Visualization and Performance Metric in Many-Objective Optimization

He, Zhenan; Yen, Gary G.

doi:10.1109/tevc.2015.2472283

Cited by 134 publications

(47 citation statements)

References 40 publications

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“…In [21], He and Yen proposed to use a polar coordinate system (PCS) to represent the approximation set. One of the major advantages of using PCS is the intrinsic dimension is two so that it is easy to interpret by the DMs.…”

Section: Visualisation Via a Transformed Coordinate Systemmentioning

confidence: 99%

“…In order to map the population from a Cartesian coordinate system to a PCS, the DMs need to have some prior knowledge of the characteristics of the PF. In [21], they only considered three cases, i.e. linear, convex and concave.…”

Section: Visualisation Via a Transformed Coordinate Systemmentioning

confidence: 99%

“…Partially similar to the second category, the last one tries to map the original data into a new coordinate system (e.g. radial coordinate visualisation [20], prosection plot [11], polar coordinate system [21]).…”

Section: Introductionmentioning

confidence: 99%

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Visualisation of Pareto Front Approximation: A Short Survey and Empirical Comparisons

Gao

Nie

2019

2019 IEEE Congress on Evolutionary Computation (CEC)

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Visualisation is an effective way to facilitate the analysis and understanding of multivariate data. In the context of multi-objective optimisation, comparing to quantitative performance metrics, visualisation is, in principle, able to provide a decision maker better insights about Pareto front approximation sets (e.g. the distribution of solutions, the geometric characteristics of Pareto front approximation) thus to facilitate the decision-making (e.g. the exploration of trade-off relationship, the knee region or region of interest). In this paper, we overview some currently prevalent visualisation techniques according to the way how data is represented. To have a better understanding of the pros and cons of different visualisation techniques, we empirically compare six representative visualisation techniques for the exploratory analysis of different Pareto front approximation sets obtained by four state-of-the-art evolutionary multi-objective optimisation algorithms on the classic DTLZ benchmark test problems. From the empirical results, we find that visual comparisons also follow the No-Free-Lunch theorem where no single visualisation technique is able to provide a comprehensive understanding of the characteristics of a Pareto front approximation set. In other words, a specific type of visualisation technique is only good at exploring a particular aspect of the data.

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Section: Visualisation Via a Transformed Coordinate Systemmentioning

confidence: 99%

Section: Visualisation Via a Transformed Coordinate Systemmentioning

confidence: 99%

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Visualisation of Pareto Front Approximation: A Short Survey and Empirical Comparisons

Gao

Nie

2019

2019 IEEE Congress on Evolutionary Computation (CEC)

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“…When the number of objectives equals or larger than four, visualization becomes a challenge. Existing approaches can be divided into three classes, namely parallel coordinate, mapping, and aggregation tree [179]. The approaches based on parallel coordinates provide the visualization of individual solutions by a parallel coordinate system.…”

Section: Visualizationmentioning

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.

126

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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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“…A second option is to show all objectives in a single graph (He & Yen, 2016;Ibrahim, Rahnamayan, Martin, & Deb, 2016M. Li, Zhen, & Yao, 2017;Pryke, Mostaghim, & Nazemi, 2007;Walker, Fieldsend, & Everson, 2012).…”

Section: Visualization In Many-objective Optimizationmentioning

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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Visualization and Performance Metric in Many-Objective Optimization

Cited by 134 publications

References 40 publications

Visualisation of Pareto Front Approximation: A Short Survey and Empirical Comparisons

Visualisation of Pareto Front Approximation: A Short Survey and Empirical Comparisons

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

An overview on evolutionary algorithms for many‐objective optimization problems

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