A Modified Seagull Optimization Algorithm for Fixed Point Approximation in Nonlinear Functions
Natasha Clarissa Maharani, Mohamad Muslikh, and Abdul Rouf alghofari

Department of Mathematics, Faculty of Mathematics and Natural Science, Brawijaya University, 65145 Malang, Indonesia

Abstract

This paper proposes a modified version of the Seagull Optimization Algorithm (SOA), called NuM-SOA, to solve nonlinear fixed point problems. The enhancement involves introducing a decay-based parameter &#957- to dynamically control the exploration behavior of the seagulls during the optimization process. The performance of NuM-SOA is evaluated on three fixed point problems and compared against several methods: the original SOA, the Bat Algorithm (BA) as a representative of swarm intelligence techniques, and state-of-the-art mathematical methods including the SuperMann Algorithm and the Extragradient Method. Experimental results demonstrate that NuM-SOA achieves the lowest mean squared error (MSE) in all three problems and offers high precision in identifying fixed points. While the original SOA and BA show competitive behavior in certain cases, NuM-SOA consistently outperforms them, particularly in terms of accuracy and robustness. These results highlight NuM-SOA^s effectiveness and its potential as a powerful tool for solving nonlinear fixed point problems.

Keywords: Fixed Point, Seagulls Optimization Algorithm, Nonlinear Function, Swarm Intelligent

Topic: Mathematics and Mathematics Education