The Algorithm to Search for All Local Minima by Using a Coupled Multi-agents System

Abstract

This paper is concerned with a computational method to search for all local minima. In the proposed method, a coupled multi-agents dynamical model is used, in which a single agents moves on the gradient model under repulsion from other agents as well as under repellent from trapped agents on a local minimum. These repulsion and repellent mechanisms are effective to avoid from the discovered local minima and to search for the undiscovered local minimum. Lastly, the behavior of this algorithm is investigated with simulations for several examples.