基于免疫优化的单目标多模态期望值规划  

Single-Objective Multi-modal Expected Value Programming Based on Immune Optimization

作　　者：杨凯[1] 张著洪[1,2] 

机构地区：[1]贵州大学计算机科学与技术学院,贵州贵阳550025 [2]贵州大学电子信息学院,贵州贵阳550025

出　　处：《西南交通大学学报》2014年第6期1061-1067,共7页Journal of Southwest Jiaotong University

基　　金：国家自然科学基金资助项目(61065010);教育部博士点基金资助项目(20125201110003)

摘　　要：为了求解未知随机变量分布下单目标多模态期望值规划,通过引入检测候选解是否为局部最优解的随机函数,将该期望值规划问题转化为多目标期望值规划问题,并进一步探寻问题的转化关系,获得在一定条件下有效解是最优解的结论;根据样本平均近似化思想,将多目标规划转化为非恒定样本采样的近似化模型,并基于克隆选择和免疫记忆的机理,通过设计递归非支配分层、样本自适应采样和自适应繁殖与变异方案,引导进化种群往优质个体所在区域转移,提出了求解该近似化模型的免疫优化算法.仿真结果表明:与参与比较的多目标优化算法相比,该算法搜索多个最优解方面有明显优势,搜索效果稳定,噪声抑制能力强;求解低、高维标准测试问题获得最优解的数量分别平均提高了20%和70%.To solve the problem of single-objective multi-modal expected value programming with unknown noisy distribution, a multi-objective immune optimization algorithm based on immune response principles was proposed. By means of a random function used for checking whether a candidate solution was a locally optimal solution, the expected value problem was converted into a multi-objective expected value programming problem. Moreover, some relations between the original problem and the transformed problem were studied, and a conclusion that an efficient solution must be an optimal solution under certain conditions was developed. Relying upon the idea of sample average approximation, the multi-objective programming was further transformed into an approximate model with variable sampling sizes. Based on the metaphors of clonal selection and immune memory, one such optimization approach was obtained to deal with the approximation model. It searched high-quality individuals toward some regions which the optimal solutions existed, depending on several main modules： recursive non-dominated sorting, adaptive sampling, adaptive proliferation, and adaptive mutation. By comparison with the multi-objective optimization algorithms, the simulation results show that the proposed algorithm with strong noise suppression can achieve averagely about a seventy percent increase in the number of optimal solutions found for the high-dimensional benchmark problem and a twenty percent increase for the low-dimensional benchmark problem; it can gain the stable search effect and has the prominent advantage in solving multiple optimal solutions.

关 键 词：随机规划 多模态期望值规划 多目标优化 免疫优化 自适应采样 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]