jMetal 多目标优化实例：NSGA-II 算法求解 ZDT1 问题

以下是一个基于 jMetal 的完整例子，用于求解多目标优化问题：

import org.uma.jmetal.algorithm.multiobjective.nsgaII.NSGAIIBuilder;
import org.uma.jmetal.operator.crossover.CrossoverOperator;
import org.uma.jmetal.operator.crossover.impl.SBXCrossover;
import org.uma.jmetal.operator.mutation.MutationOperator;
import org.uma.jmetal.operator.mutation.impl.PolynomialMutation;
import org.uma.jmetal.problem.Problem;
import org.uma.jmetal.problem.multiobjective.zdt.ZDT1;
import org.uma.jmetal.solution.DoubleSolution;
import org.uma.jmetal.util.JMetalException;
import org.uma.jmetal.util.AlgorithmRunner;
import org.uma.jmetal.util.evaluator.impl.SequentialSolutionListEvaluator;

public class NSGAIIExample {
  public static void main(String[] args) throws JMetalException {
    Problem<DoubleSolution> problem;
    problem = new ZDT1();

    CrossoverOperator<DoubleSolution> crossover;
    crossover = new SBXCrossover(0.9, 20.0);

    MutationOperator<DoubleSolution> mutation;
    mutation = new PolynomialMutation(1.0/problem.getNumberOfVariables(), 20.0);

    int populationSize = 100;

    NSGAIIBuilder<DoubleSolution> builder;
    builder = new NSGAIIBuilder<>(problem, crossover, mutation, populationSize)
            .setSelectionOperator(new BinaryTournamentSelection<>())
            .setMaxEvaluations(25000)
            .setSolutionListEvaluator(new SequentialSolutionListEvaluator<>());

    AlgorithmRunner algorithmRunner = new AlgorithmRunner.Executor(builder.build())
            .execute();

    List<DoubleSolution> solutions = algorithmRunner.getAlgorithm().getResult();
    long computingTime = algorithmRunner.getComputingTime();

    JMetalLogger.logger.info('Total execution time: ' + computingTime + 'ms');

    printSolutions(solutions);
  }

  private static void printSolutions(List<DoubleSolution> solutions) {
    for (int i = 0; i < solutions.size(); i++) {
      JMetalLogger.logger.info('Solution ' + i + ': ' + solutions.get(i).getObjective(0) + ', ' + solutions.get(i).getObjective(1));
    }
  }
}

上述代码中，我们使用了 NSGA-II 算法来解决 ZDT1 多目标优化问题。其中，我们使用了 SBX 交叉和多项式变异作为遗传算子，选择了二元锦标赛选择算子，设置了种群大小为 100，在 25000 次迭代后停止算法运行，并使用了顺序解列表估计器来评估解的质量。

最后，我们输出了所有求解得到的 Pareto 前沿解。