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Convergence of stochastic search algorithms to gap-free pareto front approximations

Published: 07 July 2007 Publication History

Abstract

Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of ε-dominance. Though bounds on the quality of the limit approximation -- which are entirely determined by the archiving strategy and the value of ε -- have been obtained, the strategies do not guarantee to obtain a gap-free Pareto front approximation. Since such approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included into the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs we give somenumerical results to visualize the behavior of the different archiving strategies.

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  • (2018)Multi-objective OptimizationHandbook of Heuristics10.1007/978-3-319-07153-4_17-1(1-28)Online publication date: 16-Jan-2018
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cover image ACM Conferences
GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation
July 2007
2313 pages
ISBN:9781595936974
DOI:10.1145/1276958
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 07 July 2007

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Author Tags

  1. convergence
  2. epsilon-dominance
  3. multi-objective optimization
  4. stochastic search algorithms

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GECCO '07 Paper Acceptance Rate 266 of 577 submissions, 46%;
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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  • (2022)A bounded archive based for bi-objective problems based on distance and e-dominance to avoid cyclic behaviorProceedings of the Genetic and Evolutionary Computation Conference10.1145/3512290.3528840(583-591)Online publication date: 8-Jul-2022
  • (2019)Archivers for the representation of the set of approximate solutions for MOPsJournal of Heuristics10.1007/s10732-018-9383-z25:1(71-105)Online publication date: 1-Feb-2019
  • (2018)Multi-objective OptimizationHandbook of Heuristics10.1007/978-3-319-07153-4_17-1(1-28)Online publication date: 16-Jan-2018
  • (2018)Multi-objective OptimizationHandbook of Heuristics10.1007/978-3-319-07124-4_17(177-204)Online publication date: 14-Aug-2018
  • (2017)Generating Epsilon-Efficient Solutions in Multiobjective Optimization by Genetic AlgorithmApplied Mathematics10.4236/am.2017.8303208:03(395-409)Online publication date: 2017
  • (2016)The directed search method for multi-objective memetic algorithmsComputational Optimization and Applications10.1007/s10589-015-9774-063:2(305-332)Online publication date: 1-Mar-2016
  • (2012)Runtime analysis of an evolutionary algorithm for stochastic multi-objective combinatorial optimizationEvolutionary Computation10.1162/EVCO_a_0005020:3(395-421)Online publication date: 1-Sep-2012
  • (2012)Stochastic ConvergenceHandbook of Natural Computing10.1007/978-3-540-92910-9_27(847-869)Online publication date: 2012
  • (2011)On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization ProblemIEEE Transactions on Evolutionary Computation10.1109/TEVC.2010.206432115:4(444-455)Online publication date: 1-Aug-2011
  • (2011)A fast steady-state ε-dominance multi-objective evolutionary algorithmComputational Optimization and Applications10.1007/s10589-009-9241-x48:1(109-138)Online publication date: 1-Jan-2011
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