This paper on "General Method to Find the Best Compromise in Optimization Problems with Multiple Objective Functions" was presented at the NAFEMS World Congress on Design, Simulation & Optimisation: Reliability & Applicability of Computational Methods - 9-11 April 1997, Stuttgart, Germany.

Abstract

A method has been developed that allows to search very effectively for the best compromise in the case of optimization problems with several different objective functions. The required and normally problematic weighting of each objective function by weighting factors has been replaced by specifying upper and lower limits for the objective functions. The weighting will be derived from this. This has the advantage that the user does not have to select or adapt weighting factors. As the objective functions describe the requirements on the system that has to be optimized, the upper and lower limits of these functions will ordinarily be specified in a simple way by the design engineer or the analyst. By this way of weighting it is also possible to make more precise statements about the potential of improvement of each objective function in the optimization space.
The method has been implemented into the finite element analysis package ANSYS, using its macro-language APDL and the complete functionality of the existing ANSYS optimization module.
The application of the method will be demonstrated by a practical problem that has been solved.