Abdelkader Ziadi, Samia Khelladi and Yves Cherruault
Classical multidimensional global optimization methods are difficult to implement in high dimensions. To show that the Alienor method coupled with the Brent algorithm can avoid…
Abstract
Purpose
Classical multidimensional global optimization methods are difficult to implement in high dimensions. To show that the Alienor method coupled with the Brent algorithm can avoid this difficulty.
Design/methodology/approach
Use is made of the Alienor method and the Brent algorithm to obtain algorithms that were applied to test functions having several local minima.
Findings
Interesting results concerning the number of evaluation points were obtained. It was shown that this coupling can be improved if α‐dense curves of minimal length were used.
Research limitations/implications
Multidimensional global optimization problems have proven to be difficult to implement in high dimensions. This research continues the search for improved methods by coupling existing established methods such as Alienor with others such as the Brent algorithm.
Originality/value
A new coupled method has been developed and algorithms obtained to tackle such global optimization problems. The coupling is unique and the algorithms are tested numerically on selected functions.
Details
Keywords
Abdelkader Ziadi, Djaouida Guettal and Yves Cherruault
Aims to present study of the coupling of the Alienor method with the algorithm of Piyavskii‐Shubert for global optimization applications.
Abstract
Purpose
Aims to present study of the coupling of the Alienor method with the algorithm of Piyavskii‐Shubert for global optimization applications.
Design/methodology/approach
The Alienor method allows us to transform a multivariable function into a function of a single variable for which it is possible to use an efficient and rapid method for calculating the global optimum. This simplification is based on the use of the established Alienor methodology.
Findings
The Alienor method allows us to transform a multidimensional problem into a one‐dimensional problem of the same type. It was then possible to use the Piyavskii‐Shubert method based on sub‐estimators of the objectives function. The obtained algorithm from coupling the two methods was found to be simple and easy to implement on any multivariable function.
Research limitations/implications
This method does not require derivatives and the convergence of the algorithm is relatively rapid if the Lipschitz constant is small.
Practical implications
The classical multidimensional global optimization methods involve great difficulties for their implementation to high dimensions. The coupling of two established methods produces a practical easy to implement technique.
Originality/value
New method couples two established ones and produces a simple and user‐friendly technique.