Framework for Many-Objective Test Problems with Both Simple and Complicated Pareto-Set Shapes

Saxena, Dhish Kumar; Zhang, Qingfu; Duro, João A.; Tiwari, Ashutosh

doi:10.1007/978-3-642-19893-9_14

Cited by 34 publications

(19 citation statements)

References 16 publications

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“…This result is quite intriguing given the increased number of reports showing decomposition-based algorithms outperforming their Pareto-based counterparts for multi-objective problems [22,23,37,20,42]. However, we have only shown that the above equality holds for one particular trajectory and not necessarily for every possible trajectory towards any point on the Pareto front.…”

Section: Decomposition Methods For Multi-objective Problemsmentioning

confidence: 70%

Methods for multi-objective optimization: An analysis

Giagkiozis

Fleming

2015

Information Sciences

196

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Decomposition-based methods are often cited as the solution to multi-objective nonconvex optimization problems with an increased number of objectives. These methods employ a scalarizing function to reduce the multi-objective problem into a set of single objective problems, which upon solution yield a good approximation of the set of optimal solutions. This set is commonly referred to as Pareto front. In this work we explore the implications of using decomposition-based methods over Pareto-based methods on algorithm convergence from a probabilistic point of view. Namely, we investigate whether there is an advantage of using a decomposition-based method, for example using the Chebyshev scalarizing function, over Pareto-based methods. We find that, under mild conditions on the objective function, the Chebyshev scalarizing function has an almost identical effect to Paretodominance relations when we consider the probability of finding superior solutions for algorithms that follow a balanced trajectory. We propose the hypothesis that this seemingly contradicting result compared with currently available empirical evidence, signals that the disparity in performance between Pareto-based and decomposition-based methods is due to the inability of the former class of algorithms to follow a balanced trajectory. We also link generalized decomposition to the results in this work and show how to obtain optimal scalarizing functions for a given problem, subject to prior assumptions on the Pareto front geometry.

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Section: Decomposition Methods For Multi-objective Problemsmentioning

confidence: 70%

Methods for multi-objective optimization: An analysis

Giagkiozis

Fleming

2015

Information Sciences

196

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“…For this problem an algorithm with more aggressive stochastic operators would require more function evaluations compared to PSO. Problems with this structure are prevalent in evolutionary algorithm test functions, for example see , Huband et al 2006, Saxena et al 2011. For the same reasons differential evolution would have the potential to perform well in such a class of problems.…”

Section: So Why Not a Single Approach?mentioning

confidence: 99%

An overview of population-based algorithms for multi-objective optimisation

Giagkiozis

Purshouse

Fleming

2013

International Journal of Systems Science

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In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognized that population-based multi-objective optimization techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimization methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelizable and can generate an approximation of the entire Pareto front (PF) at each iteration. A critique of their capabilities is also provided.

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“…In many-objective optimization, several scalable continuous benchmark function suites, such as DTLZ [9] and WFG [10], have been commonly used. Recently, researchers have also designed/presented some problem suites specially for many-objective optimization [11][12][13][14][15][16]. However, all of these problem suites only represent one or several aspects of real-world scenarios.…”

Section: Introductionmentioning

confidence: 99%

A benchmark test suite for evolutionary many-objective optimization

Cheng

Tian

et al. 2017

Complex Intell. Syst.

401

118

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In the real world, it is not uncommon to face an optimization problem with more than three objectives. Such problems, called many-objective optimization problems (MaOPs), pose great challenges to the area of evolutionary computation. received little attention. Several test problem suites which were designed for multi-objective optimization have still been dominantly used in many-objective optimization. In this paper, we carefully select (or modify) 15 test problems with diverse properties to construct a benchmark test suite, aiming to promote the research of evolutionary many-objective optimization (EMaO) via suggesting a set of test problems with a good representation of various real-world scenarios.Also, an open-source software platform with a user-friendly GUI is provided to facilitate the experimental execution and data observation.

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Framework for Many-Objective Test Problems with Both Simple and Complicated Pareto-Set Shapes

Cited by 34 publications

References 16 publications

Methods for multi-objective optimization: An analysis

Methods for multi-objective optimization: An analysis

An overview of population-based algorithms for multi-objective optimisation

A benchmark test suite for evolutionary many-objective optimization

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