Title: Analyses of inverted generational distance for many-objective optimisation algorithms

Authors: Xingjuan Cai; Maoqing Zhang; Hui Wang; Meng Xu; Jinjun Chen; Wensheng Zhang

Addresses: Complex System and Computational Intelligence Laboratory, Taiyuan University of Science and Technology, Taiyuan, Shanxi, 030024, China ' Department of Control Science and Engineering, Tongji University, Shanghai, 201804, China ' School of Information Engineering, Nanchang Institute of Technology, Nanchang, 330099, China ' Information Faculty, Beijing University of Technology, Beijing, 100124, China ' Department of Computer Science and Software Engineering, Swinburne University of Technology, Melbourne, 3000, Australia ' State Key Laboratory of Intelligent Control and Management of Complex Systems, Institute of Automation Chinese Academy of Sciences, Beijing, 100190, China

Abstract: Inverted generational distance is a widely used indicator for evaluating many-objective optimisation algorithms. In the past several years, numerous researchers have paid much attention to the improvement of many-objective optimisation algorithms, while few researchers have mathematically analysed inverted generational distance. In this paper, we present detailed mathematical analyses of inverted generational distance, and then reveal the relation between generational distance and inverted generational distance. The conclusion is drawn that convergence plays different roles in different stages. Experimental results on seven many-objective benchmark problems verify our analyses.

Keywords: inverted generational distance; IGD; generational distance; many-objective optimisation algorithm; mathematical analyses.

DOI: 10.1504/IJBIC.2019.101189

International Journal of Bio-Inspired Computation, 2019 Vol.14 No.1, pp.62 - 68

Received: 14 Jan 2019
Accepted: 15 Feb 2019
Published online: 26 Jul 2019 *

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