Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front

In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximat...

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Veröffentlicht in:Evolutionary computation Jg. 25; H. 2; S. 309 - 349
Hauptverfasser: Saborido, Rubén, Ruiz, Ana B, Luque, Mariano
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States 01.06.2017
Schlagworte:
Algorithms
Biological Evolution
Models, Biological
Pareto optimal solutions
Achievement scalarizing function
Evolutionary algorithm
Multiobjective optimization
ISSN:1530-9304
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Abstract In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.
AbstractList In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.
Author Ruiz, Ana B
Luque, Mariano
Saborido, Rubén
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  surname: Saborido
  fullname: Saborido, Rubén
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  givenname: Ana B
  surname: Ruiz
  fullname: Ruiz, Ana B
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  organization: Universidad de Málaga, Department of Applied Economics (Mathematics), Calle Ejido 6, 29071 Málaga, Spain abruiz@uma.es
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  givenname: Mariano
  surname: Luque
  fullname: Luque, Mariano
  email: mluque@uma.es
  organization: Universidad de Málaga, Department of Applied Economics (Mathematics), Calle Ejido 6, 29071 Málaga, Spain mluque@uma.es
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Keywords Pareto optimal solutions
Achievement scalarizing function
Evolutionary algorithm
Multiobjective optimization
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Snippet In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing...
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SubjectTerms Algorithms
Biological Evolution
Models, Biological
Title Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front
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