On the effect of normalization in MOEA/D for multi-objective and many-objective optimization

Ishibuchi, Hisao; Doi, Ken; Nojima, Yusuke

doi:10.1007/s40747-017-0061-9

Cited by 63 publications

(18 citation statements)

References 28 publications

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“…Due to the inaccuracy in ideal and nadir point estimation and their changing values from generation to generation, population members are not properly associated with its right decomposition vector and any distance computation along or orthogonal to 158 Evolutionary Computation Volume 29, Number 1 decomposition vectors (needed in PBI-based methods) becomes erroneous introducing noise in the selection operation of an EMO algorithm. This phenomenon was noticed by some researchers and experimental studies have been conducted to examine the effect of objective normalization on the performance of MOEA/D (Ishibuchi et al, 2017). In this article, we estimate the sensitivity of association and distances of population members to specific decomposition vectors due to the variation of estimated ideal and nadir vectors (z 0 and z 1 ) with generations.…”

Section: Introductionmentioning

confidence: 95%

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

Chen

Deb

Liu

et al. 2021

Evolutionary Computation

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An objective normalization strategy is essential in any evolutionary multi- or manyobjective 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 paper, we make a theoretical analysis of the effect of instabilities in the normalization process on the performance of PBIbased 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 paper makes important theoretical conclusions on PBI-based decomposition algorithms derived from the study.

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Section: Introductionmentioning

confidence: 95%

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

Chen

Deb

Liu

et al. 2021

Evolutionary Computation

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“…The first category is motivated to deal with scaled objectives by normalizing the objective values. For MOEAs in this category, the objective values of all the candidate solutions in the population are usually normalized according to the intercept of each axis and the hyperplane constructed by the extreme solutions [26]. NSGA-III [9], I-DBEA [27] and θ-DEA [28], which show consistent performance on MOPs with badly-scaled PFs, are three representative MOEAs belonging to this category.…”

Section: A Moeas For Enhancing the Performance Consistency In Solvinmentioning

confidence: 99%

Guiding Evolutionary Multiobjective Optimization With Generic Front Modeling

Tian

Zhang

Cheng

et al. 2020

IEEE Trans. Cybern.

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In evolutionary multi-objective optimization, the Pareto front is approximated using a set of representative candidate solutions with good convergence and diversity. However, most existing multi-objective evolutionary algorithms have general difficulty in the approximation of Pareto fronts with complicated geometries. To address this issue, we propose a generic front modeling method for evolutionary multi-objective optimization, where the shape of the nondominated front is estimated by training a generalized simplex model. On the basis of the estimated front, we further develop a multi-objective evolutionary algorithm, where both the mating selection and environmental selection are driven by the approximate non-dominated fronts modeled during the optimization process. For performance assessment, the proposed algorithm is compared with several state-of-the-art evolutionary algorithms on a wide range of benchmark problems with various types of Pareto fronts and different numbers of objectives. Experimental results demonstrate that the proposed algorithm performs consistently on a variety of multi-objective optimization problems. Index Terms-Evolutionary algorithm, multi-and manyobjective optimization, front modeling, fitness function I. INTRODUCTION M ULTI-objective optimization problems (MOPs) often involve two or more conflicting objectives to be optimized simultaneously, which widely exist in real-world applications [1], [2]. When the number of objectives is larger than three, MOPs are also known as many-objective optimization problems (MaOPs) [3]. Since there does not exist a single solution that optimizes Manuscript received- .

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“…Besides the number of objectives and their interrelations, experiments show (Ishibuchi, Doi, & Nojima, 2017) that when each objective has a different range of objective values, some MOEAs specially designed to deal with MaOPs may not obtain the desired performance; therefore, objective normalization is needed. Unfortunately, there is a lack of an effective and robust normalization method for MaOP, and consequently, it is still an open research area (Ishibuchi, Doi, & Nojima, 2017). Moreover, observations suggest that the influence in performance of the normalization is strongly problem dependent (Ishibuchi, Doi, & Nojima, 2017).…”

Section: Search Difficulties In Many Objectivementioning

confidence: 99%

“…Unfortunately, there is a lack of an effective and robust normalization method for MaOP, and consequently, it is still an open research area (Ishibuchi, Doi, & Nojima, 2017). Moreover, observations suggest that the influence in performance of the normalization is strongly problem dependent (Ishibuchi, Doi, & Nojima, 2017).…”

Section: Search Difficulties In Many Objectivementioning

confidence: 99%

An overview on evolutionary algorithms for many‐objective optimization problems

Lücken

Brizuela

Barán

2018

WIREs Data Min & Knowl

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Multiobjective evolutionary algorithms (MOEAs) effectively solve several complex optimization problems with two or three objectives. However, when they are applied to many‐objective optimization, that is, when more than three criteria are simultaneously considered, the performance of most MOEAs is severely affected. Several alternatives have been reported to reproduce the same performance level that MOEAs have achieved in problems with up to three objectives when considering problems with higher dimensions. This work briefly reviews the main search difficulties, visualization, evaluation of algorithms, and new procedures in many‐objective optimization using evolutionary methods. Approaches for the development of evolutionary many‐objective algorithms are classified into: (a) based on preference relations, (b) aggregation‐based, (c) decomposition‐based, (d) indicator‐based, and (e) based on dimensionality reduction. The analysis of the reviewed works indicates the promising future of such methods, especially decomposition‐based approaches; however, much still need to be done to develop more robust, faster, and predictable evolutionary many‐objective algorithms. This article is categorized under: Technologies > Computational Intelligence

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On the effect of normalization in MOEA/D for multi-objective and many-objective optimization

Cited by 63 publications

References 28 publications

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

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

Guiding Evolutionary Multiobjective Optimization With Generic Front Modeling

An overview on evolutionary algorithms for many‐objective optimization problems

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