基于繁殖策略的求解昂贵约束单目标进化算法Apropagation Strategy based Evolutionary Optimization Algorithm for Expensive Constrained Single-objective Problem
谭瑛,张何萧,王浩,李晓波
摘要(Abstract):
实际工程优化中存在大量约束优化问题,且有一些优化问题目标函数和约束函数的评价非常耗时,导致该类问题无法直接使用传统优化算法求解。为此,为了在评价次数有限的情况下获得较好的可行解,针对昂贵单目标约束优化问题,为评价费时的目标函数和约束函数建立径向基函数(Radial Basis Function, RBF)预测模型,以及根据估值自适应选择个体的繁殖策略,以期能产生较好的可行解。在7个标准测试函数及3个工业测试函数上的测试结果表明,相比于其它现有针对昂贵约束问题的优化方法,本方法无需确保初始种群中必须有可行解,且能在优化目标和约束函数评价次数有限的情况下找到更好的解。
关键词(KeyWords): 约束优化;进化算法;径向基函数;昂贵单目标
基金项目(Foundation): 国家自然科学基金(61876123);; 山西省自然科学基金(201901D111262)
作者(Author): 谭瑛,张何萧,王浩,李晓波
参考文献(References):
- [1] ANESCU G.An adaptive penalty function method for constrained continuous optimization in populationbased meta-heuristic optimization methods [C]//Intern-ational Symposium on Symbolic and Numeric Algorithms for Scientific Computing,Timisoara,Romania,2018.
- [2] XU B,CHEN X,TAO L L.Differential evolution with adaptive trial vector generation strategy and cluste rrepl acement-based feasibility rule for constrained optimization [J].Information Sciences,2018,43(5):240-262.
- [3] RUNARSSON T P,YAO X.Stochastic ranking for constr-ained evolutionary optimization[J].IEEE Transactions on Evolutionary Computation,2000,4(3):284-294.
- [4] KUMAR V.Algorithms for constraint-satisfaction problems:a survey[J].Ai Magazine,1992,13(1):32-44.
- [5] SURRY P D,RADCLIFFE N J.The COMOGA method:constrained optimization by multi-objective genetic algorithms[J].Control & Cybernetics,1997,26(3):391-412.
- [6] WU Y,XIE Y,YING W,et al.A Partitioning Parallelization with Hybrid Migration of MOEA/D for Biobjective Optimization on Message-Passing Clusters[J].Ieice Transactions on Fundamentals of Electronics Communications & Computer Sciences,2016,E99.A(4):843-848.
- [7] ADELI H,CHENG N T.Augmented Lagrangian Genetic Algorithm for Structural Optimization[J].Journal of Aerospace Engineering,1994,7(1):104-118.
- [8] DEB K.An efficient constraint handling method for genetic algorithms[J].Computer Methods in Applied Mechanics & Engineering,2000,186(2-4):311-338.
- [9] CHOON O H,HOONG L C,HUEY T S.A functional approximation comparison between neural networks and polynomial regression[J].WS-EAS Transactions on Mathematics,2008,7(6):353-363.
- [10] REGIS R G.Multi-objective constrained black-box optimization using radial basis function surrogates[J].Journal of Computational Science,2016,16:140-155.
- [11] SéBASTIEN V,MARREL D,Amandine.Gaussian process regression with linear inequality constraints[J].Reliability Engineering and System Safety,2020,195:106732-106749.
- [12] 叶年辉,龙腾,武宇飞,等.基于Kriging代理模型的约束差分进化算法[J].航空学报,2021,42(6):581-593.
- [13] 高鸽,孙超利,曾建潮.约束函数估值策略辅助的微粒群算法[J].太原科技大学学报,2014,35(4):246-252.
- [14] JIAO R W,ZENG S Y,LI C H,etal.A complete expected improvement criterion for Gaussian process assisted highly constrained expensive optimization[J].Information Sciences,2019,471:80-96.
- [15] 张坚,李国成.解决约束伪凸优化问题的神经网络模型[J].北京信息科技大学学报,2021,36(3):24-33.
- [16] GARG H.A hybrid GSA-GA algorithm for constrained optimization problems[J].Information Sciences,2019,478:499-523.