A covering method for continuous global optimisation. (7th September 2021)

• Record Type: Journal Article
• Authors: Ziadi, Raouf; Becherif-Madani, Abdelatif
• Is Part Of: International journal of computing science and mathematics. Volume 13:Number 4(2021)
• Page Start: 369
• Page End: 390
• Publication Date: 2021-09-07
• Subjects: global optimisation -- covering algorithm -- reducing transformation method -- α-dense curves -- Evtushenko's algorithm -- Hooke-Jeeves algorithm; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

Abstract

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.