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Computing gap-free Pareto front approximations with stochastic search algorithms

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 approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a ∈ A, is “large.” Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in 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 some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy---multi-objective continuation methods---by showing that the concept of ε-dominance can be integrated into this approach in a suitable way.
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https://hal.inria.fr/hal-00750950
Contributor : Talbi El-Ghazali Connect in order to contact the contributor
Submitted on : Monday, November 12, 2012 - 5:23:25 PM
Last modification on : Thursday, January 20, 2022 - 5:27:52 PM

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Oliver Schütze, Marco Laumanns, Emilia Tantar, Carlos Coello Coello, El-Ghazali Talbi. Computing gap-free Pareto front approximations with stochastic search algorithms. Evolutionary Computation, Massachusetts Institute of Technology Press (MIT Press), 2010, 18 (1), pp.65-96. ⟨10.1162/evco.2010.18.1.18103⟩. ⟨hal-00750950⟩

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