A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

Alberto Pajares, Xavier Blasco, Juan Manuel Herrero and Miguel A. Martínez
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Alberto Pajares: Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain
Xavier Blasco: Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain
Juan Manuel Herrero: Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain
Miguel A. Martínez: Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2021, vol. 9, issue 9, 1-28

Abstract: In a multi-objective optimization problem, in addition to optimal solutions, multimodal and/or nearly optimal alternatives can also provide additional useful information for the decision maker. However, obtaining all nearly optimal solutions entails an excessive number of alternatives. Therefore, to consider the nearly optimal solutions, it is convenient to obtain a reduced set, putting the focus on the potentially useful alternatives. These solutions are the alternatives that are close to the optimal solutions in objective space, but which differ significantly in the decision space. To characterize this set, it is essential to simultaneously analyze the decision and objective spaces. One of the crucial points in an evolutionary multi-objective optimization algorithm is the archiving strategy. This is in charge of keeping the solution set, called the archive, updated during the optimization process. The motivation of this work is to analyze the three existing archiving strategies proposed in the literature ( A r c h i v e U p d a t e P Q , ? D x y , A r c h i v e _ n e v M O G A , and t a r g e t S e l e c t ) that aim to characterize the potentially useful solutions. The archivers are evaluated on two benchmarks and in a real engineering example. The contribution clearly shows the main differences between the three archivers. This analysis is useful for the design of evolutionary algorithms that consider nearly optimal solutions.

Keywords: multi-objective optimization; nearly optimal solutions; archiving strategy; evolutionary algorithm; non-linear parametric identification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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