Optimize an Unconstrained Utility Based Multi Objective Model
S. D. Asaduzzaman
Department of Mechanical Engineering, Rajshahi University of Engineering and Technology, Rajshahi, Bangladesh
ABSTRACT: One way to optimize multi objective mathematical models is to employ utility functions for the objectives. Recent studies on utility based multi objective optimization consider exactly one utility function for each objective. But, in reality it is not clarified that each objective function should correspond to only one utility function. Here, we consider an unconstrained multi objective mathematical model in which several utility functions are associated to each objective. A fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective. Since these utility functions are under uncertainty and in fuzzy environment, the total utility function of the problem will be a fuzzy nonlinear mathematical model, but there is not any conventional approach to solve such a model. So we should use a defuzzification method to change the total utility function to a crisp nonlinear model. In order to do this, Maximum Technique is applied to defuzzify the conditional utility functions. Then, we use an existing method to optimize this final single objective nonlinear model. The effectiveness of the proposed approach is shown by solving test problems.
Keywords: Multi objective optimization; Fuzzy probabilistic; Utility function.