Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-Indicator

Bringmann, Karl; Friedrich, Tobias; Klitzke, Patrick

doi:10.1007/978-3-319-10762-2_51

Cited by 44 publications

(24 citation statements)

References 22 publications

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“…In some studies [34]- [36], an unbounded external archive was used to evaluate existing EMO algorithms. In Bringmann et al [34], it was demonstrated that the performance of EMO algorithms was improved by solution selection where a pre-specified number of solutions were selected from stored non-dominated solutions. Their computational experiments were performed only for two-objective problems due to high computational complexity of indicator-based solution selection.…”

Section: Proposed Emo Frameworkmentioning

confidence: 99%

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A New Framework of Evolutionary Multi-Objective Algorithms with an Unbounded External Archive

Ishibuchi¹,

Pang²,

Shang³

2020

Preprint

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This paper proposes a new framework for the design of evolutionary multi-objective optimization (EMO) algorithms. The main characteristic feature of the proposed framework is that the optimization result of an EMO algorithm is not the final population but a subset of the examined solutions during its execution. As a post-processing procedure, a pre-specified number of solutions are selected from an unbounded external archive where all the examined solutions are stored. In the proposed framework, the final population does not have to be a good solution set. The point of the algorithm design is to examine a wide variety of solutions over the entire Pareto front and to select well-distributed solutions from the archive. In this paper, first we explain difficulties in the design of EMO algorithms in the existing two frameworks: non-elitist and elitist. Next, we propose the new framework of EMO algorithms. Then we demonstrate advantages of the proposed framework over the existing ones through computational experiments. Finally we suggest some interesting and promising future research topics.

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Section: Proposed Emo Frameworkmentioning

confidence: 99%

“…Whereas an unbounded external archive was used in [34]- [36] for continuous multi-objective optimization, its purpose was for performance evaluation/comparison of existing EMO algorithms. In this paper, we propose the use of an unbounded external archive for the design of new EMO algorithms.…”

Section: Proposed Emo Frameworkmentioning

confidence: 99%

A New Framework of Evolutionary Multi-Objective Algorithms with an Unbounded External Archive

Ishibuchi¹,

Pang²,

Shang³

2020

Preprint

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“…Obviously, the obtained archive cardinality can be large, and a possible post-processing procedure can actually compute a subset of a limited size maximizing an indicator-value, which corresponds to an ISSP. Its has been shown in [9] that such a post-processing phase allows for a significant improvement compared against the final population obtained by the corresponding EMO algorithm, without any overhead in terms of function evaluations.…”

Section: Examplementioning

confidence: 99%

“…In addition, the corresponding indicator-based subset selection problem relevantly arises when a post-processing phase has to be designed, after a multiobjective optimizer had gathered a whole set of solutions from which one has to choose only a subset. In such a scenario, the goal is to select the best representative subset from all solutions recorded during the search process [9].…”

Section: Introductionmentioning

confidence: 99%

Experiments on Greedy and Local Search Heuristics for d dimensional Hypervolume Subset Selection

Basseur

Derbel

Goëffon

et al. 2016

Proceedings of the Genetic and Evolutionary Computation Conference 2016

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Subset selection constitutes an important stage of any evolutionary multiobjective optimization algorithm when truncating the current approximation set for the next iteration. This appears to be particularly challenging when the number of solutions to be removed is large, and when the approximation set contains many mutually non-dominating solutions. In particular, indicator-based strategies have been intensively used in recent years for that purpose. However, most solutions for the indicator-based subset selection problem are based on a very simple greedy backward elimination strategy. In this paper, we experiment additional heuristics that include a greedy forward selection and a greedy sequential insertion policies, a first-improvement hill-climbing local search, as well as combinations of those. We evaluate the effectiveness and the efficiency of such heuristics in order to maximize the enclosed hypervolume indicator of candidate subsets during a hypothetical evolutionary process, or as a post-processing phase. Our experimental analysis, conducted on randomly generated as well as structured two-, three-and four-objective mutually non-dominated sets, allows us to appreciate the benefit of these approaches in terms of quality, and to highlight some practical limitations and open challenges in terms of computational resources.

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“…In [25], [26], exact optimization algorithms were examined to find the best solution subset with respect to the hypervolume. A two-objective solution selection problem was formulated in [27], [28] where the hypervolume is maximized and the number of selected solutions is minimized.…”

Section: Solution Selectionmentioning

confidence: 99%

Comparing solution sets of different size in evolutionary many-objective optimization

Ishibuchi

Masuda

Nojima

2015

2015 IEEE Congress on Evolutionary Computation (CEC)

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When the performance of different evolutionary multiobjective optimization (EMO) algorithms is compared, the same population size is usually used for all EMO algorithms in computer simulations. This setting is to obtain a solution set of the same size from a different algorithm. However, in general, each algorithm may have its own best parameter specifications for each test problem. Thus, it may be difficult to appropriately specify the same population size for all algorithms for their fair comparison. A different algorithm may be evaluated as being the best for a different specification of the population size. An alternative setting is to allow each algorithm to use its own best population size. In this setting, a solution set of different size is obtained from each algorithm. It may be difficult to perform fair comparison using solution sets of different size. In this paper, we discuss the difficulty in comparing EMO algorithms under these two settings of the population size: the same specification for all algorithms and a different specification for each algorithm. First, we discuss the effect of the number of non-dominated solutions on some performance indicators. Next we show the difficulty in the first setting: Performance of each algorithm depends on the population size. Then we discuss the difficulty in the second setting: The size of a solution set obtained by each algorithm is not the same. In this setting, we examine the use of solution selection as a post-processing procedure to choose the same number of solutions from each solution set of different size. The selected solutions are used for performance comparison.

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Generic Postprocessing via Subset Selection for Hypervolume and Epsilon-Indicator

Cited by 44 publications

References 22 publications

A New Framework of Evolutionary Multi-Objective Algorithms with an Unbounded External Archive

A New Framework of Evolutionary Multi-Objective Algorithms with an Unbounded External Archive

Experiments on Greedy and Local Search Heuristics for d dimensional Hypervolume Subset Selection

Comparing solution sets of different size in evolutionary many-objective optimization

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