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Kyungpook Mathematical Journal 2024; 64(1): 95-111

Published online March 31, 2024

Copyright © Kyungpook Mathematical Journal.

Polynomial-Filled Function Algorithm for Unconstrained Global Optimization Problems

Salmah, Ridwan Pandiya

Department of Mathematics, Universitas Gadjah Mada, Sekip Utara BLS 21 Yogyakarta 55281, Indonesia
e-mail : syalmah@yahoo.com

Department of Informatics, Institut Teknologi Telkom Purwokerto, Jawa Tengah 53147, Indonesia
e-mail : ridwanpandiya@ittelkom-pwt.ac.id

Received: January 23, 2023; Revised: July 6, 2023; Accepted: January 22, 2024

Abstract

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, non-logarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

Keywords: Global optimization, filled function method, nonlinear programming, global minimizer, auxiliary function approach