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Modeling and solving the bi-objective minimum diameter-cost spanning tree problem

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Abstract

The bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard problem and models several practical applications in transportation and network design. We propose a bi-objective multiflow formulation for the problem and effective multi-objective metaheuristics: a multi-objective evolutionary algorithm and a fast nondominated sorting genetic algorithm. Some guidelines on how to optimize the problem whenever a priority order can be established between the two objectives are provided. In addition, we present bi-MDCST polynomial cases and theoretical bounds on the search space. Results are reported for four representative test sets.

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Authors and Affiliations

  1. ICD-LOSI, Université de Technologie de Troyes, 12, rue Marie Curie, CS 42060, 10004 , Troyes Cedex, France

    Andréa Cynthia Santos

  2. Universidade do Estado do Rio Grande do Norte, UERN, Rua Almino Afonso, 478, CEP 59.610-210 , Mossoró, RN, Brasil

    Diego Rocha Lima & Dario José Aloise

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  1. Andréa Cynthia Santos
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  2. Diego Rocha Lima
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  3. Dario José Aloise
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Correspondence to Andréa Cynthia Santos.

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Santos, A.C., Lima, D.R. & Aloise, D.J. Modeling and solving the bi-objective minimum diameter-cost spanning tree problem. J Glob Optim 60, 195–216 (2014). https://doi.org/10.1007/s10898-013-0124-4

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  • DOI: https://doi.org/10.1007/s10898-013-0124-4

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