Abstract: A Multi-objective Estimation of Distribution Algorithm with Pareto neighborhood crossover operation （MEDAP） is proposed to solve multi-objective optimization problems.Compared to the sampling method of generating population in original EDA，MEDAP employs the sampling method and Pareto neighborhood crossover operation to generate new population.A scaling factor used to balance contributions of sampling and crossover can be adjusted in on-line manner using a simulated annealing method.The offspring population is generated by the selection strategy of NSGA-II.Numerical experiments are done in two groups，one compares with NSGA-II，SPEA2 and MOPSO on eight benchmark problems.The simulation results show the effectiveness of the proposed MEDAP algorithm.The other one compares with the basic multi-objective estimation of distribution algorithm.The numerical results verify that the Pareto neighborhood crossover operation improves the performance of algorithm.

Key words: multi-objective optimization, estimation of distribution, sampling method, Pareto neighborhood crossover operation, simulated annealing

摘要： 将分布估计算法用于多目标优化问题，提出一种融合Pareto邻域交叉算子的多目标分布估计算法（MEDAP）。与一般分布估计算法只通过采样方法产生新种群不同，MEDAP算法利用采样和交叉相结合的方法产生新种群，并通过模拟退火技术在线调节尺度因子，以此来控制采样和交叉的贡献量，根据NSGA-II的选择策略选出下一代进化种群。数值实验分为两组，一组选取8个常用测试函数并与NSGA-II、SPEA2、MOPSO三个多目标算法进行比较，数值实验结果表明了MEDAP算法的有效性。另一组与不加Pareto邻域交叉算子的多目标分布估计算法进行比较，数值实验结果验证了Pareto邻域交叉算子的加入提高了算法的性能。

关键词: 多目标优化, 分布估计, 采样方法, Pareto邻域交叉算子, 模拟退火