Hybrid of "Intersection" Algorithm for Multi-Objective Optimization with Response Surface Methodology and its Application

Abstract

Recently, a new "intersection" method for multi-objective optimization was developed in the points of view set theory and probability theory, which introduces a new idea of favorable probability to reflect the favorable degree of the utility of performance indicator in multi-objective optimization, and the product of all partial favorable probabilities of entire utilities of performance indicators makes the overall / total favorable probability of the candidate. Here, in this paper, the new "intersection" algorithm for multi-objective optimization is combined effectively with response surface methodology (RSM) by taking each response as one objective, which transfers the multi-response optimization problem into a single response one with the help of the overall / total favorable probability of each scheme. The overall / total favorable probability is the uniquely decisive index of the scheme in the optimization. Applications of the hybrid approach with two examples in material technology are given, proper predictions are obtained.