Savings based ant colony optimization for the capacitated minimum spanning tree problem

• Published in: Computers & operations research Vol. 33; no. 6; pp. 1794 - 1822
• Main Authors: REIMANN, Marc, LAUMANNS, Marco
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Science 01.06.2006; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Exact sciences and technology; Flows in networks. Combinatorial problems; Heuristic; Operational research and scientific management; Operational research. Management science; Operations research; Optimization; Studies; Tree(graph); Spanning tree; Vehicle routing problem; NP hard problem; Capacity constraint; Swarm intelligence; Ant colony Optimization; Capacitated minimum spanning tree problem; Minimum spanning tree MST
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2004.11.019

The problem of connecting a set of client nodes with known demands to a root node through a minimum cost tree network, subject to capacity constraints on all links is known as the capacitated minimum spanning tree (CMST) problem. As the problem is NP-hard, we propose a hybrid ant colony optimization (ACO) algorithm to tackle it heuristically. The algorithm exploits two important problem characteristics: (i) the CMST problem is closely related to the capacitated vehicle routing problem (CVRP), and (ii) given a clustering of client nodes that satisfies capacity constraints, the solution is to find a MST for each cluster, which can be done exactly in polynomial time. Our ACO exploits these two characteristics of the CMST by a solution construction originally developed for the CVRP. Given the CVRP solution, we then apply an implementation of Prim's algorithm to each cluster to obtain a feasible CMST solution. Results from a comprehensive computational study indicate the efficiency and effectiveness of the proposed approach. [PUBLICATION ABSTRACT]