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Comparison between Single and Multi-Objective Evolutionary Algorithms to Solve the Knapsack Problem and the Travelling Salesman Problem

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  • Mohammed Mahrach

    (Departamento de Ingeniería Informática y de Sistemas, Universidad de La Laguna, Apto. 456, 38200 San Cristóbal de La Laguna, Tenerife, Spain)

  • Gara Miranda

    (Departamento de Ingeniería Informática y de Sistemas, Universidad de La Laguna, Apto. 456, 38200 San Cristóbal de La Laguna, Tenerife, Spain)

  • Coromoto León

    (Departamento de Ingeniería Informática y de Sistemas, Universidad de La Laguna, Apto. 456, 38200 San Cristóbal de La Laguna, Tenerife, Spain)

  • Eduardo Segredo

    (Departamento de Ingeniería Informática y de Sistemas, Universidad de La Laguna, Apto. 456, 38200 San Cristóbal de La Laguna, Tenerife, Spain)

Abstract

One of the main components of most modern Multi-Objective Evolutionary Algorithms (MOEAs) is to maintain a proper diversity within a population in order to avoid the premature convergence problem. Due to this implicit feature that most MOEAs share, their application for Single-Objective Optimization (SO) might be helpful, and provides a promising field of research. Some common approaches to this topic are based on adding extra—and generally artificial—objectives to the problem formulation. However, when applying MOEAs to implicit Multi-Objective Optimization Problems (MOPs), it is not common to analyze how effective said approaches are in relation to optimizing each objective separately. In this paper, we present a comparative study between MOEAs and Single-Objective Evolutionary Algorithms (SOEAs) when optimizing every objective in a MOP, considering here the bi-objective case. For the study, we focus on two well-known and widely studied optimization problems: the Knapsack Problem (KNP) and the Travelling Salesman Problem (TSP). The experimental study considers three MOEAs and two SOEAs. Each SOEA is applied independently for each optimization objective, such that the optimized values obtained for each objective can be compared to the multi-objective solutions achieved by the MOEAs. MOEAs, however, allow optimizing two objectives at once, since the resulting Pareto fronts can be used to analyze the endpoints, i.e., the point optimizing objective 1 and the point optimizing objective 2. The experimental results show that, although MOEAs have to deal with several objectives simultaneously, they can compete with SOEAs, especially when dealing with strongly correlated or large instances.

Suggested Citation

  • Mohammed Mahrach & Gara Miranda & Coromoto León & Eduardo Segredo, 2020. "Comparison between Single and Multi-Objective Evolutionary Algorithms to Solve the Knapsack Problem and the Travelling Salesman Problem," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2018-:d:443884
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    References listed on IDEAS

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    1. Florios, Kostas & Mavrotas, George, 2014. "Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems," MPRA Paper 105074, University Library of Munich, Germany.
    2. Beume, Nicola & Naujoks, Boris & Emmerich, Michael, 2007. "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1653-1669, September.
    3. Carlos Segura & Carlos A. Coello Coello & Gara Miranda & Coromoto León, 2016. "Using multi-objective evolutionary algorithms for single-objective constrained and unconstrained optimization," Annals of Operations Research, Springer, vol. 240(1), pages 217-250, May.
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