NSGA-Ⅱ求解多目标优化综合精度的研究

Study on accuracy of NSGA-Ⅱ on Multi-objective process synthesis

多目标过程综合可归结为1个多目标混合整数非线性规划(MOMINLP),主要有2大类求解技术:多目标数学规划法和以多目标遗传算法(MOGA)为代表的进化算法。MOGA能并行处理多个目标,鲁棒性强,近年来得到长足发展。但由于无法从理论上保证得到问题的真正非劣解,应用受到了一定限制。本文应用多目标遗传算法NSGA-Ⅱ对废料最少问题进行求解,得到近似非劣解集。提出1个逐步插值算法,对近似解集中的点依次进行筛选,给出了所选点的搜索目标函数的构造方法,并应用SQP法对其寻优,得到真正的非劣解。将精确解与近似解进行比较表明,NSGA-Ⅱ的求解精度较高,绝大部分近似解的最大可能误差不超过3%,可为实际工程中的初步决策提供依据。

Multi-objective process synthesis can be described as a multi-objective mixed-integer nonlinear programming（MOMINLP）which can be solved by multi-objective mathematic programming and multi-objective evolutionary algorithms such as multi-objective genetic algorithms（MOGA）. MOGA has made remarkable progress which can optimize multiple objectives in parallel and has highly robust.But MOGA cannot achieve the real non-inferior solution set by a convergence criterion that limits its application.In this paper NSGA-II is used to solve a waste minimization problem.A successive interpolation method is proposed to choose some points in approximate solution set achieved from NSGA-Ⅱand objective function is constructed to optimize in order to get the real non-inferior solutions.The maximum error of most NSGA-Ⅱsolutions is less than 3%.The results show the accuracy of NSGA-Ⅱis high enough to meet the preliminary decision needing in engineering.