Goal Functions from Minimax to Maximin in Multicriteria Choice and Optimization

Abstract

A technique is proposed for constructing a continuous range of goal functions from minimax to maximin using the generalized form of a weighted power mean (WPM). Each item of multicriteria choice or alternative variant in an optimization problem is characterized by a vector of performance parameters and it is assumed that each performance parameter is constrained by its target value. An “imperfect maximin-minimax” principle of multiobjective optimality is suggested as well as the technique for its implementation. The technique is based on expert evaluation of each performance parameter’s degree of freedom expressed as the worst compensable deviation from its target value. The data obtained in an expert evaluation is sufficient for calculating the order and weights of a WPM on the basis of which the goal function is to be built.