Who´s better? PESA or NSGA II?

According to the no free lunch (NFL) theorems all black-box algorithms perform equally well when compared over the entire set of optimization problems. An important problem related to NFL is finding a test problem for which a given algorithm is better than another given algorithm. In this paper we propose an evolutionary approach for solving this problem: we will evolve multi-objective test functions for which a given algorithm A is better than another given algorithm B. The evolved functions are represented as binary strings. Several numerical experiments involving PESA and NSGA II are performed. The results show the effectiveness of the proposed approach. Several multi-objective problems for which PESA performs better than NSGA II and several multi-objective test problems for which NSGA II performs better than PESA have been evolved.