HYBRID THE ARITHMETIC OPTIMIZATION ALGORITHM FOR CONSTRAINED OPTIMIZATION PROBLEMS

Abstract

Since many real-world problems can be designed as optimization problems, heuristic algorithms are increasingly preferred by researchers. The Arithmetic Optimization Algorithm (AOA) is a newly developed heuristic algorithm. It uses four arithmetic operations in its structure. The addition and subtraction operators enhanced the AOA's local search capability, while the multiplication and division operators enhanced the AOA's global search capability. It has been hybridized with the Tree Seed Algorithm (TSA) to increase the success of AOA. Thus, hybrid AOA-TSA (HAOA) has been proposed. The seed production mechanism of TSA is placed in the random walking stage of AOA. New candidate solutions (seeds) have been produced with the arithmetic operators involved in AOA and the candidate solutions have been compared with the existing solutions. Thus, the performance of AOA has increased. In this study, the success of AOA and HAOA was tested in thirteen constrained optimization problems. The success of AOA and HAOA has been tested for their performance in six different population sizes. The Wilcoxon Signed-Rank test was applied to the obtained results and its success has been proved statistically. The results proved the superiority of HAOA. HAOA has been compared with other heuristic methods in the literature and the success of HAOA has been shown. Additionally, AOA and HAOA have also been tested on three different engineering design problems. The results are discussed and evaluated.

Keywords

• Constrained optimization
• Arithmetic optimization algorithm
• Tree Seed Algorithm

Kısıtlı Optimizasyon Problemleri İçin Hibrit Aritmetik Optimizasyon Algoritması

Abstract

Pek çok gerçek dünya problemi optimizasyon problemleri olarak tasarlanabildiğinden, sezgisel algoritmalar araştırmacılar tarafından giderek daha fazla tercih edilmeye başlanmıştır. Aritmetik Optimizasyon Algoritması (AOA), yeni geliştirilmiş bir sezgisel algoritmadır. Yapısında dört aritmetik işlem kullanır. Toplama ve çıkarma operatörleri, AOA'nın yerel arama kabiliyetini geliştirirken, çarpma ve bölme operatörleri AOA'nın küresel arama kabiliyetini geliştirmiştir. AOA'nın başarısını artırmak için Ağaç Tohum Algoritması (TSA) ile hibritlenmiştir. Bu çalışmada, Hibrit AOA-TSA (HAOA) önerilmiştir. TSA'nın tohum üretim mekanizması, AOA'nın rastgele yürüme aşamasına yerleştirilmiştir. AOA'da yer alan aritmetik operatörler ile yeni aday çözümler (tohumlar) üretilmiş ve aday çözümler mevcut çözümlerle karşılaştırılmıştır. Böylece, AOA'nın performansı artmıştır. Bu çalışmada, AOA ve HAOA'nın başarısı on üç kısıtlı optimizasyon probleminde test edilmiştir. AOA ve HAOA'nın başarısı altı farklı popülasyon büyüklüğünde test edilmiştir. Elde edilen sonuçlara Wilcoxon Signed-Rank testi uygulanmış ve başarısı istatistiksel olarak kanıtlanmıştır. Sonuçlar HAOA'nın üstünlüğünü kanıtlamıştır. HAOA, literatürdeki diğer sezgisel yöntemlerle karşılaştırılmış ve HAOA'nın başarısı gösterilmiştir. Ek olarak, AOA ve HAOA, üç farklı mühendislik tasarım probleminde de test edilmiştir.

Keywords

• Kısıtlı optimizasyon
• Aritmetik optimizasyon algoritması
• Ağaç tohum algoritması

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