Balancing Exploration and Exploitation by an Elitist Ant System with Exponential Pheromone Deposition Rule

TL;DR

This paper introduces an exponential pheromone deposition rule in ant system algorithms, demonstrating through stability analysis and simulations that it significantly outperforms the classical constant deposition method in finding optimal routes.

Contribution

The paper proposes a novel exponential pheromone deposition rule and provides stability analysis, empirical parameter tuning, and comparative performance results against the classical approach.

Findings

Exponential deposition outperforms constant deposition in route optimization.

Stability conditions for the ant system are derived via differential equations.

Optimal parameter settings are identified through exhaustive experiments.

Abstract

The paper presents an exponential pheromone deposition rule to modify the basic ant system algorithm which employs constant deposition rule. A stability analysis using differential equation is carried out to find out the values of parameters that make the ant system dynamics stable for both kinds of deposition rule. A roadmap of connected cities is chosen as the problem environment where the shortest route between two given cities is required to be discovered. Simulations performed with both forms of deposition approach using Elitist Ant System model reveal that the exponential deposition approach outperforms the classical one by a large extent. Exhaustive experiments are also carried out to find out the optimum setting of different controlling parameters for exponential deposition approach and an empirical relationship between the major controlling parameters of the algorithm and some features of problem environment.