Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem
Annals of Operations Research - Special issue on Tabu search
Cyclic transfer algorithms for multivehicle routing and scheduling problems
Operations Research
Formulations and Algorithms for the Capacitated Minimal Directed Tree Problem
Journal of the ACM (JACM)
MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows
New ideas in optimization
A Graph-based Ant system and its convergence
Future Generation Computer Systems
Future Generation Computer Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Savings Based Ant System For The Vehicle Routing Problem
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
D-Ants: savings based ants divide and conquer the vehicle routing problem
Computers and Operations Research
Ant Colony Optimization
Ant colony system: a cooperative learning approach to the traveling salesman problem
IEEE Transactions on Evolutionary Computation
A short convergence proof for a class of ant colony optimizationalgorithms
IEEE Transactions on Evolutionary Computation
Ant system: optimization by a colony of cooperating agents
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
The hyper-cube framework for ant colony optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Operations Research Letters
Enhanced second order algorithm applied to the capacitated minimum spanning tree problem
Computers and Operations Research
Design of capacitated minimum spanning tree with uncertain cost and demand parameters
Information Sciences: an International Journal
Computers and Industrial Engineering
A hybrid algorithm for the vehicle routing problem
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
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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.