Hypervolume approximation using achievement scalarizing functions for evolutionary many-objective optimization

Ishibuchi, Hisao; Tsukamoto, Noritaka; Sakane, Yuji; Nojima, Yusuke

doi:10.1109/cec.2009.4982991

Cited by 37 publications

(13 citation statements)

References 35 publications

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“…To increase the robustness of the preference-based MOEAs to DMs, the light beam is used [127] to replace the reference point in the achievement scalarizing function [128]. Moreover, the achievement scalarizing function has been employed to approximate hypervolume [34,129,130]. Based on ASF, an interactive MOEA termed I-SIBEA [131] is proposed by selecting new solutions according to a weighted hypervolume.…”

Section: Evolutionary Preference-based Optimization Methodsmentioning

confidence: 99%

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

Wang

Olhofer

Jin

2017

Complex Intell. Syst.

128

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Evolutionary multi-objective optimization aims to provide a representative subset of the Pareto front to decision makers. In practice, however, decision makers are usually interested in only a particular part of the Pareto front of the multi-objective optimization problem. This is particularly true when the number of objectives becomes large. Over the past decade, preference-based multi-objective optimization has attracted increasing attention from both academia and industry due to its significance in both theory and practice. Significant progress has been made in evolutionary multiobjective optimization and multi-criteria decision communities, although many open issues still remain to be addressed. This paper provides a concise review on preference-based multi-objective optimization, including various preference modeling methods and existing preference-based optimization methods, as well as a brief discussion of the main future challenges.

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Section: Evolutionary Preference-based Optimization Methodsmentioning

confidence: 99%

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

Wang

Olhofer

Jin

2017

Complex Intell. Syst.

128

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“…Suppose a line follows the direction λ, passes through r * and intersects with the attainment surface of the solution set A at p, then the length of the line segment with the end points r * and p is determined by min a∈A g 2tch (a|λ, r * ) . R 2tch The idea of using different line segments starting from a reference point to the attainment surface of the solution sets for the hypervolume approximation was firstly proposed in [10] as shown in Fig. 2 (b).…”

Section: B R2 Indicator For Hypervolume Approximationmentioning

confidence: 99%

“…Whereas several fast hypervolume calculation methods [2], [3], [4], [5] have been proposed, it has been proved that the exact hypervolume calculation is #P-hard in the number of dimensions [6]. Therefore, efforts in the hypervolume approximation have been done to increase the applicability of the hypervolume to high-dimensional spaces, including the Monte Carlo sampling method [7], [8], [9] and the achievement scalarizing function method [10], [11].…”

Section: Introductionmentioning

confidence: 99%

R2-Based Hypervolume Contribution Approximation

Shang

Ishibuchi

2020

IEEE Trans. Evol. Computat.

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In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use.

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“…Several works [129][130][131][132]126,127] propose exact-andapproximate techniques to calculate the hyper-volume. In this work we consider the exact approach proposed by Auger et al [129].…”

Section: Performance Measuresmentioning

confidence: 99%

Multi-objective routing and wavelength converter allocation under uncertain traffic

Pinto-Roa¹,

Brizuela

Barán³

2015

Optical Switching and Networking

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Hypervolume approximation using achievement scalarizing functions for evolutionary many-objective optimization

Cited by 37 publications

References 35 publications

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

A mini-review on preference modeling and articulation in multi-objective optimization: current status and challenges

R2-Based Hypervolume Contribution Approximation

Multi-objective routing and wavelength converter allocation under uncertain traffic

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