求解约束多目标区间优化问题的改进NSGA-Ⅱ  

Improved NSGA-Ⅱ for Constrained Multi-objective Optimization Problems with Interval Numbers

作　　者：陈志旺[1,2] 陈林[1,2] 

机构地区：[1]燕山大学工业计算机控制工程河北省重点实验室,河北秦皇岛066004 [2]燕山大学国家冷轧板带装备及工艺工程技术研究中心,河北秦皇岛066004

出　　处：《小型微型计算机系统》2014年第11期2502-2506,共5页Journal of Chinese Computer Systems

基　　金：河北省自然科学基金青年基金项目(F2014203099)资助;燕山大学青年教师自主研究计划课题项目(13LGA006)资助

摘　　要：针对约束多目标区间非线性优化问题,利用泰勒一阶展开将非线性函数转化成线性形式,降低了计算量,提出一种改进的NSGA-II(INSGA-II)解决上述线性形式的优化问题.该算法基于可能度定义了P占优支配关系,依据此关系求出解的序值,进而根据序值对解进行排序.利用区间数距离公式,求出各序值中解的区间拥挤距离(ICD),并对各序值中的解进行进一步排序.此外引入约束锦标赛准则,通过计算约束违背度并与约束允许违背度比较选择出种群中相对满足约束条件的解.本文将传统的NSGA-II改进成可以解决约束多目标区间优化问题的INSGA-II.仿真结果表明该算法的有效性.For the constrained multi-objective nonlinear optimization problems with interval numbers, firstly, in order to reduce the computational complexity,nonlinear functions of optimization problems are transformed into linear ones by using the first-order Taylor expansion, then the improved NSGA-Ⅱ（INSGA-Ⅱ）is proposed for the transformed linear optimization problems. In INSGA-Ⅱ, P dom- inance relationship is defined based on the interval possibility degree, which is applied in getting the rank values of solutions. Further- more, each solution is sorted according to its rank value. Secondly, the proposed algorithm utilizes the interval distance formula to eval- uate the interval crowding distance （ICD） of solutions of the same rank value then sorts solutions in order of their interval crowding distance. Finally, a constrained tournament rule is used to select the solutions of correspondingly satisfying constraint from the popula- tion, and the constraint violation degree of solutions are compared with the allowable constraint violation degree in the rule. In the pa- per, the traditional NSGA-Ⅱ for the certainty optimization is improved so that it can solve the constrained multi-objective optimization problems with interval numbers. The feasibility of the proposed algorithm is validated by simulation results.

关 键 词：多目标优化 约束优化 NSGA-II 区间数 可能度 区间拥挤距离 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]