基于正交设计模型的多目标进化算法

摘要

为提高多目标进化算法在求解复杂多目标问题上的收敛性和解集多样性,提出了一种基于正交设计模型的多目标进化算法.该算法在基于分解技术的多目标进化算法框架下,将正交实验设计方法同分解技术相融合.利用正交实验设计方法,有针对性地对父代个体进行重组,并生成多个保留优良基因的子代个体,避免了盲目性搜索以提高算法收敛性,并应用分解技术选择优秀个体来维持全局搜索和局部寻优的动态平衡.将该算法与目前典型的优异算法在18个标准测试函数集上进行对比测试,仿真结果表明所提算法相比另外4种算法具有良好的竞争力,在保持良好收敛性的同时,所获得的Pareto前端分布更加均匀,尤其在求解具有复杂Pareto解集的问题时,能保持较好的搜索性能.为了测试算法在求解含有约束问题的性能,将其应用于I型主梁多目标优化设计中,获得的Pareto前沿较均匀,且解集域较宽广,对比分析表明了算法的工程实用性.%Aiming to improve the convergence and diversity of multi-objective evolutionary algorithms (MOEAs) for solving complicated high dimensional multi-objective optimization problems,a multiobjective evolutionary algorithm based on orthogonal designing model (MOEA/D-OD) was proposed.Under the framework of multi-objective evolutionary algorithm with decomposition scheme as typical characteristics,the orthogonal designing model (ODM) was incorporated into decomposition mechanism.By utilizing ODM,the good genes carried by the recombinant parents were obtained by offspring to avoid blindness of searching to improve the convergence of the proposed algorithm.The decomposition mechanism was applied to selection to balance exploitation and exploration.MOEA/D-OD was compared with four state-of-the-art MOEAs on 18 benchmark testing problems.Experimental results indicated that MOEA/D-OD can obtain good convergence while having uniform distribution and wild coverage for Pareto sets.The searching performance can stay well when solving complex problems with complicated PS.To validate its performance on constraint multi-objective optimization problems,the proposed MOEA/D-OD was applied to solve the Ⅰ-beam with two conflict objectives.Compared with other algorithms,the uniformly distributed Pareto sets obtained by MOEA/D-OD showed its practicability for engineering problems,which was an effective approach for solving high dimensional and complicated multi-objective optimization problems.