Author(s)

Richard A. Formato

Consulting Engineer & Registered Patent Attorney, Cataldo & Fisher LLC (Emeritus), Harwich, MA, USA.

This note describes optimally matching the seminal Fano Load using Central Force Optimization with Negative Gravity. This approach improves the best fitness by more than eighteen percent and suggests that some measure of Negative Gravity should be used in all CFO runs. CFO is a deterministic Global Search and Optimization metaheuristic based on an analogy to gravitational kinematics, the motion of bodies moving under the influence of gravity. Positive gravity causes objects to move towards each other, whereas negative gravity causes them to fly apart. A small amount of negative gravity in CFO improves the algorithm’s exploration of the decision space by sampling regions that have been under-sampled or perhaps not sampled at all. The Fano Load problem illustrates this effect. While the possibility of Negative Gravity was mentioned in the original CFO paper, it was not used until recently when it was injected into optimization runs for Yagi-Uda antenna arrays. The results were compelling and led to the Fano Load problem being revisited.

Central Force Optimization, Fano Load, Negative Gravity, Optimization Metaheuristic, Global Search and Optimization

Formato, R. (2025) Fano Load Redux: CFO with Negative Gravity. Journal of Applied Mathematics and Physics, 13, 2113-2127. doi: 10.4236/jamp.2025.136118.