ARS Combination with an Evolutionary Algorithm for Solving MINLP Optimization Problems

Adaptive Random Searches (ARS) are simple and effective optimization methods used for handling complicated nonconvex / multimodal nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. ARS iteratively adapt search characteristics according to the past successful / failure steps. Periodic search domain expansions and contractions improve significantly the reliability in locating the global optimum. However, most of the ARS parameters are apriori set, and then the algorithm cannot be used at their maximum effectiveness. The present paper proposes a combination of ARS with parallel search in competitive members ('families') and an evolutive algorithm (EA) to automatically adapt ARS parameters and search characteristics. The analysis is applied to the MMA-ARS of Maria [1,2] adapted in the form of MMAMI for handling MINLP problems, and then coupled as MMAMI-EA rule. The effectiveness, expressed as computational effort and reliability in locating the global solution, is checked for comparison with genetic algorithms (GA), simulated annealing (SA), ARS, and EA reported results in solving six MINLP test problems. While MMAMI reports a significant decrease of computational effort comparatively with ES, GA, and SA, the combination MMAMI-EA considerably improves the search reliability.