中文摘要：

含有大规模变量的多目标优化问题是目前多目标进化算法领域的研究重点.多目标粒子群优化方法具有收敛性良好、计算简单和参数设置少等优点,但随着优化问题决策变量的增多,“变量维度”成为了瓶颈.针对上述问题,文中提出的变量随机分解策略,增加关联变量分配到同组的概率,使得算法更好的保留变量间的关联性,并将合作协同进化框架融合到算法中,提出了基于大规模变量分解的多目标粒子群优化算法（CCMOPSO）.将该算法在经典标准测试函数ZDT1、ZDT2、ZDT3、DTLZ1、DTLZ2变量扩展后进行仿真对比实验,采用加法二进制ε指标和超体积指标（HV）对算法收敛性和多样性进行对比分析,实验结果表明,在解决大规模变量的多目标函数中,变量维度越高,该算法比经典多目标算法MOPSO、NSGA-Ⅱ、MOEA/D以及GDE3越具有更好的多样性与收敛性,同时使得计算复杂度明显降低.

英文摘要：

The multi-obiective optimization of problems with large scale variable has become a focus in multi-objective evolutionary algorithm research field. Multi-objective particle swarm optimization algorithm is of better convergence, easier calculation and less parameter settings, yet ＂variable dimensionality＂ will be triggered as strategic variables increase. To solve the problem, this paper proposes random variable decomposition strategy, i.e. to promote the possibility of distributing associated variables into one group by random variable decomposition on the basis of variable groups, so as to realize better maintenance in association between variable groups. CCMOPSO is proposed through the integration of cooperative co-evolution evolutionary frame into the large scale variable decomposition. Comparative simulation experiment is conducted after the variable extension on typical standard functions of ZDT1, ZDT2, ZDT3, DTLZ1 and DTLZ2. Comparison between convergence and diversity of the algorithm with the binary addition index e and hyper-volume indicator （HV）, shows this algorithm is of better diversity, convergence and easiness in multi-objective function with large scale variable than MOPSO, NSGA-II, MOEA/D and GDE3, and computational complexity is decreased.