Apply Ant Colony Algorithm to Search All Extreme Points of Function

To find all extreme points of multimodal functions is called extremum problem, which is a well known difficult issue in optimization fields. Applying ant colony optimization (ACO) to solve this problem is rarely reported. The method of applying ACO to solve extremum problem is explored in this paper. Experiment shows that the solution error of the method presented in this paper is less than 10^-8. keywords: Extremum Problem; Ant Colony Optimization (ACO)

💡 Research Summary

The paper addresses the problem of locating all extreme points (both local maxima and minima) of multimodal continuous functions, a task commonly referred to as the extremum problem. While numerous meta‑heuristic methods such as Genetic Algorithms, Simulated Annealing, and Particle Swarm Optimization have been applied to global optimization, they typically focus on finding a single optimum and are not well suited for exhaustively enumerating every extreme point. The authors propose a novel adaptation of Ant Colony Optimization (ACO) that transforms the continuous search space into a discrete set of intervals and exploits the collective behavior of artificial ants to progressively narrow the search region around the true extrema.

The algorithm begins by partitioning the domain (