Journal of Theoretical
and Applied Mechanics

42, 3, pp. 565-584, Warsaw 2004

Some methods for multicriteria design optimization using evolutionary algorithms

Andrzej Osyczka, Stanislaw Krenich
In this paper new multicriteria design optimization methods are discussed. These methods are evolutionary algorithm based methods, and their aim is to make the process of generating the Pareto front very effective. Firstly, the multistage evolutionary algorithm method is presented. In this method, in each stage only a bicriterion optimization problem is solved and then an objective function is transformed to the constrain function. The process is repeated till all the objective functions are considered. Secondly, the preference vector method is presented. In this method, an evolutionary algorithm finds the ideal vector. This vector provides the decision maker with the information about possible ranges of the objective functions. On the basis of this information the decision maker can establish the preference vector within which he expects to find a preferred solution. For this vector, a set of Pareto solutions is generated using an evolutionary algorithm based method. Finally, the method for selecting a representative subset of Pareto solutions is discussed. The idea of this method consists in reducing the set of Pareto optimal solutions using the indiscernibility interval method after running a certain number of generations. To show how the methods discussed work each of them in turn is applied to solve a design optimization problem. These examples show clearly that using the proposed methods the computation time can be reduced significantly and that the generated solutions are still on the Pareto front.
Keywords: multicriteria design optimization; evolutionary algorithms; Pareto front