A covering method for continuous global optimisation. (7th September 2021) - Ziadi, Raouf; Becherif-Madani, Abdelatif
In this paper, we improve the reducing transformation method for solving a large class of global optimisation problems. The reducing transformation method allows us to transform a multidimensional problem into a one-dimensional one of the same type, and then use the one-dimensional Evtushenko algorithm to obtain the global minimum. To accelerate the corresponding mixed algorithm (Reducing transformation-Evtushenko), we have incorporated the Hook-Jeeves algorithm to explore promising regions. Our approach is suitable for solving a large class of global optimisation problems on a rectangle of ℝ n where the objective function is only continuous. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy δ > 0. Numerical experiments are achieved on some typical test problems and a comparison with well known methods is carried out to show the performance of our algorithm.