A two-phase heuristic coupled DIRECT method for bound constrained global optimization

Abstract

In this paper, we investigate the use of a simple heuristic in the DIRECT method context, aiming to select a set of the hyperrectangles that have the lowest function values in each size group. For solving bound constrained global optimization problems, the proposed heuristic divides the region where the hyperrectangles with the lowest function values in each size group lie into three subregions. From each subregion, different numbers of hyperrectangles are selected depending on the subregion they lie. Subsequently, from those selected hyperrectangles, the potentially optimal ones are identified for further division. Furthermore, the two-phase strategy aims to firstly encourage the global search and secondly enhance the local search. Global and local phases differ on the number of selected hyperrectangles from each subregion. The process is repeated until convergence. Preliminary numerical experiments show that the proposed two-phase heuristic coupled DIRECT method is effective in converging to the optimal solution.FCT – Fundação para a Ciência e Tecnologia within the Projects Scope: UID/CEC/00319/2019 and UID/MAT/ 00013/2013