Abstract
Traditionally, minimum cost transshipment problems have been simplified as linear cost problems, which are not practical in real applications. Some advanced local search algorithms have been developed to solve concave cost bipartite network problems. These have been found to be more effective than the traditional linear approximation methods and local search methods. Recently, a genetic algorithm and an ant colony system algorithm were employed to develop two global search algorithms for solving concave cost transshipment problems. These two global search algorithms were found to be more effective than the advanced local search algorithms for solving concave cost transshipment problems. Although the particle swarm optimization algorithm has been used to obtain good results in many applications, to the best of our knowledge, it has not yet been applied in minimum concave cost network flow problems. Thus, in this study, we employ an arc-based particle swarm optimization algorithm, coupled with some genetic algorithm and threshold accepting method techniques, as well as concave cost network heuristics, to develop a hybrid global search algorithm for efficiently solving minimum cost network flow problems with concave arc costs. The proposed algorithm is evaluated by solving several randomly generated network flow problems. The results indicate that the proposed algorithm is more effective than several other recently designed methods, such as local search algorithms, genetic algorithms and ant colony system algorithms, for solving minimum cost network flow problems with concave arc costs.
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References
Yan S., Luo S.C.: A tabu search-based algorithm for concave cost transportation network problems. J. Chin. Inst. Eng. 21, 327–335 (1998)
Yan S., Luo S.C.: Probabilistic local search algorithms for concave cost transportation network problems. Eur. J. Oper. Res. 117, 511–521 (1999)
Ahuja R.K., Maganti T.L., Orlin J.B.: Network Flows, Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs (1993)
Garey M.R., Johnson D.S.: Computers and Intractability: A Guide to The Theory of NP-Completeness. WH Freeman and Co, San Francisco (1979)
Jordan, W.C.: Scale economies on multi-commodity networks. GMR-5579, Operating Systems Research Dept., GM Research Laboratories (1986)
Thach P.T.: A decomposition method using a pricing mechanism for min concave cost flow problems with a hierarchical structure. Math. Programm. 53, 339–359 (1992)
Gallo G., Sandi C.: Adjacent extreme flows and application to min concave cost flow problems. Networks 9, 95–121 (1979)
Gallo G., Sandi C., Sodini C.: An algorithm for the min concave cost flow problem. Eur. J. Oper. Res. 4, 248–255 (1980)
Bazlamacci C., Hindi K.: Enhanced adjacent extreme-point search and tabu search for the minimum concave cost uncapacitated transshipment problem. J. Oper. Res. Soc. 47, 1150–1165 (1996)
Yan S., Juang D.H., Chen C.R., Lai W.S.: Global and local search algorithms for concave cost transshipment problems. J. Global. Optim. 33(1), 123–156 (2005)
Goldberg D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA (1989)
Yan, S., Shih, Y.L., Wang, C.L.: An ant colony system-based hybrid algorithm for square root concave cost transshipment problems. J. Eng. Optim. (2009) (in press)
Fonte D.B.M.M., Gonçalves J.F.: Heuristic solutions for general concave minimum cost network flow problems. Networks 50(1), 67–76 (2007)
Kennedy J., Eberhart R.C.: Particle swarm optimization. IEEE Int. Conf. Neural Netw. IV, 1942–1948 (1995)
Reynolds C.: Flocks, herds and schools: a distributed behavioral model. Comp. Graph. 21, 25–34 (1987)
Heppner, F., Grenander, U.: A stochastic nonlinear model for coordinated bird flocks. In: Krasner, S. (ed.) The Ubiquity of Chaos. AAAS Publications, Washington (1990)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: The Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. IEEE service center, Piscataway, NJ, Nagoya, Japan (1995)
Kennedy J., Eberhart R.C.: A discrete binary version of the particle swarm optimization. IEEE Int. Conf. Neural Netw. V, 4104–4108 (1997)
Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: IEEE International Conference on Evolutionary Computation, pp. 69–73. IEEE Press, Piscataway, NJ (1998)
Shi, Y., Eberhart, R.C.: Particle swarm optimization: developments, applications, and resources. In: Proceedings of the Congress on Evolutionary Computation 2001 IEEE Service Center, Piscataway, NJ, Seoul, Korea (2001)
Shi Y.: Particle swarm optimization. IEEE Connect. 2, 8–13 (2004)
Kennedy, J., Spears, W.: Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. In: IEEE World Congress on Computational Intelligence, pp. 74–77 (1998)
Shi, Y., Eberhart, R.C.: Parameter selection in particle swarm optimization. In: Evolutionary Programming VII: Proceedings of the EP 98, pp. 591–600. Springer-Verlag, New York (1998)
Salerno, J.: Using the particle swarm optimization technique to train a recurrent neural model. In: Ninth IEEE International Conference on Tools with Artificial Intelligence, pp. 45–49 (1997)
Yan S., Yang D.H.: A decision support framework for handling schedule perturbation. Transp. Res. 30B, 405–419 (1996)
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Yan, S., Shih, YL. & Lee, WT. A particle swarm optimization-based hybrid algorithm for minimum concave cost network flow problems. J Glob Optim 49, 539–559 (2011). https://doi.org/10.1007/s10898-010-9548-2
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DOI: https://doi.org/10.1007/s10898-010-9548-2