A $\boldsymbol{\varepsilon}$-indicator-based shuffled frog leaping algorithm for many-objective optimization problems

doi:10.21629/JSEE.2020.01.15

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (1): 142-155.doi: 10.21629/JSEE.2020.01.15

收稿日期:2018-08-13 出版日期:2020-02-20 发布日期:2020-02-25

A $\boldsymbol{\varepsilon}$-indicator-based shuffled frog leaping algorithm for many-objective optimization problems

Na WANG^1,^2,*(), Yuchao SU¹(), Xiaohong CHEN¹(), Xia LI^1,²(), Dui LIU¹()

¹ College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China
² Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, Shenzhen 518060, China

Received:2018-08-13 Online:2020-02-20 Published:2020-02-25
Contact: Na WANG E-mail:wangna@szu.edu.cn;yuchaosu@126.com;chenxh@szu.edu.cn;lixia@szu.edu.cn;liud@szu.edu.cn
About author:WANG Na was born in 1977. She received her B.S. degree in electronic engineering from Dalian Maritime University in 1998. She later took a successive postgraduate and doctoral programs of study and was conferred a Ph.D. degree on signal and information processing by Dalian Maritime University in 2003. Now she is a professor of College of Electronics and Information Engineering at Shenzhen University. Her main research interests include intelligent computing, machine learning and pattern recognition. E-mail: wangna@szu.edu.cn|SU Yuchao was born in 1992. He received his B.S. degree from Minnan Normal University, Zhang-zhou, China in 2016. He is pursuing his M.S. degree in Shenzhen University, China. His research interests include single-, multi-, and many-objective optimization, and artificial neural network. E-mail: yuchaosu@126.com|CHEN Xiaohong was born in 1977. She received her B.S. and M.S. degrees in electronic engineering and signal and information processing from Liaoning University in 2003 and 2006 respectively. She later was conferred a Ph.D. degree on signal and information processing by Shenzhen University in 2015. Her main research interests include intelligent computing, machine learning and pattern recognition. E-mail: chenxh@szu.edu.cn|LI Xia was born in 1968. She received her B.S. and M.S. degrees in electronic engineering and signal and information processing from Xidian University in 1989 and 1992 respectively. She was later conferred a Ph.D. degree in Department of Information Engineering by the Chinese University of Hong Kong in 1997. She is a director of Shenzhen Key Laboratory of Advanced Communication and Information Processing. Her research interests include intelligent computing and its applications, image processing and pattern recognition. E-mail: lixia@szu.edu.cn|LIU Dui was born in 1995. He received his B.S. degree from the College of Electronics and Information Engineering of Shenzhen University in 2017, where he is currently pursuing his M.S. degree. His main research interests include intelligent computing and machine learning. E-mail: liud@szu.edu.cn
Supported by:
the Shenzhen Innovation Technology Program(JCYJ20160422112909302);This work was supported by the Shenzhen Innovation Technology Program (JCYJ20160422112909302)

摘要/Abstract

Abstract:

Many-objective optimization problems take challenges to multi-objective evolutionary algorithms. A number of non-dominated solutions in population cause a difficult selection towards the Pareto front. To tackle this issue, a series of indicator-based multi-objective evolutionary algorithms (MOEAs) have been proposed to guide the evolution progress and shown promising performance. This paper proposes an indicator-based many-objective evolutionary algorithm called $ \boldsymbol{\varepsilon} $ -indicator-based shuffled frog leaping algorithm ($\boldsymbol{\varepsilon}$ -MaOSFLA), which adopts the shuffled frog leaping algorithm as an evolutionary strategy and a simple and effective $\boldsymbol{\varepsilon}$ -indicator as a fitness assignment scheme to press the population towards the Pareto front. Compared with four state-of-the-art MOEAs on several standard test problems with up to 50 objectives, the experimental results show that $\boldsymbol{\varepsilon}$ -MaOSFLA outperforms the competitors.

Key words: evolutionary algorithm, many-objective optimization, shuffled frog leaping algorithm (SFLA), $\boldsymbol{\varepsilon}$

. [J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 142-155.

Na WANG, Yuchao SU, Xiaohong CHEN, Xia LI, Dui LIU. A $\boldsymbol{\varepsilon}$-indicator-based shuffled frog leaping algorithm for many-objective optimization problems[J]. Journal of Systems Engineering and Electronics, 2020, 31(1): 142-155.

图/表 15

参考文献 45

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Problem	Number of variables	Geometry of PF
DTLZ1	$M$+4	Linear
DTLZ2	$M$+9	Concave
DTLZ3	$M$+9	Concave
DTLZ4	$M$ +9	Concave
DTLZ7	$M$ +9	Disconnected, mixed
WFG2	$M$ +19	Convex, disconnected
WFG3	$M$ +19	Linear, degenerate
WFG4	$M$ +19	Concave

Test problem	Reference point
DTLZ1	$(1.5, 1.5, \ldots)$
DTLZ2-4	$(2, 2, \ldots)$
DTLZ7	$(2, 2, \ldots, 2M+1)$
WFG2-4	$(3, 5, \ldots, 2M+1)$

$M$	2$\times $50	4$\times $25	5$\times $20	10$\times $10
3	7.292 8	7.388 8	7.374 8	7.364 8
5	31.566 9	31.573 6	31.512 1	31.419 6
10	1 020	1 022	1.020	1 016

$M$	$t = 0.8m$	$t = m$	$t = 1.2 m$
3	7.374 1	7.381 5	7.379 0
5	31.476 0	31.559 9	31.529 1
10	1 021	1 019	1 021

A $\boldsymbol{\varepsilon}$-indicator-based shuffled frog leaping algorithm for many-objective optimization problems

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