MODELING AND OPTIMIZATION OF MULTI-RESPONSE SURFACE PROBLEMS WITH FUZZY APPROACH

Abstract

The most widely used approach for solving multi response surface problems is response surface methodology. It is thought to be that the response surface methodology is inadequate for evaluation of unexplained vagueness in real world problems. Therefore in the study, fuzzy approach is proposed as an alternative to solve the multi response surface problems. The main aim of this study is to represent the applicability of the fuzzy approach for solving of the multi-response problems in which the probability distributions of the response variables cannot be determined. At the modeling stage, the fuzzy least squares regression analysis, based on Diamond's distance metric, is used. In the optimization stage, the problem is considered as a fuzzy multi-objective optimization problem. Nondominated Sorting Genetic Algorithm-II (NSGA-II), defined in the literature, is adapted by using centroid index fuzzy ranking approach then called Fuzzy NSGA-II (FNSGA-II). Fuzzy Pareto solution set is obtained by optimizing the problem, which is composed of fuzzy objective functions, with FNSGA-II. The proposed fuzzy solution approaches are applied on a data set defined in the literature. Thus, it is seen that an obtained fuzzy Pareto solution is a set of acceptable different response values for the performed multi-response experiments at the defined levels of input variables.

Keywords

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BULANIK YAKLAŞIM İLE ÇOK YANITLI YÜZEY PROBLEMLERİNİN MODELLENMESİ VE OPTİMİZASYONU

Abstract

Çok yanıtlı yüzey problemlerinin çözümünde en sık kullanılan yaklaşım yanıt yüzey yöntemidir. Gerçek dünya problemlerinde, açıklanamayan, belirsizlik durumlarının varlığı söz konusu olduğunda yanıt yüzey yönteminin yetersiz olduğu düşünülmektedir. Bu nedenle çalışmada, çok yanıtlı bir problemin çözümü için alternatif olarak bulanık yaklaşımın kullanılması önerilmiştir. Bu çalışmanın asıl amacı, yanıt değişkenlerinin olasılık dağılımlarının belirlenemediği durumlarda, çok yanıtlı problemlerin çözümünde bulanık yaklaşımın uygulanabilirliğinin göstermektir. Modelleme aşamasında, Diamond’ın uzaklık metriğine dayalı bulanık en küçük kareler regresyon analizi kullanılmıştır. Optimizasyon aşamasında ise problem, bulanık çok amaçlı optimizasyon problemi biçiminde ele alınmıştır. Literatürde tanımlı Baskın Sıralı Genetik Algoritma-II (BSGA-II) yöntemi, ağırlık merkezi indeksine dayalı bulanık sıralama yaklaşımı ile uyarlanarak, Bulanık BSGA-II (BBSGA-II) olarak adlandırılmıştır. Bulanık yanıtlardan oluşan problemin BBSGA-II ile optimizasyonu sonucu bulanık Pareto kümesine ulaşılmıştır. Önerilen bulanık çözümleme yaklaşımları, literatürde tanımlı çok yanıtlı bir veri setine uygulanmıştır. Böylece, elde edilen bir bulanık Pareto çözümün, belirlenen girdi değişken düzeylerinde yapılan çok yanıtlı deneyler için kabul edilebilir farklı yanıt değerlerinin bir kümesi olduğu görülmüştür.

Keywords

• Çok yanıtlı yüzey problemi, Bulanık çok amaçlı optimizasyon, Bulanık sıralama, Bulanık Baskın Sıralı Genetik Algoritma-II (BBSGA-II), Bulanık pareto çözüm kümesi

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