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遗传算法组卷系统实现（Java版）

news 2025/5/11 6:15:25

遗传算法组卷系统实现（Java版）

下面是一个完整的遗传算法组卷系统的Java实现，包含题目表示、适应度计算、选择、交叉和变异等核心操作。

1. 核心类设计

1.1 题目实体类（Question.java）

public class Question {private String id;private String content;private String type; // 题型：单选、多选、填空等private double difficulty; // 难度系数 0-1private double score; // 题目分值private String knowledgePoint; // 知识点// 构造函数、getter和setter省略...
}

1.2 试卷个体类（Paper.java）
import java.util.List;

public class Paper {
private List questions;
private double fitness; // 适应度

public Paper(List<Question> questionPool, int questionCount) {// 随机初始化试卷Collections.shuffle(questionPool);this.questions = new ArrayList<>(questionPool.subList(0, questionCount));this.fitness = 0;
}public Paper(List<Question> questions) {this.questions = questions;this.fitness = 0;
}// 计算试卷总分
public double getTotalScore() {return questions.stream().mapToDouble(Question::getScore).sum();
}// 计算试卷平均难度
public double getAverageDifficulty() {return questions.stream().mapToDouble(Question::getDifficulty).average().orElse(0);
}// getter和setter...

}

1.3 组卷规则类（PaperRule.java）

public class PaperRule {private double totalScore; // 试卷总分private double difficulty; // 期望难度private int questionCount; // 题目数量private Map<String, Integer> typeDistribution; // 题型分布private Map<String, Integer> knowledgeDistribution; // 知识点分布// 构造函数、getter和setter...
}

2. 遗传算法核心实现

2.1 遗传算法主类（GAExamPaper.java）

import java.util.*;public class GAExamPaper {private List<Question> questionPool; // 题库private PaperRule rule; // 组卷规则private int populationSize; // 种群大小private double crossoverRate; // 交叉概率private double mutationRate; // 变异概率private int maxGeneration; // 最大迭代次数private List<Paper> population; // 种群public GAExamPaper(List<Question> questionPool, PaperRule rule, int populationSize, double crossoverRate, double mutationRate, int maxGeneration) {this.questionPool = questionPool;this.rule = rule;this.populationSize = populationSize;this.crossoverRate = crossoverRate;this.mutationRate = mutationRate;this.maxGeneration = maxGeneration;initPopulation();}// 初始化种群private void initPopulation() {population = new ArrayList<>();for (int i = 0; i < populationSize; i++) {population.add(new Paper(questionPool, rule.getQuestionCount()));}}// 运行遗传算法public Paper evolve() {for (int generation = 0; generation < maxGeneration; generation++) {// 计算适应度calculateFitnessForAll();// 选择List<Paper> newPopulation = selection();// 交叉crossover(newPopulation);// 变异mutation(newPopulation);// 更新种群population = newPopulation;// 输出当前最优解Paper best = getBestPaper();System.out.printf("Generation %d: Best Fitness=%.4f%n", generation, best.getFitness());// 提前终止条件if (best.getFitness() >= 0.95) {break;}}return getBestPaper();}// 计算所有个体的适应度private void calculateFitnessForAll() {for (Paper paper : population) {paper.setFitness(calculateFitness(paper));}}// 计算单个个体的适应度private double calculateFitness(Paper paper) {// 1. 总分差异（越小越好）double scoreDiff = Math.abs(paper.getTotalScore() - rule.getTotalScore());double scoreFitness = 1 - scoreDiff / rule.getTotalScore();// 2. 难度差异（越小越好）double difficultyDiff = Math.abs(paper.getAverageDifficulty() - rule.getDifficulty());double difficultyFitness = 1 - difficultyDiff;// 3. 题型分布符合度double typeFitness = calculateTypeFitness(paper);// 4. 知识点分布符合度double knowledgeFitness = calculateKnowledgeFitness(paper);// 综合适应度（权重可根据需要调整）return 0.3 * scoreFitness + 0.2 * difficultyFitness + 0.25 * typeFitness + 0.25 * knowledgeFitness;}// 计算题型分布适应度private double calculateTypeFitness(Paper paper) {Map<String, Integer> actualCount = new HashMap<>();for (Question q : paper.getQuestions()) {actualCount.merge(q.getType(), 1, Integer::sum);}double fitness = 0;for (Map.Entry<String, Integer> entry : rule.getTypeDistribution().entrySet()) {int expected = entry.getValue();int actual = actualCount.getOrDefault(entry.getKey(), 0);fitness += 1 - (double) Math.abs(expected - actual) / expected;}return fitness / rule.getTypeDistribution().size();}// 计算知识点分布适应度private double calculateKnowledgeFitness(Paper paper) {// 类似题型分布的计算方法// ...}// 选择操作（轮盘赌选择）private List<Paper> selection() {List<Paper> newPopulation = new ArrayList<>();// 计算总适应度double totalFitness = population.stream().mapToDouble(Paper::getFitness).sum();// 轮盘赌选择for (int i = 0; i < populationSize; i++) {double slice = Math.random() * totalFitness;double sum = 0;for (Paper paper : population) {sum += paper.getFitness();if (sum >= slice) {newPopulation.add(new Paper(new ArrayList<>(paper.getQuestions())));break;}}}return newPopulation;}// 交叉操作（单点交叉）private void crossover(List<Paper> newPopulation) {for (int i = 0; i < newPopulation.size() - 1; i += 2) {if (Math.random() < crossoverRate) {Paper parent1 = newPopulation.get(i);Paper parent2 = newPopulation.get(i + 1);// 随机选择交叉点int crossoverPoint = (int) (Math.random() * parent1.getQuestions().size());// 执行交叉List<Question> child1Questions = new ArrayList<>();child1Questions.addAll(parent1.getQuestions().subList(0, crossoverPoint));child1Questions.addAll(parent2.getQuestions().subList(crossoverPoint, parent2.getQuestions().size()));List<Question> child2Questions = new ArrayList<>();child2Questions.addAll(parent2.getQuestions().subList(0, crossoverPoint));child2Questions.addAll(parent1.getQuestions().subList(crossoverPoint, parent1.getQuestions().size()));// 替换原个体newPopulation.set(i, new Paper(child1Questions));newPopulation.set(i + 1, new Paper(child2Questions));}}}// 变异操作private void mutation(List<Paper> newPopulation) {for (Paper paper : newPopulation) {if (Math.random() < mutationRate) {// 随机选择变异位置int mutationPos = (int) (Math.random() * paper.getQuestions().size());// 从题库中随机选择一道不同的题目替换Question oldQuestion = paper.getQuestions().get(mutationPos);Question newQuestion;do {newQuestion = questionPool.get((int) (Math.random() * questionPool.size()));} while (newQuestion.equals(oldQuestion));paper.getQuestions().set(mutationPos, newQuestion);}}}// 获取当前种群中最优个体private Paper getBestPaper() {return Collections.max(population, Comparator.comparingDouble(Paper::getFitness));}
}

3. 使用示例

public class Main {public static void main(String[] args) {// 1. 准备题库List<Question> questionPool = prepareQuestionPool();// 2. 设置组卷规则PaperRule rule = new PaperRule();rule.setTotalScore(100);rule.setDifficulty(0.6);rule.setQuestionCount(50);Map<String, Integer> typeDistribution = new HashMap<>();typeDistribution.put("单选", 30);typeDistribution.put("多选", 10);typeDistribution.put("填空", 10);rule.setTypeDistribution(typeDistribution);// 3. 创建遗传算法组卷实例GAExamPaper ga = new GAExamPaper(questionPool, rule, 100, 0.8, 0.1, 200);// 4. 执行组卷Paper bestPaper = ga.evolve();// 5. 输出结果System.out.println("最佳试卷：");System.out.println("总分：" + bestPaper.getTotalScore());System.out.println("平均难度：" + bestPaper.getAverageDifficulty());System.out.println("适应度：" + bestPaper.getFitness());}private static List<Question> prepareQuestionPool() {// 这里应该从数据库或文件加载题目List<Question> questions = new ArrayList<>();// 添加各种题目...return questions;}
}