The Gradient Subspace Approximation as Local Search Engine within Evolutionary Multi-objective Optimization Algorithms

Authors

  • Sergio Alvarado Computer Science Department, CINVESTAV-IPN
  • Carlos Segura Center for Research in Mathematics (CIMAT), Guanajuato
  • Oliver Schütze Computer Science Department, CINVESTAV-IPN
  • Saúl Zapotecas Department of Applied Mathematics and Systems, Division of Natural Sciences and Engineering, Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.13053/cys-22-2-2948

Keywords:

multi-objective optimization, evolutionary computation, gradient subspace approximatin (GSA), memetic algorithms, gradient-free local search, line search method

Abstract

In this paper, we argue that the gradient subspace approximation (GSA) is a powerful local search tool with in memetic algorithms for the treat mentof multi-objective optimization problems. The GSA utilizes the neighborhood information within the current population in order to compute the best approximation of the gradient at a given candidate solution. The computation of the search direction comes hence for free in terms of additional function evaluations within population based search algorithms such as evolutionary algorithms. Its benefits have recently been discussed in the context of scalar optimization. Here, we discuss and adapt the GSA for the case that multiple objectives have to be considered concurrently. We will further on hybridize line searchers that utilize GSA to obtain the search direction with two different multi-objective evolutionary algorithms. Numerical results on selected bench mark problems indicate thes trength of the GSA-based local search within the evolutionary strategies.

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Published

2018-06-29

Issue

Vol. 22 No. 2 (2018): Thematic Issue on Numerical and Evolutionary Optimization (Guest editors: L. Trujillo, Y. Maldonado, O. Schuetze)

Section

Articles of the Thematic Issue

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