基于非欧几何权向量产生策略的分解多目标优化算法  

Decomposition Multi-objective Optimizaiton Algorithm with Weight Vector Generation Strategy Based on Non-Euclidean Geometry

作　　者：孙良旭[1] 李林林[1] 刘国莉 SUN Liangxu;LI Linlin;LIU Guoli(College of Computer and Software Engineering,University of Science and Technology Liaoning,Anshan,Liaoning 114051,China;College of Mechanical Engineering,Shenyang University of Technology,Shenyang 110300,China)

机构地区：[1]辽宁科技大学计算机与软件工程学院,辽宁鞍山114051 [2]沈阳工业大学机械工程学院,沈阳110300

出　　处：《计算机科学》2024年第11期280-291,共12页Computer Science

基　　金：国家自然科学基金(61903169,71301066);辽宁省教育厅项目(2020LNQN05);辽宁省振兴人才计划(XLYC2007182)。

摘　　要：随着目标数量的增加,多目标优化问题(Multi Objective Problems,MOPs)的求解越来越困难。基于分解的多目标进化算法表现出更好的性能,但在求解具有复杂Pareto前沿的MOPs时,此类算法易出现种群多样性不足、算法性能下降等问题。为了解决这些问题,提出了一种基于非欧几何权向量产生策略的分解多目标优化算法,通过在非欧几何空间中拟合非支配前沿并进行参数估计,再利用对非支配解目标变量的正态统计采样生成权向量,以此引导种群的进化方向并保持种群的多样性。同时在非欧几何空间中周期性重新确定子问题的邻域,提高分解算法协同进化的效率,进而提高算法的性能。基于MaF基准测试函数的实验结果表明,相比MOEA/D,NSGA-Ⅲ和AR-MOEA算法,所提算法在求解多目标和众目标优化问题方面具有明显的优势。With the increase of the number of objectives,mult-objective problems(MOPs)are more and more difficult to solve.Decomposition-based multi-objective evolutionary algorithms show better performance.However,when solving MOPs with complex Pareto fronts,decomposition-based algorithms show poor diversity in population and the performance deteriorates.To address these issues,this paper proposes a decomposition multi-objective optimization algorithm with weight vector generation strategy based on non-Euclidean geometry.By fitting the non-dominated frontier in the non-Euclidean geometric space and estimating the parameters,the normal statistical sampling of the target variable of the non-dominated solution is used to generate the weight vector,so as to guide the evolution direction of the population and maintain the diversity of the population.Meanwhile,the neighborhood of sub-problems can be rebuilt periodically,to improve the efficiency of the co-evolution of decomposition algorithm and improve the performance of the algorithm.Experiment results based on the MaF benchmark test problems show that,compared with MOEA/D,NSGA-III and AR-MOEA algorithms,the proposed algorithm has significant performance in solving multi-objective optimization problems.

关 键 词：分解 多目标 权向量 非支配前沿 非欧几何 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]