Implementation of Grey Wolf Optimization Algorithm to P-Median Problems

Gülşen Orucova Büyüköz; Hüseyin Haklı

Makale detayları

Implementation of Grey Wolf Optimization Algorithm to P-Median Problems

Yazarlar:

Gülşen Orucova Büyüköz | Hüseyin Haklı

Yayıncı:

Necmettin Erbakan University

Ana Başlıklar:

Evrimsel Hesaplama | Memnuniyet ve Optimizasyon

Dergi:

Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.6 Issue 1, pp.166-177

Belge Tipi:

Makale

Yayın Tarihi:

4/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001316252

pISSN:

2667-7989

Anahtar kelimeler:

Özet:

 In this study, the P-Median problem, which is in the Np-hard problem class, is tried to be solved with the Gray Wolf Optimization GWO algorithm. Since the GWO algorithm is proposed for continuous search space, it is not possible to directly apply this algorithm to the P-Median problem, which has a combinatorial structure. For this reason, the GWO algorithm needs to be adapted to operate in the discrete search space. In this process, inspired by the search strategy of the Differential Evolution Algorithm, the crossover technique was used together with the GWO algorithm. First, the uniform crossover technique was utilized in the study. Then, taking into account the parameter in the GWO algorithm, which varies depending on the iteration, a crossover technique called adaptive uniform crossover was created. This proposed algorithm is tested on 40 P-Median problems. When the solutions obtained are compared, it is seen that the adaptive crossover technique gives better results than the uniform crossover technique in all 40 problems. In addition, in order to compare the results obtained using the two crossover techniques numerically, the improvement ratio between the solutions was analyzed. The obtained ratios show that in all 40 problems, the adaptive uniform crossover technique significantly improves the solutions obtained with the uniform crossover technique.

 In this study, the P-Median problem, which is in the Np-hard problem class, is tried to be solved with the Gray Wolf Optimization GWO algorithm. Since the GWO algorithm is proposed for continuous search space, it is not possible to directly apply this algorithm to the P-Median problem, which has a combinatorial structure. For this reason, the GWO algorithm needs to be adapted to operate in the discrete search space. In this process, inspired by the search strategy of the Differential Evolution Algorithm, the crossover technique was used together with the GWO algorithm. First, the uniform crossover technique was utilized in the study. Then, taking into account the parameter in the GWO algorithm, which varies depending on the iteration, a crossover technique called adaptive uniform crossover was created. This proposed algorithm is tested on 40 P-Median problems. When the solutions obtained are compared, it is seen that the adaptive crossover technique gives better results than the uniform crossover technique in all 40 problems. In addition, in order to compare the results obtained using the two crossover techniques numerically, the improvement ratio between the solutions was analyzed. The obtained ratios show that in all 40 problems, the adaptive uniform crossover technique significantly improves the solutions obtained with the uniform crossover technique.

 In this study, the P-Median problem, which is in the Np-hard problem class, is tried to be solved with the Gray Wolf Optimization GWO algorithm. Since the GWO algorithm is proposed for continuous search space, it is not possible to directly apply this algorithm to the P-Median problem, which has a combinatorial structure. For this reason, the GWO algorithm needs to be adapted to operate in the discrete search space. In this process, inspired by the search strategy of the Differential Evolution Algorithm, the crossover technique was used together with the GWO algorithm. First, the uniform crossover technique was utilized in the study. Then, taking into account the parameter in the GWO algorithm, which varies depending on the iteration, a crossover technique called adaptive uniform crossover was created. This proposed algorithm is tested on 40 P-Median problems. When the solutions obtained are compared, it is seen that the adaptive crossover technique gives better results than the uniform crossover technique in all 40 problems. In addition, in order to compare the results obtained using the two crossover techniques numerically, the improvement ratio between the solutions was analyzed. The obtained ratios show that in all 40 problems, the adaptive uniform crossover technique significantly improves the solutions obtained with the uniform crossover technique.

 Bu çalışmada Np-zor problem sınıfından olan P-Medyan problemi Gri Kurt Optimizasyon GKO algoritması ile çözülmeye çalışıldı. GKO algoritmasının sürekli arama uzayı için önerilmesi nedeniyle kombinatoryal yapıya sahip olan P-Medyan problemine doğrudan bu algoritmanın uygulanması mümkün değildir. Bu sebeple GKO algoritmasının ayrık arama uzayında işlem yapabilecek şekilde uyarlanması gerekmektedir. Bu süreçte Diferansiyel Evrim Algoritmasının arama stratejisinden esinlenilerek GKO algoritması ile birlikte çaprazlama tekniği kullanılmıştır. Çalışmada öncelikle tekdüze çaprazlama tekniğinden faydalanılmıştır. Daha sonra GKO algoritmasında bulunan ve iterasyona bağlı olarak değişen parametre dikkate alınarak adaptif tekdüze çaprazlama olarak adlandırdığımız çaprazlama tekniği oluşturulmuştur. Önerilen bu algoritma 40 P-Medyan problemi üzerinde test edilmiştir. Elde edilen çözümler karşılaştırıldığında adaptif çaprazlama tekniğinin 40 problemin tamamında tekdüze çaprazlama tekniğinden daha iyi sonuçlar verdiğini görülmüştür. Ayrıca iki çaprazlama tekniği kullanılarak elde edilen sonuçların sayısal olarak karşılaştırılabilmesi için çözümler arasındaki iyileştirme oranına bakılmıştır. Elde edilen oranlar 40 problemin hepsinde adaptif tekdüze çaprazlama tekniğinin, tekdüze çaprazlama tekniğinde elde edilen çözümleri önemli oranda iyileştirdiği gözlemlenmiştir.

Makale detayları

Implementation of Grey Wolf Optimization Algorithm to P-Median Problems

Yazarlar:

Gülşen Orucova Büyüköz | Hüseyin Haklı

Yayıncı:

Necmettin Erbakan University

Ana Başlıklar:

Evrimsel Hesaplama | Memnuniyet ve Optimizasyon

Dergi:

Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.6 Issue 1, pp.166-177

Belge Tipi:

Makale

Yayın Tarihi:

4/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001316252

pISSN:

2667-7989

Grey Wolf optimization algorithm

NP-hard

P-Median problem

Uniform crossoverNP-zor

Gri Kurt Optimizasyon Algoritması

P-Medyan Problemi

Tekdüze çaprazlama

Sayı

Makale detayları

Yazarlar: Gülşen Orucova Büyüköz | Hüseyin Haklı

Yayıncı: Necmettin Erbakan University

Ana Başlıklar: Evrimsel Hesaplama | Memnuniyet ve Optimizasyon

Dergi: Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.6 Issue 1, pp.166-177

Belge Tipi: Makale

Yayın Tarihi: 4/2024

Belge Dili: Türkçe

Document ID (Org No.): 2001316252

pISSN: 2667-7989

Sayı

Yazarlar:

Gülşen Orucova Büyüköz | Hüseyin Haklı

Yayıncı:

Necmettin Erbakan University

Ana Başlıklar:

Evrimsel Hesaplama | Memnuniyet ve Optimizasyon

Dergi:

Necmettin Erbakan Üniversitesi Fen ve Mühendislik Bilimleri Dergisi Vol.6 Issue 1, pp.166-177

Belge Tipi:

Makale

Yayın Tarihi:

4/2024

Belge Dili:

Türkçe

Document ID (Org No.):

2001316252

pISSN:

2667-7989