Ant colony optimization for Chinese postman problem

Abstract

This paper aims to solve the Chinese Postman Problem (CPP) using an Ant Colony Optimization (ACO) algorithm. In graph theory, the CPP looks for the shortest closed path that visits every edge of a connected undirected graph. This problem has many applications, including route optimization, interactive system analysis, and flow design. Although numerous algorithms aimed at solving CPP are present in the literature, very few meta-heuristic algorithms are proposed, and no ACO applications have been proposed to solve them. This paper tries to fill this gap by presenting an ACO algorithm that solves CPP (ACO-CPP). To prove its consistency and effectiveness, ACO-CPP is compared with a Genetic Algorithm (GA) and a recursive algorithm throughout three experiments: (1) recursive-ACO-GA comparisons over randomly generated graphs for the attainment of the global optimum; (2) ACO-GA statistical comparisons over specifically generated graphs; (3) recursive-ACO-GA comparisons by changing ACO hyperparameters over randomly generated graphs for the attainment of the global optimum. The experiments prove that the ACO-CPP algorithm is efficient and exhibits a consistency similar to GA when the number of possible solutions to explore is relatively low. However, when that number greatly exceeds those explored, ACO outperforms GA. This suggests that ACO is more suitable for solving problems with a CPP structure.