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A genetic algorithm integrated with the initial solution procedure and parameter tuning for capacitated P-median problem

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A Correction to this article was published on 12 April 2023

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Abstract

The capacitated p-median problem is a well-known location-allocation problem that is NP-hard. We proposed an advanced Genetic Algorithm (GA) integrated with an Initial Solution Procedure for this problem to solve the medium and large-size instances. A 33 Full Factorial Design was performed where three levels were selected for the probability of mutation, population size, and the number of iterations. Parameter tuning was performed to reach better performance at each instance. MANOVA and Post-Hoc tests were performed to identify significant parameter levels, considering both computational time and optimality gap percentage. Real data of Lorena and Senne (2003) and the data set presented by Stefanello et al. (2015) were used to test the proposed algorithm, and the results were compared with those of the other heuristics existing in the literature. The proposed GA was able to reach the optimal solution for some of the instances in contrast to other metaheuristics and the Mat-heuristic, and it reached a solution better than the best known for the largest instance and found near-optimal solutions for the other cases. The results show that the proposed GA has the potential to enhance the solutions for large-scale instances. Besides, it was also shown that the parameter tuning process might improve the solution quality in terms of the objective function and the CPU time of the proposed GA, but the magnitude of improvement may vary among different instances.

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Data availability

The authors acknowledge that the data sets used in this study were obtained from [58] and [59]. The addresses of these websites are presented in the References.

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Acknowledgements

This study has been financially supported by the Turkish National Science Foundation (TUBITAK) with project number 215M143.

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Authors and Affiliations

  1. Computer Engineering Department, Erzincan Binali Yildirim University, Erzincan, Turkey

    Mehmet Kursat Oksuz

  2. Industrial Engineering Department, Karadeniz Technical University, Trabzon, Turkey

    Kadir Buyukozkan

  3. College of Engineering and Technology, American University of the Middle East, Egaila, 54200, Kuwait

    Alperen Bal

  4. Industrial Engineering Department, Istanbul Technical University, ITU Ayazaga Kampusu, Rektorluk Binasi, Sariyer, 34467, Istanbul, Turkey

    Sule Itir Satoglu

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  1. Mehmet Kursat Oksuz
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Correspondence to Sule Itir Satoglu.

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Appendix A–Results of parameter tuning

Appendix A–Results of parameter tuning

See Tables

Table 5 Fine-tuned parameter values for the test problems according to the DOE
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Table 6 Parameters for different N*P values
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Table 7 Impact of the parameter tuning
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Table 8 Analyzed parameter values for the real data problem SJC1
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Table 9 MANOVA multivariate test results
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Table 10 MANOVA tests of between-subjects effects
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Table 11 Result of Post-hoc test for the population size (p_size)
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Table 12 Result of post-hoc test for the mutation probability (mp)
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Table 13 Result of post-hoc test for the iteration number (max_iter)
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Oksuz, M.K., Buyukozkan, K., Bal, A. et al. A genetic algorithm integrated with the initial solution procedure and parameter tuning for capacitated P-median problem. Neural Comput & Applic 35, 6313–6330 (2023). https://doi.org/10.1007/s00521-022-08010-w

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