Abstract
A vehicle routing problem which reduces to an NP-complete set-partitioning problem is considered. Three parallel algorithms for simulated annealing, i.e. the independent, semi-independent and co-operating searches are investigated. The objective is to improve the accuracy of solutions to the problem by applying parallelism. The accuracy of a solution is meant as its proximity to the optimum solution. The empirical evidence supported by the statistical analysis indicate that co-operation of processes in parallel simulated annealing yields more accurate solutions to the vehicle routing problem as compared to the case when the processes run independently or semi-independently.
This research was supported in part by the State Committee for Scientific Research grant BK-280-RAu2-2001. We thank the Wroclaw Centre of Networking and Supercomputing for the computing grant No 04/97, and the Computer Center of the Silesia University of Technology for the similar computing grant which enabled us to obtain the empirical results described in this work.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aarts, E.H.L., and Korst, J.H.M., Simulated annealing and Boltzmann machines, Wiley, Chichester, 1989.
Altinkemer, K., Gavish, Parallel savings based heuristics for the delivery problem, Operations Research 39,3 (May-June 1991), 456–469.
Azencott, R., Parallel simulated annealing: An overview of basic techniques, in Azencott, R. (Ed.), Simulated annealing. Parallelization techniques, J. Wiley, NY, (1992), 37–46.
Boissin, N., and Lutton, J.-L., A parallel simulated annealing algorithm, Parallel Computing 19, (1993), 859–872.
Cěrny, V., A thermodynamical approach to the travelling salesman proble: an efficient simulation algorithm, J. of Optimization Theory and Applic. 45, (1985), 41–55.
Christofides, N., Mignozzi, A., and Toth, P., Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations, Math. Prog. 20, (1981), 255–282.
Clarke, G, and Wright, J., Scheduling of vehicles from a central depot to a number of delivery points, Opens. res. 12, (1964), 568–581.
Czech, Z.J., Parallel simulated annealing for the delivery problem, Proc. of the 9th Euromicro Workshop on Parallel and Distributed Processing, Mantova, Italy, (February 7–9, 2001), 219–226.
Fisher, M.L., and Jaikumar, R., A generalized assignment heuristic for vehicle routing, Networks 11, (1981), 109–124.
Graffigne, C., Parallel annealing by periodically interacting multiple searches: An experimental study, in Azencott, R. (Ed.), Simulated annealing. Parallelization techniques, J. Wiley, NY, (1992), 47–79.
Haimovich, M., and Rinnooy Kan, A., Bounds and heuristics for capacitated routing problems, Math. Opns. Res. 10, (1985), 527–542.
Kirkpatrick, S., Gellat, C.D., and Vecchi, M.P., Optimization by simulated annealing, Science 220, (1983), 671–680.
Lenstra, J., and Rinnooy, K., Complexity of vehicle routing and scheduling problems, Networks11, (1981), 221–227.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E., Equation of state calculation by fast computing machines, Journ. of Chem. Phys. 21, (1953), 1087–1091.
Reeves, C.R., (Ed.) Modern Heuristic Techniques for Combinatorial Problems, McGraw-Hill, London, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Czech, Z.J. (2002). Three Parallel Algorithms for Simulated Annealing. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_23
Download citation
DOI: https://doi.org/10.1007/3-540-48086-2_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43792-5
Online ISBN: 978-3-540-48086-0
eBook Packages: Springer Book Archive