Journal of Shanghai Jiao Tong University (Science) ›› 2018, Vol. 23 ›› Issue (6): 827-833.doi: 10.1007/s12204-018-2004-z

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Rigorous Running Time Analysis of a Simple Immune-Based Multi-Objective Optimizer for Bi-Objective Pseudo-Boolean Functions

ZHOU Shiyuan (周诗源), PENG Xue (彭雪), WANG Yinglin (王英林), XIA Xiaoyun (夏小云)   

  1. (1. School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China; 2. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China; 3. Office of Budget and Finance, Jiaxing University, Jiaxing 314001, Zhejiang, China; 4. College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, China)
  • 出版日期:2018-12-01 发布日期:2018-12-07
  • 通讯作者: PENG Xue (彭雪) E-mail: pxue2008@163.com

Rigorous Running Time Analysis of a Simple Immune-Based Multi-Objective Optimizer for Bi-Objective Pseudo-Boolean Functions

ZHOU Shiyuan (周诗源), PENG Xue (彭雪), WANG Yinglin (王英林), XIA Xiaoyun (夏小云)   

  1. (1. School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China; 2. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China; 3. Office of Budget and Finance, Jiaxing University, Jiaxing 314001, Zhejiang, China; 4. College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, China)
  • Online:2018-12-01 Published:2018-12-07
  • Contact: PENG Xue (彭雪) E-mail: pxue2008@163.com

摘要: A simple immune-based multi-objective optimizer (IBMO) is proposed, and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions (Bi-Trap, Bi-Plateau and Bi-Jump) is presented. The running time of a global simple evolutionary multi-objective optimizer (GSEMO) using standard bit mutation operator with IBMO using somatic contiguous hypermutation (CHM) operator is compared with these three functions. The results show that the immune-based hypermutation can significantly beat standard bit mutation on some well-known multi-objective pseudo-Boolean functions. The proofs allow us to understand the relationship between the characteristics of the problems and the features of the algorithms more deeply. These analysis results also give us a good inspiration to analyze and design a bio-inspired search heuristics.

关键词: evolutionary algorithm , running time analysis , somatic contiguous hypermutation

Abstract: A simple immune-based multi-objective optimizer (IBMO) is proposed, and a rigorous running time analysis of IBMO on three proposed bi-objective pseudo-Boolean functions (Bi-Trap, Bi-Plateau and Bi-Jump) is presented. The running time of a global simple evolutionary multi-objective optimizer (GSEMO) using standard bit mutation operator with IBMO using somatic contiguous hypermutation (CHM) operator is compared with these three functions. The results show that the immune-based hypermutation can significantly beat standard bit mutation on some well-known multi-objective pseudo-Boolean functions. The proofs allow us to understand the relationship between the characteristics of the problems and the features of the algorithms more deeply. These analysis results also give us a good inspiration to analyze and design a bio-inspired search heuristics.

Key words: evolutionary algorithm , running time analysis , somatic contiguous hypermutation

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