On the benchmarking of multiobjective optimization algorithm

Abstract

The "No Free Lunch" (NFL) theorems state that in average each algorithm has the same performance, when no a priori knowledge of single-objective cost function f is assumed. This paper extends the NFL theorems to the case of multi-objective optimization. Further it is shown that even in cases of a priori knowledge, when the performance measure is related to the set of extrema points sampled so far, the NFL theorems still hold. However, a procedure for obtaining function-dependent algorithm performance can be constructed, the so-called tournament performance, which is able to gain different performance measures for different multiobjective algorithms.