0–1 Sırt Çantası Problemleri için Transfer Fonksiyonlarına Dayalı İkili Zebra Optimizasyon Algoritması

Öz

Bu çalışma, sırt çantası problemiyle ilişkili karmaşık optimizasyon sorunlarını çözmeye yönelik olarak geliştirilen yenilikçi bir yaklaşım olan Zebra Optimizasyon Algoritması’nı (ZOA) sunmaktadır. Sırt çantası problemi, belirli bir kapasite kısıtı altında en değerli öğelerin seçimini içermekte olup, çeşitli alanlarda geniş uygulama alanına sahiptir. ZOA, uyarlanabilir yapısı ve zebraların doğal davranışlarından esinlenen yenilikçi arama stratejileriyle, geleneksel yöntemlere alternatif bir çözüm sunmaktadır. Bu çalışmada, ZOA’nın ikili optimizasyona uyarlanması ele alınmış ve sekiz farklı aktarım fonksiyonu kullanılarak İkili ZOA (BinZOA) türetilmiştir. Sırt çantası problemi üzerine yapılan karşılaştırmalı analizler, BinZOA4 varyantının en etkili BinZOA türü olduğunu ortaya koymuştur. Aktarım fonksiyonlarının tek başına sınırlı etki gösterdiği görülürken, XOR tabanlı BinZOAX varyantı tüm veri kümelerinde sıfır optimum değerden ortalama sapma (DMO) (optimal) çözümler elde ederek üstün performans sergilemiştir. BEOV3, WOS2, PSOS2, FPS2 ve BAS2 gibi mevcut yöntemlerle karşılaştırıldığında, hem BinZOA4 hem de BinZOAX doğruluk ve verimlilik açısından daha iyi sonuçlar vermiştir. Bu bulgular, ZOA çerçevesinin karmaşık ve NP-zor problemleri çözmedeki esnekliğini ve etkinliğini doğrulamaktadır. Ayrıca, bu çalışma ZOA’nın ikili optimizasyondaki potansiyelini ortaya koymakta ve algoritmanın daha geniş uygulama alanlarına yönelik kullanılabilirliğine dair ipuçları sunmaktadır. Bununla birlikte, yalnızca aktarım fonksiyonlarına dayanmanın sınırlamaları da kabul edilerek, gelecekteki çalışmalar için çeşitli metodolojilerle geliştirme yapılması önerilmektedir. ZOA’nın ikili optimizasyon problemlerine yönelik ilk uygulamasını temsil eden bu çalışma, alana yeni bakış açıları ve analitik derinlik kazandırarak, daha ileri düzey araştırmalara zemin hazırlamaktadır.

Anahtar Kelimeler

• Zebra
• Sırt Çantası Problemi
• İkili Optimizasyon
• S-Şekilli ve V-Şekilli Transfer Fonksiyonları

Binary Zebra Optimization Algorithm Based On Transfer Functions for 0–1 Knapsack Problems

Öz

This study presents the Zebra Optimization Algorithm (ZOA), an innovative approach developed to address the complex optimization challenges associated with the knapsack problem. The knapsack problem, which involves selecting the most valuable items within a given capacity constraint, has a wide range of applications across various domains. ZOA offers an alternative to traditional methods, distinguished by its adaptive structure and innovative search strategies rooted in the natural behaviors of zebras. In advancing ZOA, this paper presents its adaptation to binary optimization, incorporating eight different transfer functions to create Binary ZOA (BinZOA). A comparative study on the knapsack problem revealed BinZOA4 as the most effective BinZOA variant. While transfer functions alone showed limited impact, the XOR-based BinZOAX variant achieved optimal, zero- the deviation of the mean from the optimum value (DMO) solutions across all datasets. When compared with established methods (e.g., BEOV3, WOS2, PSOS2, FPS2, BAS2), both BinZOA4 and BinZOAX demonstrated superior performance in accuracy and efficiency. These results confirm the ZOA framework's adaptability and strength in solving complex NP-hard problems. In addition to validating the binary optimization potential of ZOA, this investigation provides a lead for the application of the algorithm in broader fields. However, the study also recognizes the limitations of relying solely on transfer functions, suggesting avenues for future improvements through diversified methodologies. Marking the first application of ZOA to binary optimization problems, this work contributes new perspectives and analytical depth to the field, paving the way for further exploration and optimization.

Anahtar Kelimeler

• Zebra
• Knapsack Problem
• Binary Optimizastion
• S-Shaped and V-Shaped Transfer Functions

Kaynakça

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