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Two-dimensional subset selection for hypervolume and epsilon-indicator

Published: 12 July 2014 Publication History

Abstract

The goal of bi-objective optimization is to find a small set of good compromise solutions. A common problem for bi-objective evolutionary algorithms is the following subset selection problem (SSP): Given n solutions P ⊂ R2 in the objective space, select k solutions P* from P that optimize an indicator function. In the hypervolume SSP we want to select k points P* that maximize the hypervolume indicator IHYP(P*, r) for some reference point r ∈ R2. Similarly, the ε-indicator SSP aims at selecting k~points P* that minimize the ε-indicator Iε(P*,R) for some reference set R ⊂ R2 of size m (which can be R=P). We first present a new algorithm for the hypervolume SSP with runtime O(n (k + log n)). Our second main result is a new algorithm for the ε-indicator SSP with runtime O(n log n + m log m). Both results improve the current state of the art runtimes by a factor of (nearly) $n$ and make the problems tractable for new applications. Preliminary experiments confirm that the theoretical results translate into substantial empirical runtime improvements.

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    cover image ACM Conferences
    GECCO '14: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation
    July 2014
    1478 pages
    ISBN:9781450326629
    DOI:10.1145/2576768
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    Published: 12 July 2014

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    Author Tags

    1. archiving algorithms
    2. epsilon indicator
    3. hypervolume indicator
    4. measurement
    5. performance

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    GECCO '14
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    GECCO '14: Genetic and Evolutionary Computation Conference
    July 12 - 16, 2014
    BC, Vancouver, Canada

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    GECCO '14 Paper Acceptance Rate 180 of 544 submissions, 33%;
    Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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    • (2024)Maximizing Weighted Dominance in the PlaneTheoretical Aspects of Computing – ICTAC 202410.1007/978-3-031-77019-7_9(153-163)Online publication date: 22-Nov-2024
    • (2024)LTR-HSS: A Learning-to-Rank Based Framework for Hypervolume Subset SelectionParallel Problem Solving from Nature – PPSN XVIII10.1007/978-3-031-70085-9_3(36-51)Online publication date: 7-Sep-2024
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    • (2023)An Improved Local Search Method for Large-Scale Hypervolume Subset SelectionIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.321908127:6(1690-1704)Online publication date: Dec-2023
    • (2023)Enhancing Diversity by Local Subset Selection in Evolutionary Multiobjective OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2022.319421127:5(1456-1469)Online publication date: Oct-2023
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    • (2023)Many-Objective Quality MeasuresMany-Criteria Optimization and Decision Analysis10.1007/978-3-031-25263-1_5(113-148)Online publication date: 29-Jul-2023
    • (2022)Fast Greedy Subset Selection From Large Candidate Solution Sets in Evolutionary Multiobjective OptimizationIEEE Transactions on Evolutionary Computation10.1109/TEVC.2021.310338626:4(750-764)Online publication date: Aug-2022
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