用java实现多目标算法代码加注释

以下是使用Java实现多目标遗传算法的代码，已经加上了注释，希望能够帮助你理解实现过程。

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

public class MultiObjectiveGA {
    // 定义目标向量，此处为2维
    private static final int NUM_OBJECTIVES = 2;
    // 定义种群大小
    private static final int POPULATION_SIZE = 100;
    // 定义交叉率
    private static final double CROSSOVER_RATE = 0.8;
    // 定义变异率
    private static final double MUTATION_RATE = 0.01;
    // 定义最大迭代次数
    private static final int MAX_ITERATIONS = 100;

    // 定义个体类
    private static class Individual {
        // 保存个体的解向量
        private int[] solution;
        // 保存个体的目标向量
        private double[] objectives;
        // 保存个体的适应度值
        private double fitness;

        // 构造函数，初始化解向量
        public Individual(int[] solution) {
            this.solution = solution;
            this.objectives = new double[NUM_OBJECTIVES];
            this.fitness = 0.0;
        }

        // 计算个体的目标向量
        public void evaluate() {
            // 计算目标函数1的值
            objectives[0] = 0.0;
            for (int i = 0; i < solution.length; i++) {
                objectives[0] += Math.pow(solution[i], 2.0);
            }
            // 计算目标函数2的值
            objectives[1] = 0.0;
            for (int i = 0; i < solution.length; i++) {
                objectives[1] += Math.pow(solution[i] - 2.0, 2.0);
            }
        }

        // 获取个体的解向量
        public int[] getSolution() {
            return solution;
        }

        // 获取个体的目标向量
        public double[] getObjectives() {
            return objectives;
        }

        // 设置个体的适应度值
        public void setFitness(double fitness) {
            this.fitness = fitness;
        }

        // 获取个体的适应度值
        public double getFitness() {
            return fitness;
        }
    }

    // 定义种群类
    private static class Population {
        // 保存种群所有个体
        private List<Individual> individuals;

        // 构造函数，初始化种群
        public Population() {
            this.individuals = new ArrayList<>();
            for (int i = 0; i < POPULATION_SIZE; i++) {
                int[] solution = new int[NUM_OBJECTIVES];
                Random rand = new Random();
                for (int j = 0; j < NUM_OBJECTIVES; j++) {
                    solution[j] = rand.nextInt(10);
                }
                Individual individual = new Individual(solution);
                individuals.add(individual);
            }
        }

        // 计算种群所有个体的目标向量和适应度值
        public void evaluate() {
            for (Individual individual : individuals) {
                individual.evaluate();
            }
            // 计算参考解集
            List<Individual> referenceSet = nonDominatedSort(individuals);
            // 计算每个个体的适应度值
            for (Individual individual : individuals) {
                int dominatedCount = countDominated(individual, referenceSet);
                individual.setFitness(dominatedCount + 1);
            }
        }

        // 选择算子，采用多目标锦标赛选择
        public Individual selection() {
            Random rand = new Random();
            Individual bestIndividual = null;
            for (int i = 0; i < 2; i++) {
                int index = rand.nextInt(individuals.size());
                Individual individual = individuals.get(index);
                if (bestIndividual == null || individual.getFitness() < bestIndividual.getFitness()) {
                    bestIndividual = individual;
                }
            }
            return bestIndividual;
        }

        // 交叉算子，采用单点交叉
        public void crossover(Individual parent1, Individual parent2) {
            Random rand = new Random();
            if (rand.nextDouble() < CROSSOVER_RATE) {
                int index = rand.nextInt(NUM_OBJECTIVES);
                for (int i = index; i < NUM_OBJECTIVES; i++) {
                    int temp = parent1.getSolution()[i];
                    parent1.getSolution()[i] = parent2.getSolution()[i];
                    parent2.getSolution()[i] = temp;
                }
            }
        }

        // 变异算子，采用随机变异
        public void mutation(Individual individual) {
            Random rand = new Random();
            if (rand.nextDouble() < MUTATION_RATE) {
                int index = rand.nextInt(NUM_OBJECTIVES);
                individual.getSolution()[index] = rand.nextInt(10);
            }
        }

        // 计算参考解集
        private List<Individual> nonDominatedSort(List<Individual> individuals) {
            List<Individual> referenceSet = new ArrayList<>();
            List<List<Individual>> fronts = new ArrayList<>();
            // 初始化第一层
            fronts.add(new ArrayList<>());
            for (Individual individual : individuals) {
                individual.setFitness(0.0);
                individual.setFitness(0.0);
                individual.setFitness(0);
                for (Individual other : individuals) {
                    if (individual == other) {
                        continue;
                    }
                    if (dominates(individual, other)) {
                        individual.getDominatedSet().add(other);
                    } else if (dominates(other, individual)) {
                        individual.setDominatedCount(individual.getDominatedCount() + 1);
                    }
                }
                if (individual.getDominatedCount() == 0) {
                    fronts.get(0).add(individual);
                    referenceSet.add(individual);
                }
            }
            // 计算剩余层
            int i = 0;
            while (!fronts.get(i).isEmpty()) {
                List<Individual> nextFront = new ArrayList<>();
                for (Individual individual : fronts.get(i)) {
                    for (Individual dominatedIndividual : individual.getDominatedSet()) {
                        dominatedIndividual.setDominatedCount(dominatedIndividual.getDominatedCount() - 1);
                        if (dominatedIndividual.getDominatedCount() == 0) {
                            nextFront.add(dominatedIndividual);
                            referenceSet.add(dominatedIndividual);
                        }
                    }
                }
                fronts.add(nextFront);
                i++;
            }
            return referenceSet;
        }

        // 判断个体1是否支配个体2
        private boolean dominates(Individual individual1, Individual individual2) {
            double[] objectives1 = individual1.getObjectives();
            double[] objectives2 = individual2.getObjectives();
            boolean dominates = true;
            for (int i = 0; i < NUM_OBJECTIVES; i++) {
                if (objectives1[i] > objectives2[i]) {
                    dominates = false;
                    break;
                }
            }
            return dominates;
        }

        // 计算个体被多少个参考解支配
        private int countDominated(Individual individual, List<Individual> referenceSet) {
            int count = 0;
            for (Individual referenceIndividual : referenceSet) {
                if (dominates(referenceIndividual, individual)) {
                    count++;
                }
            }
            return count;
        }
    }

    public static void main(String[] args) {
        // 初始化种群
        Population population = new Population();
        // 迭代计数器
        int iteration = 0;
        // 迭代
        while (iteration < MAX_ITERATIONS) {
            // 计算种群所有个体的目标向量和适应度值
            population.evaluate();
            // 输出当前代数和当前最优解
            System.out.println("Iteration " + iteration + ": " + getBestIndividual(population).getObjectives()[0] + ", " + getBestIndividual(population).getObjectives()[1]);
            // 生成下一代种群
            Population offspringPopulation = new Population();
            for (int i = 0; i < POPULATION_SIZE; i++) {
                // 选择父代个体
                Individual parent1 = population.selection();
                Individual parent2 = population.selection();
                // 交叉
                offspringPopulation.crossover(parent1, parent2);
                // 变异
                offspringPopulation.mutation(parent1);
                offspringPopulation.mutation(parent2);
            }
            // 更新种群
            population = offspringPopulation;
            // 更新迭代计数器
            iteration++;
        }
    }

    // 获取种群中最优的个体
    private static Individual getBestIndividual(Population population) {
        Individual bestIndividual = null;
        for (Individual individual : population.individuals) {
            if (bestIndividual == null || individual.getFitness() < bestIndividual.getFitness()) {
                bestIndividual = individual;
            }
        }
        return bestIndividual;
    }
}