1;
                pos1 = pos2;
                pos2 = temp;
            }
            for (int i = 0; i < CITY_NUM; i++) {
                if (i >= pos1 && i <= pos2) {
                    child[i] = parent2[i];
                } else {
                    int city = parent1[i];
                    while (contains(child, city)) {
                        city = parent1[++i % CITY_NUM];
                    }
                    child[i] = city;
                }
            }
        }
        return child;
    }

    // 变异
    private void mutate(int[] path) {
        Random random = new Random();
        if (random.nextDouble() < MUTATION_RATE) {
            int pos1 = random.nextInt(CITY_NUM);
            int pos2 = random.nextInt(CITY_NUM);
            int temp = path[pos1];
            path[pos1] = path[pos2];
            path[pos2] = temp;
        }
    }

    // 判断一个城市是否已经在路径中
    private boolean contains(int[] path, int city) {
        for (int i = 0; i < CITY_NUM; i++) {
            if (path[i] == city) {
                return true;
            }
        }
        return false;
    }

    // 初始化种群
    private void initPopulation() {
        for (int i = 0; i < POPULATION_SIZE; i++) {
            int[] path = new int[CITY_NUM];
            for (int j = 0; j < CITY_NUM; j++) {
                path[j] = j;
            }
            shuffle(path);
            population[i] = path;
        }
    }

    // 打乱数组顺序
    private void shuffle(int[] array) {
        Random random = new Random();
        for (int i = array.length - 1; i >= 1; i--) {
            int j = random.nextInt(i + 1);
            int temp = array[i];
            array[i] = array[j];
            array[j] = temp;
        }
    }

    // 遗传算法求解TSP
    public void solve() {
        // 初始化距离矩阵和种群
        initDistanceMatrix();
        initPopulation();

        // 迭代
        for (int iter = 0; iter < MAX_ITERATION; iter++) {
            // 计算适应度
            calculateFitness();

            // 生成下一代种群
            int[][] nextPopulation = new int[POPULATION_SIZE][CITY_NUM];
            for (int i = 0; i < POPULATION_SIZE; i++) {
                int parent1 = select();
                int parent2 = select();
                int[] child = crossover(population[parent1], population[parent2]);
                mutate(child);
                nextPopulation[i] = child;
            }
            population = nextPopulation;
        }

        // 找到最优解
        double minDistance = Double.MAX_VALUE;
        int[] bestPath = null;
        for (int i = 0; i < POPULATION_SIZE; i++) {
            double distance = calculateDistance(population[i]);
            if (distance < minDistance) {
                minDistance = distance;
                bestPath = population[i];
            }
        }

        // 输出结果
        System.out.println("最短路径长度为：" + minDistance);
        System.out.print("最短路径为：");
        for (int i = 0; i < CITY_NUM; i++) {
            System.out.print(bestPath[i] + " ");
        }
    }

    public static void main(String[] args) {
        TSP tsp = new TSP();
        tsp.solve();
    }
}