Feasibility Structure Modeling: An Effective Chaperone for Constrained Memetic Algorithms

An important issue in designing memetic algorithms (MAs) is the choice of solutions in the population for local refinements, which becomes particularly crucial when solving computationally expensive problems. With single evaluation of the objective/constraint functions necessitating tremendous computational power and time, it is highly desirable to be able to focus search efforts on the regions where the global optimum is potentially located so as not to waste too many function evaluations. For constrained optimization, the global optimum must either be located at the trough of some feasible basin or some particular point along the feasibility boundary. Presented in this paper is an instance of optinformatics where a new concept of modeling the feasibility structure of inequality-constrained optimization problems-dubbed the feasibility structure modeling-is proposed to perform geometrical predictions of the locations of candidate solutions in the solution space: deep inside any infeasible region, nearby any feasibility boundary, or deep inside any feasible region. This knowledge may be unknown prior to executing an MA but it can be mined as the search for the global optimum progresses. As more solutions are generated and subsequently stored in the database, the feasibility structure can thus be approximated more accurately. As an integral part, a new paradigm of incorporating the classification-rather than the regression-into the framework of MAs is introduced, allowing the MAs to estimate the feasibility boundary such that effective assessments of whether or not the candidate solutions should experience local refinements can be made. This eventually helps preventing the unnecessary refinements and consequently reducing the number of function evaluations required to reach the global optimum.