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

  • Authors:

  • Marc Reimann;Marco Laumanns

  • Affiliations:

  • Institute for Operations Research, Swiss Federal Institute of Technology Zurich, Clausiusstrasse 47, CH-8092 Zurich, Switzerland;Institute for Operations Research, Swiss Federal Institute of Technology Zurich, Clausiusstrasse 47, CH-8092 Zurich, Switzerland

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2006

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Abstract

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.