Understanding ant colony optimization search through local optima networks

Abstract

The behavior of Ant Colony Optimization (ACO) algorithms is based on a collective learning process defined by a pheromone mechanism. This process is difficult to understand due to the scheduling of pheromone deposition and evaporation, the influence of parameter values, the bias in solution construction, and the problem instance size. This work aims to extend Local Optima Networks (LONs) to understand the path traversed by the pheromone learning mechanism in the fitness landscape described by ACO algorithms. Our ant-based LONs incorporate a definition of network edges that expresses the persistence of the pheromone influence in the search process. Also, we study a simplified network, Deposit LON, that contains only nodes that deposit pheromones. We aim to analyze a population-based search algorithm’s exploitation and exploration behavior through its network features. We evaluate our proposal on a Ant System algorithm coupled with a Lin-Kernighan local search for solving the Traveling Salesman Problem. The comparative analysis of the networks reflects the exploration/exploitation balance of the algorithms, indicating the exploratory behavior of the Ant System. We study networks generated under different pheromone influence persistence levels and conclude that this setting does not significantly affect the overall network structure. To complement our analysis, we present plots of the generated networks, a detailed report of their metrics, and a comparison with other algorithms’s LONs. Our work contributes to providing a tool for analyzing ant-based algorithms’ search performance using LONs.