Modeling and Optimization of Response Surface Problems in a Fuzzy FrameWork


  • Profª Ozlem Turksen – Department of Statistics – Ankara University – Turkey
  • FCUL – Bloco C6 Piso 4 – Sala 6.4.30 – Campo Grande – 14:30 h
  • Quarta-feira, 26 de Junho de 2013
  • Referência Projeto: PEst-OE/MAT/UI0006/2011
Abstract: There are two main stages for response surface problems after data collection: (i) modeling, and (ii) optimization, which is specifically called multi-response optimization (MRO). In most practical problems, the unknown relationship between each response and input variables has complexity, nonlinearity, vagueness, and imprecision. Besides that, the number of observations can be inadequate, or there is difficulty verifying that the modeling error is normality distributed, or there is uncertain information about the data. In such cases, fuzzy numbers and fuzzy values are more proper for representing uncertain information of the data. In this work, a novel modeling and optimization tool will be presented for the solution of multi-response problems in a fuzzy framework. In the modeling stage, fuzzy least square method is used to obtain predicted fuzzy response functions, in which response variables and model parameters are considered as triangular fuzzy numbers, whereas input variables are assumed to be crisp numbers. After obtaining predicted fuzzy response functions, the MRO problem is considered as a multi-objective optimization (MOO) problem with fuzzy objectives without aggregating the fuzzy objective functions. In order to solve the fuzzy MOO problem without dimensionality reduction, a well-known multi-objective algorithm,

Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is modified by using the centroid index based fuzzy ranking method. The proposed fuzzy modified algorithm is called Fuzzy NSGA-II (FNSGA-II). The FNSGA-II provides a fuzzy Pareto solution set, consisting of fuzzy non-dominated solutions. This is done in a single run without aggregating the fuzzy objective functions. The obtained fuzzy Pareto solution set provides alternative solutions to the decision maker, and also leads to a bigger decision making region.