TY - JOUR

T1 - Savings based ant colony optimization for the capacitated minimum spanning tree problem

AU - Reimann, Marc

AU - Laumanns, Marco

PY - 2006/6

Y1 - 2006/6

N2 - 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.

AB - 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.

KW - Ant colony Optimization

KW - Capacitated minimum spanning tree problem

U2 - 10.1016/j.cor.2004.11.019

DO - 10.1016/j.cor.2004.11.019

M3 - Article

AN - SCOPUS:27344432541

VL - 33

SP - 1794

EP - 1822

JO - Surveys in Operations Research and Management Science

JF - Surveys in Operations Research and Management Science

SN - 0305-0548

IS - 6

ER -