Greedy Hypervolume Subset Selection in Low Dimensions

Guerreiro, Andreia P.; Fonseca, Carlos M.; Paquete, Luís

doi:10.1162/evco_a_00188

Cited by 43 publications

(9 citation statements)

References 19 publications

(25 reference statements)

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“…However, this type of algorithms are time-consuming due to the NP-hardness of the HSS problem [34]. Greedy algorithms [10], [36] and evolutionary algorithms [37], [38] are more efficient and practical for subset selection from large candidate solution sets. In general, greedy algorithms are more widely investigated and applied in the EMO field.…”

Section: B Subset Selection Methodsmentioning

confidence: 99%

“…However, most studies on subset selection are for environmental selection where the candidate solution set is small [15], [25], [33]. When subset selection is used as a postprocessing procedure to choose a final solution set, most studies are for two-and three-objective problems (i.e., subset selection is in low-dimensional objective spaces [8]- [10], [34]). Thus, there is a research gap on subset selection from large candidate solution sets with many objectives.…”

Section: ) Subset Selection From Large Candidate Solution Setsmentioning

confidence: 99%

“…Subset selection has been discussed in many studies in the EMO field. The most popular topic is the socalled hypervolume subset selection [8]- [10]. In this problem, a subset is selected from a candidate solution set in order to maximize the hypervolume [11] of the selected subset.…”

Section: Introductionmentioning

confidence: 99%

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Benchmarking Subset Selection from Large Candidate Solution Sets in Evolutionary Multi-objective Optimization

Shang¹,

Shu²,

Ishibuchi³

et al. 2022

Preprint

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In the evolutionary multi-objective optimization (EMO) field, the standard practice is to present the final population of an EMO algorithm as the output. However, it has been shown that the final population often includes solutions which are dominated by other solutions generated and discarded in previous generations. Recently, a new EMO framework has been proposed to solve this issue by storing all the non-dominated solutions generated during the evolution in an archive and selecting a subset of solutions from the archive as the output. The key component in this framework is the subset selection from the archive which usually stores a large number of candidate solutions. However, most studies on subset selection focus on small candidate solution sets for environmental selection. There is no benchmark test suite for large-scale subset selection. This paper aims to fill this research gap by proposing a benchmark test suite for subset selection from large candidate solution sets, and comparing some representative methods using the proposed test suite. The proposed test suite together with the benchmarking studies provides a baseline for researchers to understand, use, compare, and develop subset selection methods in the EMO field.

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Section: B Subset Selection Methodsmentioning

confidence: 99%

Section: ) Subset Selection From Large Candidate Solution Setsmentioning

confidence: 99%

See 1 more Smart Citation

Benchmarking Subset Selection from Large Candidate Solution Sets in Evolutionary Multi-objective Optimization

Shang¹,

Shu²,

Ishibuchi³

et al. 2022

Preprint

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show abstract

“…MO-GOMEA obtains an elitist archive, aimed to contain 1000 solutions. For a fair comparison to the hypervolume-based methods that obtain an approximation set of at most p solutions, we reduce the obtained elitist archive of MO-GOMEA to p solutions using greedy hypervolume subset selection (gHSS) [11], which we denote by MO-GOMEA*. As described in [18], to align MO-GOMEA with the other algorithms, we set N mo = p•N and K mo = 2p such that the overall number of solutions in the populations is the same, and all sample distributions are estimated from the same number of solutions.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Ensuring Smoothly Navigable Approximation Sets by Bézier Curve Parameterizations in Evolutionary Bi-objective Optimization

Maree

Alderliesten

Bosman

2020

Parallel Problem Solving From Nature – PPSN XVI

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The aim of bi-objective optimization is to obtain an approximation set of (near) Pareto optimal solutions. A decision maker then navigates this set to select a final desired solution, often using a visualization of the approximation front. The front provides a navigational ordering of solutions to traverse, but this ordering does not necessarily map to a smooth trajectory through decision space. This forces the decision maker to inspect the decision variables of each solution individually, potentially making navigation of the approximation set unintuitive. In this work, we aim to improve approximation set navigability by enforcing a form of smoothness or continuity between solutions in terms of their decision variables. Imposing smoothness as a restriction upon common domination-based multi-objective evolutionary algorithms is not straightforward. Therefore, we use the recently introduced uncrowded hypervolume (UHV) to reformulate the multi-objective optimization problem as a single-objective problem in which parameterized approximation sets are directly optimized. We study here the case of parameterizing approximation sets as smooth Bézier curves in decision space. We approach the resulting single-objective problem with the genepool optimal mixing evolutionary algorithm (GOMEA), and we call the resulting algorithm BezEA. We analyze the behavior of BezEA and compare it to optimization of the UHV with GOMEA as well as the domination-based multi-objective GOMEA. We show that high-quality approximation sets can be obtained with BezEA, sometimes even outperforming the domination-and UHV-based algorithms, while smoothness of the navigation trajectory through decision space is guaranteed.

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“…The hypervolume indicator also plays a prominent role as a quality indicator in the subset selection problem (see, for example, Guerreiro and Fonseca (2020)), i.e., when a subset of usually bounded cardinality is sought to represent the Pareto front. Theoretical properties as well as heuristic and exact solution approaches for subset selection problems were discussed, among many others, in Auger et al (2009Auger et al ( , 2012; Bringmann et al (2014Bringmann et al ( , 2017; Guerreiro et al (2016); Kuhn et al (2016). We particularly mention Emmerich et al (2014) for a detailed analysis of hypervolume gradients in the context of subset selection problems, a special case of which is considered in this work.…”

Section: Introductionmentioning

confidence: 99%

Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

et al. 2021

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In engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation of the probability of failure under external loads. The PDE formulation of the mechanical state equation is discretized by a finite element method on a regular grid. To solve the discretized biobjective shape optimization problem we suggest a hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints to the problem formulation. FurthIn this section, general properties of the hypervolumeermore, maximizing the dominated hypervolume supports the decision maker in identifying compromise solutions. We investigate the relation of the hypervolume scalarization to the weighted sum scalarization and to direct multiobjective descent methods. Since gradient information can be efficiently obtained by solving the adjoint equation, the scalarized problem can be solved by a gradient ascent algorithm. We evaluate our approach on a 2 D test case representing a straight joint under tensile load.

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Greedy Hypervolume Subset Selection in Low Dimensions

Cited by 43 publications

References 19 publications

Benchmarking Subset Selection from Large Candidate Solution Sets in Evolutionary Multi-objective Optimization

Benchmarking Subset Selection from Large Candidate Solution Sets in Evolutionary Multi-objective Optimization

Ensuring Smoothly Navigable Approximation Sets by Bézier Curve Parameterizations in Evolutionary Bi-objective Optimization

Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

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