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The Use of Fuzzy Logic in Various Combinatorial Optimization Problems

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Artificial Intelligence: Theory and Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 973))

Abstract

Conventional models of many combinatorial optimization problems rarely encompass real-life problems, because real-life problems usually contain a high degree of uncertainty. These uncertainties can be modeled using various methods, including fuzzy sets. Apart from the precise description from the problems’ nature, fuzzy variables can describe the problem better, improve the solution and reduce costs for decision makers. In this chapter we show how fuzzy logic can be used for modeling uncertainties in combinatorial problems and improve their quality. The focus will be on the Location Set Covering Problem (LSCP), the Maximal Covering Location Problem (MCLP) and the Minimal Covering Location Problem (MinCLP) as a special modification of the MCLP, but the same method could be applied to other problems. These problems are applicable in searching for optimal places for desired and undesired facilities under the given conditions. Each problem will be formally described with its own mathematical model and some of their instances will be solved. Firstly, small-size instances of the problems will be solved with an exact algorithm using the CPLEX optimizer tool, and when a dimension becomes too big for exact solving, the instances will be then solved with a Particle Swarm Optimization (PSO) meta-heuristic.

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Author information

Authors and Affiliations

  1. NAVER LABS Europe, Meylan, France

    Darko Drakulić

  2. Faculty of Technology, University of Novi Sad, Novi Sad, Serbia

    Aleksandar Takači

  3. Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

    Miroslav Marić

Authors
  1. Darko Drakulić
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  2. Aleksandar Takači
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  3. Miroslav Marić
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Corresponding author

Correspondence to Aleksandar Takači .

Editor information

Editors and Affiliations

  1. Singidunum University, Belgrade, Serbia

    Endre Pap

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Drakulić, D., Takači, A., Marić, M. (2021). The Use of Fuzzy Logic in Various Combinatorial Optimization Problems. In: Pap, E. (eds) Artificial Intelligence: Theory and Applications. Studies in Computational Intelligence, vol 973. Springer, Cham. https://doi.org/10.1007/978-3-030-72711-6_8

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