Problems of a Utopia Point Setting in Transformation of Individual Objective Functions in Multi-Objective Optimization

In an optimal processes control, where the considered goals are in general observed as concurrently conflicted, a multi-objective approach fits the best. Commonly used scalarization techniques in multi-objective optimization need a transformation of the individual single-objective functions involved into a scalar multi-criteria objective function. There are many parameters which can influence the optimization results solutions, including an unreachable utopia point value. In this study, the authors compare the multi-objective problem solutions found via two ways of the individual objectives transformation with the respect to setting the utopia point. The methods are used in the area of production control in a case study for a batch production system. To find the solutions, The Weighted Sum Method with a priori articulated preferences under specific constraints as the scalar multi-objective optimization method is applied in simulation optimization.