Prof. Dr. Klaus Truemper
University of Texas at Dallas, USA

Multi-objective optimization using expensive black-box functions

There is strong and growing demand for methods that solve the following optimization problem: Given are several functions f_i(x) and g_j(x) that are not explicitly given but whose values can be obtained via black boxes, each of which requires a significant amount of time for evaluation. The functions need not be differentiable or even continuous. Some of the variables are constrained to be integer, while the remaining variables are continuous. All variables are constrained by lower and upper bounds. Task: Find the Pareto region S of points that simultaneously minimize the functions f_i(x) over the feasible region, which is given by g_j(x) <= 0, for all j. Applications abound in Engineering, for example, in the design of efficient heat exchangers or of analog circuits. There are numerous methods available for solving the problem. We discuss a method of particular simplicity that nevertheless produces very good results.