TITLE:
Pseudorandomness in Central Force Optimization
AUTHORS:
Richard A. Formato
KEYWORDS:
Central Force Optimization (CFO), Pseudorandom Variables (PRV), Global Search and Optimization (GSO), Deterministic Metaheuristics, Decision Space (DS) Exploration
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.12,
December
29,
2025
ABSTRACT: This note examines the utility of pseudorandom variables (prv) in Global Search and Optimization (GSO) using Central Force Optimization (CFO) as an example. Most GSO metaheuristics are stochastic in nature, but not all. CFO is a completely deterministic GSO metaheuristic, but it nevertheless benefits from injecting prv’s, thereby preserving its deterministic nature while improving its decision space (DS) exploration. CFO benefits substantially from the inclusion of a pseudorandom component, that is, a numerical sequence that is precisely known by specification, or by calculation, or both, but which is otherwise arbitrary. The essential requirement is that the sequence be uncorrelated with DS’s topology, so that its effect is to pseudorandomly distribute probes throughout the landscape. While this process may appear to be similar to the randomness in an inherently stochastic algorithm, it is in fact fundamentally different because CFO remains deterministic at every step. Injecting prv’s is not limited to CFO. It is an approach that can be used in any metaheuristic, stochastic or not. In this note three different pseudorandom methods are discussed for CFO (initial probe distribution, repositioning factor, and decision space adaptation). A sample benchmark problem is presented in detail, and summary data are included for a 23-function benchmark suite. In addition, two sample “real world” problems in electromagnetics are presented. CFO’s performance with prv’s is quite good compared to other highly developed, state-of-the-art algorithms.