Using Co-solvability to Model and Exploit Synergetic Effects in Evolution

We introduce, analyze, and experimentally verify the concept of co-solvability, meant as the ability of a solution maintained by an evolutionary run to solve (correctly process) a pair of fitness cases (tests). The method based on this concept can be considered as a second-order implicit fitness sharing, where solutions compete for the rewards granted for solving pairs of tests, rather than single tests. We prove that co-solvability fitness function is by definition synergistic and imposes selection pressure which is qualitatively different from that induced by standard fitness function or implicit fitness sharing. The results of experimental verification on eight genetic programming tasks demonstrate that evolutionary runs driven by the proposed fitness function usually converge faster to global optima than other methods.