The cross-entropy method for solving bi-criteria network flow problems in discrete-time dynamic networks

References

• R.K. Ahuja, M. Magnanti, and J. Orlin, Network Flows. Theory, Algorithms and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1993.
   Google Scholar
• R.K. Ahuja, J.B. Orlin, S. Pallottino, and M.G. Scutella, Dynamic shortest paths minimizing travel times and costs, Networks 41 (2003), pp. 197–205. doi: 10.1002/net.10072
   Web of Science ®Google Scholar
• A. Azaron and F. Kianfar, Dynamic shortest path in stochastic dynamic networks: Ship routing problem, Eur. J. Oper. Res. 144 (2003), pp. 138–156. doi: 10.1016/S0377-2217(01)00385-X
   Web of Science ®Google Scholar
• R. Batta and S.S. Chiu, Optimal obnoxious paths on a network: Transportation of hazardous materials, Oper. Res. 36 (1988), pp. 84–92. doi: 10.1287/opre.36.1.84
   Web of Science ®Google Scholar
• R.E. Bellman, On a routing problem, Quart. Appl. Math. 16 (1958), pp. 87–90.
   Google Scholar
• H.P. Benson, Vector maximization with two objective functions, J. Optim. Theory Appl. 28(2) (1979), pp. 253–257. doi: 10.1007/BF00933245
   Web of Science ®Google Scholar
• C. Chitra and P. Subbaraj, A nondominated sorting genetic algorithm solution for shortest path routing problem in computer networks, Expert Syst. Appl. 39 (2012), pp. 1518–1525. doi: 10.1016/j.eswa.2011.08.044
   Web of Science ®Google Scholar
• M. Claudio, S. Rocco, and J.E. Ramirez-Marquez, A bi-objective approach for shortest-path network interdiction, Comput. Ind. Eng. 59 (2010), pp. 232–240. doi: 10.1016/j.cie.2010.04.004
   Web of Science ®Google Scholar
• J.C.N. Climaco and E.Q.V. Martins, On the determination of the nondominatedpaths in a multiobjective network problem, Methods Oper. Res. 40 (1981), pp. 255–258
   Google Scholar
• L. Cooke and E. Halsey, The shortest route through a network with time-dependent intermodal transit times, J. Math. Anal. Appl. 14 (1966), pp. 492–498.
   Google Scholar
• H.W. Corley and I.D. Moon, Shortest paths in networks with vector weights, J. Optim. Theory Appl. 46 (1985), pp. 79–86.
   Web of Science ®Google Scholar
• J.R. Current and M. Marsh, Multi objective transportation network design and routing problems: Taxonomy and annotation, Eur. J. Oper. Res. 103 (1993), pp. 426–438.
   Google Scholar
• J.R. Current and H. Min, Multiobjective design of transportation networks: Taxonomy and annotation, Eur. J. Oper. Res. 26 (1986), pp. 187–201. doi: 10.1016/0377-2217(86)90180-3
   Web of Science ®Google Scholar
• K. Deb, Multiobjective Optimization Using Evolutionary Algorithms, Wiley, Chichester, 2001.
   Google Scholar
• M. Desrochers and F. Soumis, A reoptimization algorithm for the shortest path problem with time windows, Eur. J. Oper. Res. 35 (1988), pp. 242–254. doi: 10.1016/0377-2217(88)90034-3
   Web of Science ®Google Scholar
• F. Ergun, R. Sinha, and L. Zhang, An improved FPTAS for restricted shortest path, Inform. Process. Lett. 83 (2002), pp. 287–291.
   Web of Science ®Google Scholar
• L.R. Ford and D.R. Fulkerson, Constructing maximal dynamic flows from static flows, Oper. Res. 6 (1958), pp. 419–433. doi: 10.1287/opre.6.3.419
   Web of Science ®Google Scholar
• L.R. Ford and D.R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
   Google Scholar
• X. Gandibleux, F. Beugnies, and S. Randriamasy, Martins’ algorithm revisited for multi-objective shortest path problems with a MaxMin cost function, Quart. J. Oper. Res. 4 (2006), pp. 47–59. doi: 10.1007/s10288-005-0074-x
   Google Scholar
• K. Ghoseiri and B. Nadjari, An ant colony optimization algorithm for the bi-objective shortest path problem, Appl. Softw. Comput. 10(4) (2010), pp. 1237–1246. doi: 10.1016/j.asoc.2009.09.014
   Web of Science ®Google Scholar
• F. Guerriero and L.D.P. Pugliese, Multi-dimensional labeling approaches to solve the linear fractional elementary shortest path problem with time windows, Optim. Methods Softw. 26(2) (2011), pp. 295–340. doi: 10.1080/10556780903483364
   Web of Science ®Google Scholar
• P. Hansen, Bicriterion path problems, in Multicriteria Decision Making Theory and Applications, G. Fandel and T. Gal, eds., Lecture Notes in Economics and Mathematical Systems, Vol. 177, Springer, Berlin, Heidelberg, 1980, pp. 109–127.
   Google Scholar
• R. Hassin, Approximation schemes for the restricted shortest path problem, Math. Oper. Res. 17 (1992), pp. 36–42. doi: 10.1287/moor.17.1.36
   Web of Science ®Google Scholar
• H. He and G. Song, Optimal paths in dynamic networks with dependent random link travel times, Transp. Res. B 46 (2012), pp. 579–598. doi: 10.1016/j.trb.2012.01.005
   Web of Science ®Google Scholar
• D.P. Kroese and R.Y. Rubinstein, The cross-entropy method for combinatorial optimization, rare event simulation and neural computation, Ann. Oper. Res. 134(1) (2005), pp. 137–151.
   Web of Science ®Google Scholar
• L. Liu, H. Mu, H. Luo, and X. Li, A simulated annealing for multi-criteria network path problems, Comput. Oper. Res. 39(12) (2012), pp. 3119–3135. doi: 10.1016/j.cor.2012.03.013
   Web of Science ®Google Scholar
• D.H. Lorenze and D. Raz, A simple efficient approximation scheme for the restricted shortest path problem, Oper. Res. Lett. 28 (2001), pp. 213–219. doi: 10.1016/S0167-6377(01)00069-4
   Web of Science ®Google Scholar
• E.Q.V. Martins, On a multicriteria shortest path problem, Eur. J. Oper. Res. 16 (1984), pp. 236–245. doi: 10.1016/0377-2217(84)90077-8
   Web of Science ®Google Scholar
• E. Miller-Hooks and H. Mahmassani, Least expected time paths in stochastic, time-varying transportation networks, Transp. Sci. 34(2) (2000), pp. 198–215. doi: 10.1287/trsc.34.2.198.12304
   Web of Science ®Google Scholar
• E. Nasrabadi and S.M. Hashemi, Minimum cost time-varying network flow problems, Optim. Methods Softw. 25(3) (2010), pp. 429–447. doi: 10.1080/10556780903239121
   Web of Science ®Google Scholar
• L.D.P. Pugliese and F. Guerriero, Dynamic programming approaches to solve the shortest path problem with forbidden paths, Optim. Methods Softw., Version of record first published: 21 Nov 2011.
   Web of Science ®Google Scholar
• L.B. Reinhardt and D. Pisinger, Multi-objective and multi-constrained non additive shortest path problems, Comput. Oper. Res. 38(3) (2011), pp. 605–616. doi: 10.1016/j.cor.2010.08.003
   Web of Science ®Google Scholar
• R.Y. Rubinstein and D.P. Kroese, The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning, Springer, New York, 2004.
   Google Scholar
• V.N. Sastry, T.N. Janakiraman, and S.I. Mohideen, New algorithms for multi objective shortest path problem, Opsearch 40 (2003), pp. 278–298.
   Google Scholar
• V.N. Sastry, T.N. Janakiraman, and S.I. Mohideen, Newpolynomial time algorithmsto compute a set of Pareto optimal paths for multi-objective shortest pathproblems, Int. J. Comput. Math. 82 (2005), pp. 289–300.
   Web of Science ®Google Scholar
• C.T. Tung and K.L. Chew, A multicriteria Pareto-optimal path algorithm, Eur. J. Oper. Res. 62 (1992), pp. 203–209. doi: 10.1016/0377-2217(92)90248-8
   Web of Science ®Google Scholar
• A. Warburton, Approximation of Pareto optima in multiple-objective shortest path problems, Oper. Res. 35 (1987), pp. 70–79. doi: 10.1287/opre.35.1.70
   Web of Science ®Google Scholar
• A. Wijerante, M. Turnquist, and P. Mirchandani, Multiobjective routing of hazardous materials in stochastic networks, Eur. J. Oper. Res. 65 (1993), pp. 33–43. doi: 10.1016/0377-2217(93)90142-A
   Web of Science ®Google Scholar
• E. Zitzler, K. Deb, and L. Thiele, Comparison of multi objective evolutionary algorithms: Empirical results, Evol. Comput. 8(2) (2000), pp. 173–195. doi: 10.1162/106365600568202
   PubMed Web of Science ®Google Scholar