Extending the class of order-k delineable problems for the gene expression messy genetic algorithm

This paper revisits the recently introduced gene expression messy genetic algorithm (GEMGA) and offers some modifications to the extend the class of order-k delineable problems (class of problems that can be solved using a bounded order of relations) in GEMGA. The fundamental components that control the delineability of relations are reviewed in the light of the recently proposed SEARCH framework. Modified class and relation comparison statistics of GEMGA are proposed. The sample complexity of this improved version of GEMGA is shown to be subquadratic. Theoretical conclusions are also substantiated by experimental results for large, multimodal order-k delineable problems with respect to class average comparison statistic. We also present results for the recently constructed Goldberg-Lewei test functions.