A Comprehensive Comparison of Binary Archimedes Optimization Algorithms on Uncapacitated Facility Location Problems

Year 2022, Volume: 10 Issue: 1, 27 - 38, 31.01.2022

Ahmet Cevahir Çınar

https://doi.org/10.29130/dubited.876284

Abstract

Metaheuristic optimization algorithms are widely used in solving NP-hard continuous optimization problems. Whereas, in the real world, many optimization problems are discrete. The uncapacitated facility location problem (UFLP) is a pure discrete binary optimization problem. Archimedes optimization algorithm (AOA) is a recently develop metaheuristic optimization algorithm and there is no binary variant of AOA. In this work, 17 transfer functions (TF1-TF17) are used for mapping continuous values to binary values. 17 binary variants of AOA (BAOA1- BAOA17) are proposed for solving UFLPs. 16 to 100-dimensional UFLPs were solved with binary variants of AOA. Stationary and non-stationary transfer functions were compared in terms of solution quality. The non-stationary transfer functions were produced better solutions than stationary transfer functions. Peculiar parameter analyzes for binary optimization problems were performed in the best variant (BAOA9) produced with TF9 transfer function.

Keywords

Binary optimization, Uncapacitated facility location problem, Archimedes optimization algorithm

Thanks

The authors wish to thank Scientific Research Projects Coordinatorship at Selcuk University and The Scientific and Technological Research Council of Turkey for their institutional supports.

Kapasitesiz Tesis Yerleşim Problemleri Üzerinde İkili Arşimet Optimizasyon Algoritmalarının Kapsamlı Bir Karşılaştırması

Abstract

Meta-sezgisel optimizasyon algoritmaları, NP-zor sürekli optimizasyon problemlerinin çözümünde yaygın olarak kullanılmaktadır. Oysa gerçek dünyada pek çok optimizasyon problemi ayrıktır. Kapasitesiz tesis yerleşimi problemi, saf bir ayrık ikili optimizasyon problemidir. Arşimet optimizasyon algoritması (AOA), yakın zamanda geliştirilmiş bir meta-sezgisel optimizasyon algoritmasıdır ve AOA'nın ikili bir varyantı yoktur. Bu çalışmada, sürekli değerleri ikili değerlere eşlemek için 17 transfer fonksiyonu (TF1-TF17) kullanılmıştır. UFLP'leri çözmek için AOA'nın (BAOA1-BAOA17) 17 ikili varyantı önerilmiştir. 16 ila 100 boyutlu UFLP'ler, AOA'nın ikili varyantları ile çözülmüştür. Durağan ve durağan olmayan transfer fonksiyonları çözüm kalitesi açısından karşılaştırılmıştır. Durağan olmayan transfer fonksiyonları, sabit transfer fonksiyonlarından daha iyi çözümler üretmiştir. İkili optimizasyon problemleri için özel parametre analizleri, TF9 transfer fonksiyonu ile üretilmiş olan en iyi varyantta (BAOA9) gerçekleştirilmiştir.

Keywords

İkili optimizasyon, Kapasitesiz tesis yerleşimi problemi, Arşimet optimizasyon algoritması

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