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Carlos A. Coello Coello
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Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2022) 30 (2): 195–219.
Published: 01 June 2022
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Most state-of-the-art Multiobjective Evolutionary Algorithms ( moea s) promote the preservation of diversity of objective function space but neglect the diversity of decision variable space. The aim of this article is to show that explicitly managing the amount of diversity maintained in the decision variable space is useful to increase the quality of moea s when taking into account metrics of the objective space. Our novel Variable Space Diversity-based MOEA ( vsd-moea ) explicitly considers the diversity of both decision variable and objective function space. This information is used with the aim of properly adapting the balance between exploration and intensification during the optimization process. Particularly, at the initial stages, decisions made by the approach are more biased by the information on the diversity of the variable space, whereas it gradually grants more importance to the diversity of objective function space as the evolution progresses. The latter is achieved through a novel density estimator. The new method is compared with state-of-art moea s using several benchmarks with two and three objectives. This novel proposal yields much better results than state-of-the-art schemes when considering metrics applied on objective function space, exhibiting a more stable and robust behavior.
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Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2010) 18 (1): 65–96.
Published: 01 March 2010
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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 ɛ-dominance. Though bounds on the quality of the limit approximation—which are entirely determined by the archiving strategy and the value of ɛ—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 ɛ-dominance can be integrated into this approach in a suitable way.
Journal Articles
Publisher: Journals Gateway
Evolutionary Computation (2007) 15 (4): 493–517.
Published: 01 December 2007
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Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is ε-dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, ε-dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of ε-dominance, which we call Pareto-adaptive ε-dominance ( pa ε-dominance). Our proposed approach tries to overcome the main limitation of ε-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.