Filled Fonksiyonunda Yeni Bir Stokastik Arama Yöntemi

Year 2020, Volume: 7 Issue: 1, 111 - 123, 31.01.2020

İhsan Pençe , Melike Şişeci Çeşmeli

https://doi.org/10.31202/ecjse.596633

Abstract

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.

Keywords

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

A New Stochastic Search Method for Filled Function

Abstract

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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