Desirability function approach to multiobjective optimization problems

Decision problems in real world applications, generally require simultaneous solutions of a number of objectives. Multi-objective optimization is related to this kind of problems. Optimum solution set, so-called Pareto-optimal set, which is found by multi-objective optimization methods, consists of a set of the best solutions in a given domain instead of only one solution point. Recently, multiobjective evolutionary optimization methods, developed by using evolution strategies in biology and multiobjective optimization algorithms together, make a significant contribution on Pareto-optimal solution set of the problem. Whereas these solution methods provide a hypervolume-set allowing decision makers to have a correct and proper choice, at the same time they cause a selection problem of determining the best point as a solution in this set. The aim of the thesis is to recommend a method supporting decision maker on this selection problem. A new solution approach, found by desirability functions used in multi-response surface analysis in statistics, is adapted to multiobjective optimization problems. This new method, adapted-desirability function method, is applied on hypervolume Pareto-optimal sets of test functions and real world problems in literature. Results show that adapted-desirability function provides help in selecting an optimum point in Pareto-optimal set. Especially, this method reaches a better solution point than that of Pareto-optimal set in constrained case. The adapted-desirability function is suggested as a method to be used together with multiobjective optimization by evolutionary algorithms as a support for decision makers instead of an alternative method to it. Keywords: Multiobjective Optimization, Desirability Function, Evolutionary Algorithms