A hybrid meta heuristic algorithm for bi-objective minimum cost flow (BMCF) problem

In this paper we study the bi-objective minimum cost flow (BMCF) problem which can be categorized as multi objective minimum cost flow problems. Generally, the exact computation of the efficient frontier is intractable and there may exist an exponential number of extreme non-dominated objective vectors. Hence, it is better to employ an approximate method to compute solutions within reasonable time. Therefore, we propose a hybrid meta heuristic algorithm (memetic algorithm hybridized with simulated annealing MA/SA) to develop an efficient approach for solving this problem. In order to show the efficiency of the proposed MA/SA some problems have been generated and solved by both the MA/SA and an exact method. It is perceived from this evaluation that the proposed MA/SA outputs are very close to the exact solutions. It is shown that when the number of arcs and nodes exceed 30 (large problems) the MA/SA model will be more preferred because of its strongly shorter computational time in comparison with exact methods.

[1]  G. Rote,et al.  Approximation of convex curves with application to the bicriterial minimum cost flow problem , 1989 .

[2]  C. Goh,et al.  A method for convex curve approximation , 1997 .

[3]  Y. Aneja,et al.  BICRITERIA TRANSPORTATION PROBLEM , 1979 .

[4]  P. Simin Pulat,et al.  Bicriteria network flow problems: Continuous case , 1991 .

[5]  Tapan P. Bagchi,et al.  Multiobjective Scheduling by Genetic Algorithms , 1999 .

[6]  G. Rote,et al.  Sandwich approximation of univariate convex functions with an application to separable convex programming , 1991 .

[7]  Horst W. Hamacher,et al.  Multiple objective minimum cost flow problems: A review , 2007, Eur. J. Oper. Res..

[8]  P. Simin Pulat,et al.  Efficient solutions for the bicriteria network flow problem , 1992, Comput. Oper. Res..

[9]  Günther Ruhe,et al.  Complexity results for multicriterial and parametric network flows using a pathological graph of Zadeh , 1988, ZOR Methods Model. Oper. Res..

[10]  Konstantinos G. Margaritis,et al.  Performance comparison of memetic algorithms , 2004, Appl. Math. Comput..

[11]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[12]  Günther Ruhe,et al.  Flüsse in Netzwerken: Komplexität und Algorithmen , 1988 .

[13]  Lawrence J. Fogel,et al.  Intelligence Through Simulated Evolution: Forty Years of Evolutionary Programming , 1999 .

[14]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[15]  M. C. Puri,et al.  Bi-criteria network problem , 1984 .

[16]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[17]  David K. Smith.  Network Flows: Theory, Algorithms, and Applications , 1994 .

[18]  Antonio Sedeño-Noda,et al.  The biobjective minimum cost flow problem , 2000, Eur. J. Oper. Res..