Chaos Based Gravitational Search Algorithms (CbGSA-X) for Benchmark Functions

Abstract

The heuristic algorithms used in the solution of optimization problems may not be able to reach the best result for each problem resolutely due to their different designs. As a consequence, literature denotes some developing structures which are added to these heuristic algorithms. Within this scope, we evaluated the performance of gravitational search algorithm (GSA), which is one of the most prominent heuristic algorithm. In the study, aiming to increase the convergence speed of the algorithm, a new algorithm has been created by integrating some chaotic mapping methods to GSA. This new algorithm has been called chaos-based gravitational search algorithm (CbGSA-X). In order to make a performance evaluation for each mapping method, we utilized test functions which were solved with GSA in literature. Finally we introduce our solutions and performed evaluations.

Keywords

• Optimization
• Meta-heuristic algorithms
• Gravitational search algorithm
• Chaotic maps
• Benchmark functions

Test Fonksiyonları için Kaos Tabanlı Yerçekimsel Arama Algoritmaları (CbGSA-X)

Abstract

Optimizasyon problemlerinin çözümünde kullanılan sezgisel algoritmalar farklı tasarımlarından dolayı, her problem için en iyi sonuca kararlı bir şekilde ulaşamayabilir. Bu nedenle literatürde bu sezgisel algoritmalara bazı geliştirici yapıların eklendiği çalışmalara sıklıkla rastlanmaktadır. Benzer şekilde bu çalışmada sezgisel algoritmalardan biri olan yerçekimsel arama algoritmasının (GSA) performansının geliştirilmesine çalışılmıştır. Çalışmada algoritmanın yakınsama hızının artırılması amaçlanarak GSA’ya bazı kaotik haritalama metotları entegre edilerek, yeni bir algoritma ortaya çıkartılmıştır. Bu yeni algoritmaya Kaos tabanlı yerçekimsel arama algoritması (CbGSA-X) adı verilmiştir. Çalışmada CbGSA-X’deki ilk popülasyondaki ajanlar oluşturulurken ilk ajan arama uzayında rastgele konumlandırılırken, diğer ajanlar ise bu ajana bağlı olarak 5 farklı (X=1, 2, 3, 4, 5) kaotik haritalama yöntemi kullanılarak konumlandırılmıştır. Her haritalama metodu için performans değerlendirilmesi yapılabilmesi için literatürde GSA ile çözümü yer alan test fonksiyonları ele alınmış ve çözümü yapılarak sonuçlar değerlendirilmiştir.

Keywords

• Optimizasyon
• Sezgisel algoritmalar
• Yerçekimsel arama algoritması
• Kaotik haritalar
• Test fonksiyonları

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