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Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems

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  • Shah, Ruchit
  • Reed, Patrick

Abstract

This study analyzes multiobjective d-dimensional knapsack problems (MOd-KP) within a comparative analysis of three multiobjective evolutionary algorithms (MOEAs): the [epsilon]-nondominated sorted genetic algorithm II ([epsilon]-NSGAII), the strength Pareto evolutionary algorithm 2 (SPEA2) and the [epsilon]-nondominated hierarchical Bayesian optimization algorithm ([epsilon]-hBOA). This study contributes new insights into the challenges posed by correlated instances of the MOd-KP that better capture the decision interdependencies often present in real world applications. A statistical performance analysis of the algorithms uses the unary [epsilon]-indicator, the hypervolume indicator and success rate plots to demonstrate their relative effectiveness, efficiency, and reliability for the MOd-KP instances analyzed. Our results indicate that the [epsilon]-hBOA achieves superior performance relative to [epsilon]-NSGAII and SPEA2 with increasing number of objectives, number of decisions, and correlative linkages between the two. Performance of the [epsilon]-hBOA suggests that probabilistic model building evolutionary algorithms have significant promise for expanding the size and scope of challenging multiobjective problems that can be explored.

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  • Shah, Ruchit & Reed, Patrick, 2011. "Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 211(3), pages 466-479, June.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:466-479
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    Cited by:

    1. Marcella S. R. Martins & Myriam R. B. S. Delgado & Ricardo Lüders & Roberto Santana & Richard A. Gonçalves & Carolina P. Almeida, 2018. "Hybrid multi-objective Bayesian estimation of distribution algorithm: a comparative analysis for the multi-objective knapsack problem," Journal of Heuristics, Springer, vol. 24(1), pages 25-47, February.
    2. Probst, Malte & Rothlauf, Franz & Grahl, Jörn, 2017. "Scalability of using Restricted Boltzmann Machines for combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 256(2), pages 368-383.
    3. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    4. Mavrotas, George & Florios, Kostas & Figueira, José Rui, 2015. "An improved version of a core based algorithm for the multi-objective multi-dimensional knapsack problem: A computational study and comparison with meta-heuristics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 25-43.
    5. Madjid Tavana & Kaveh Khalili-Damghani & Amir-Reza Abtahi, 2013. "A fuzzy multidimensional multiple-choice knapsack model for project portfolio selection using an evolutionary algorithm," Annals of Operations Research, Springer, vol. 206(1), pages 449-483, July.
    6. Marcella S. R. Martins & Mohamed El Yafrani & Myriam Delgado & Ricardo Lüders & Roberto Santana & Hugo V. Siqueira & Huseyin G. Akcay & Belaïd Ahiod, 2021. "Analysis of Bayesian Network Learning Techniques for a Hybrid Multi-objective Bayesian Estimation of Distribution Algorithm: a case study on MNK Landscape," Journal of Heuristics, Springer, vol. 27(4), pages 549-573, August.
    7. Alexandros Nikas & Angelos Fountoulakis & Aikaterini Forouli & Haris Doukas, 2022. "A robust augmented ε-constraint method (AUGMECON-R) for finding exact solutions of multi-objective linear programming problems," Operational Research, Springer, vol. 22(2), pages 1291-1332, April.

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