为了更加有效解决多目标优化问题,提出了一种基于差分变异和扰动变异相结合的多目标克隆选择算法(MCSA-MDD).该算法对非支配抗体进行克隆操作,从而有利于向着理想Pareto前端搜索;采用差分变异与扰动变异相结合的方式来进行免疫基因操作,有利于解的多样性.数值实验分为两组,一组选取4个常用测试函数并与其它五个多目标算法进行比较,数值实验结果表明了MCSA-MDD算法的有效性.另一组仅用差分变异和扰动变异的多目标免疫克隆算法进行比较,数值实验结果验证了采用差分变异与扰动变异相结合的免疫操作提高了算法的性能.

In this note,a kind of generalized strongly convex set-valued mappings,termed h-strongly convex set-valued mappings,are introduced in real normed spaces.Then,by employing R(a)dstr(o)m cancellation law,some basic properties of h-strongly convex set-valued mappings are proposed.Finally,a characterization of inner product spaces involving the h-strongly convex set-valued mapping is presented.

This paper investigates the optimality conditions of approximate solutions in set-valued optimization problems involving generalized cone-preinvexity by utilizing contingent epiderivative.Firstly,the concept of cone-subpreinvex set-valued mapping is presented.Then,the two properties of cone-subpreinvex set-valued mapping are obtained.Finally,under the assumption of cone-subpreinvexity,the sufficient optimality conditions are established for weak approximate efficient and strong approximate minimizer elements,respectively.