Page 150 - 《软件学报》2021年第12期

软件学报 ISSN 1000-9825, CODEN RUXUEW E-mail: jos@iscas.ac.cn
Journal of Software,2021,32(12):3814−3828 [doi: 10.13328/j.cnki.jos.006109] http://www.jos.org.cn
©中国科学院软件研究所版权所有. Tel: +86-10-62562563

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面向多目标优化的多样性代理辅助进化算法

孙哲人, 黄玉划, 陈志远

(南京航空航天大学 计算机科学与技术学院,江苏 南京 211106)
通讯作者: 孙哲人, E-mail: szheren2k@163.com

摘 要: 代理辅助进化算法(SAEA)是目前解决昂贵优化问题的一种有效途径.提出一种基于多样性的代理辅助
进化算法(DSAEA)来解决昂贵多目标优化问题.DSAEA 采用 Kriging 模型近似每个目标来代替原目标函数进行评
估,加速了进化算法的优化过程.其引入参考向量把问题分解为多个子问题,根据解与参考向量之间的角度大小建立
它们的相关性,然后计算出最小相关解集.在此基础上,候选解生成算子和选择算子会趋向于保留多样性的解.另外,
训练集 A 在每次迭代后会进行更新,根据多样性删除价值不大的样本以减少建模时间.实验部分对 DSAEA 与目前
流行的代理辅助进化算法在大规模2目标和3目标优化问题上进行对比实验.每个算法在不同的测试问题上分别独
立运行 30 次,并计算和统计反向迭代距离(IGD)、超体积(HV)和运行时间,最后使用秩和检验分析实验结果.结果表
明:DSAEA 在多数实验测试问题上表现更好,因此具有有效性和可行性.
关键词: 代理模型;进化算法;多目标优化;昂贵问题;参考向量;模型管理;Kriging
中图法分类号: TP18

中文引用格式: 孙哲人,黄玉划,陈志远.面向多目标优化的多样性代理辅助进化算法.软件学报,2021,32(12):3814−3828.
http://www.jos.org.cn/1000-9825/6109.htm
英文引用格式: Sun ZR, Huang YH, Chen ZY. Diversity based surrogate-assisted evolutionary algorithm for expensive multi-
objective optimization problem. Ruan Jian Xue Bao/Journal of Software, 2021,32(12):3814−3828 (in Chinese). http://www.jos.
org.cn/1000-9825/6109.htm

Diversity Based Surrogate-assisted Evolutionary Algorithm for Expensive Multi-objective
Optimization Problem

SUN Zhe-Ren, HUANG Yu-Hua, CHEN Zhi-Yuan

(College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China)
Abstract: The surrogate-assisted evolutionary algorithm (SAEA) is an effective way to solve expensive problems. This study proposed a
diversity-based surrogate-assisted evolutionary algorithm (DSAEA) to solve the expensive multi-objective optimization problem. DSAEA
approximates each objective with the Kriging model to replace the original objective function evaluation, accelerating the optimization
process of the evolutionary algorithm. It decomposes the problem into several subproblems with the reference vectors. The correlation
between the solution and the reference vector is established according to the angle between them. Then the minimum correlative solution
set is computed. Based on it, the candidate producing operator and the selection operator tend to preserve the solutions of diversity. In
addition, as the training set, Archive A is updated after each iteration, deleting the little value samples according to diversity to reduce the
modeling time. In the experiment section, large scale 2- and 3-objective comparative experiments for DSAEA and several current popular
SAEAs were done. Each algorithm on different test problems ran 30 times independently, and the inverted generational distance (IGD),
hypervolume (HV), and running time were calculated and collected. At last, rank sum test was used to analyze the experimental results.
The results show that DSAEA performs better on the most experimental test problems, therefore, it is effective and feasible.

∗ 基金项目: 江苏省科技支撑计划(BE2013879)
Foundation item: Science & Technology Support Plan of Jiangsu Province (BE2013879)
收稿时间: 2020-02-21; 修改时间: 2020-04-13, 2020-06-07; 采用时间: 2020-06-27