Bi-objective decision making in global optimization based on statistical models

Abstract

A global optimization problem is considered where the objective functions are assumed “black box” and “expensive”. An algorithm is theoretically substantiated using a statistical model of objective functions and the theory of rational decision making under uncertainty. The search process is defined as a sequence of bi-objective selections of sites for the computation of the objective function values. It is shown that two well known (the maximum average improvement, and the maximum improvement probability) algorithms are special cases of the proposed general approach.