Effect of Objective Normalization and Penalty Parameter on Penalty Boundary Intersection Decomposition-Based Evolutionary Many-Objective Optimization Algorithms

An objective normalization strategy is essential in any evolutionary multiobjective or many-objective optimization (EMO or EMaO) algorithm, due to the distance calculations between objective vectors required to compute diversity and convergence of population members. For the decomposition-based EMO/...

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Bibliographic Details
Published in:Evolutionary computation Vol. 29; no. 1; p. 157
Main Authors: Chen, Lei, Deb, Kalyanmoy, Liu, Hai-Lin, Zhang, Qingfu
Format: Journal Article
Language:English
Published: United States 01.03.2021
Subjects:
many-objective optimization
Sensitivity analysis
objective normalization
evolutionary algorithm
ISSN:1530-9304, 1530-9304
Online Access:Get more information
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Summary:An objective normalization strategy is essential in any evolutionary multiobjective or many-objective optimization (EMO or EMaO) algorithm, due to the distance calculations between objective vectors required to compute diversity and convergence of population members. For the decomposition-based EMO/EMaO algorithms involving the Penalty Boundary Intersection (PBI) metric, normalization is an important matter due to the computation of two distance metrics. In this article, we make a theoretical analysis of the effect of instabilities in the normalization process on the performance of PBI-based MOEA/D and a proposed PBI-based NSGA-III procedure. Although the effect is well recognized in the literature, few theoretical studies have been done so far to understand its true nature and the choice of a suitable penalty parameter value for an arbitrary problem. The developed theoretical results have been corroborated with extensive experimental results on three to 15-objective convex and non-convex instances of DTLZ and WFG problems. The article, makes important theoretical conclusions on PBI-based decomposition algorithms derived from the study.
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ISSN:1530-9304
1530-9304
DOI:10.1162/evco_a_00276