In this paper we present a new definition on the globally concavized filled function for the continuous global minimization problem, which was modified from that by Ge . A new class of globally concavized filled functions are constructed. These functions contain two easily determinable parameters, which are not dependent on the radius of the basin at the current local minimizer. A randomized algorithm is designed to solve the box constrained continuous global minimization problem basing on the globally concavized filled functions, which can converge asymptotically with probability one to a global minimizer of the problem. Preliminary numerical experiments are presented to show the practicability of the algorithm.
Department of Computer Science and Technology, Fuzhou University, Fuzhou 350002, China