Filled Fonksiyonunda Yeni Bir Stokastik Arama Yöntemi

Bu çalışmada, yeni bir stokastik arama yaklaşımı, klasik filled fonksiyon arama stratejisine daha hızlı ve daha verimli bir alternatif olarak sunulmuştur. Deterministik bir yöntem olan L tipi filled fonksiyonunu hızlandırmak için stokastik bir yöntem olan kümeleme ve parabolik yaklaşım tabanlı kısıtsız global optimizasyon yöntemi (GOBC-PA) kullanılmıştır. Filled fonksiyonun havza bölgelerinin aranması GOBC-PA tarafından gerçekleştirilmiştir. Bu çalışmada kullanılan yöntemler popülerlikleri, hızları ve gürbüzlükleri nedeniyle tercih edilmişlerdir. Stokastik yöntemin amaç fonksiyonunu, havza bölgesinin yerini belirleyen gradyanın epsilon değeri oluşturmaktadır. Bu nedenle, stokastik yöntemin tüm amacı global optimumu bulmak değil, havza bölgesini bulmaktır. Global minimumun bulunma rolü deterministik yönteme bırakılmıştır. Geliştirilen yöntem, 11 kıyaslama fonksiyonu kullanılarak klasik filled fonksiyona karşı test edilip bu işlem 10 kez tekrarlanmıştır. Elde edilen sonuçlar incelendiğinde, stokastik arama yaklaşımının ortalama hata, standart sapma ve geçen süre değerlerinde klasik yaklaşıma göre üstünlüğü görülmektedir. Bu sonuçlar, deterministik ve stokastik yöntemlerin kombinasyonunun, klasik deterministik yönteme karşı küresel minimumun bulunmasında daha başarılı olabileceğini göstermektedir.

Anahtar Kelimeler:

Stokastik arama, GOBC-PA, L tipi filled fonksiyonu, global optimizasyon

A New Stochastic Search Method for Filled Function

In this study, a new stochastic search approach is presented as a faster and more efficient alternative to classic filled function search strategy. An unconstrained global optimization method based on clustering and parabolic approximation (GOBC-PA) has been used as a stochastic method for accelerating the L type filled function as a deterministic method. Searching the basin regions of the filled function is performed by GOBC-PA. The methods used in this study are preferred due to their popularity, speed and robustness. The objective function of the stochastic method is the epsilon value of the gradient that gives the location of basin region. Therefore, the whole purpose of the stochastic method is not to find the global optimum but to find the basin region. The role of finding the global minimum has been left to the deterministic method. The developed method has been tested against classical filled function using 11 benchmark functions and process repeated 10 times. When the obtained results are examined, it is seen that the stochastic search approach has superiority over the mean error, standard deviation and elapsed time values according to the classical approach. These results show that the combination of deterministic and stochastic methods can be more successful in finding the global minimum against the classic deterministic method.

Keywords:

Stochastic search, GOBC-PA, L type filled function, global optimization,

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