Identifying on-line behavior and some sources of difficulty in two competitive approaches for constrained optimization

In this paper, we present an empirical study whose aim is twofold: (1) to analyze the on-line behavior of two state-of-the-art approaches for constrained optimization, whose results provided in a well-known benchmark were competitive, in order to identify features of a problem which makes it difficult to solve when using an evolutionary algorithm and (2) to propose a new set of problems whose features cover those sources of difficulty. The on-line behavior analyzed consists on using three performance measures to know how fast the technique reaches the feasible region and to also know the capabilities of the algorithm to improve feasible solutions previously found. Besides, we analyze the ability of the approaches to maintain diversity (to have solutions inside and outside the feasible region as well). Based on the obtained results we propose a set of eleven test problems (either artificial or real-world problems) taken from the literature in order to re-test the approaches. The results are discussed and some conclusions are drawn.