Abstract
The paper considers sequencing problems, the traveling salesman problem being their natural representative. It studies a rollout approach that employs a cyclic heuristic as its main base algorithm. The theoretical analysis establishes that it is guaranteed to improve (at least in a weak sense) the quality of any feasible solution to a given sequencing problem. Besides other applications, the paper shows that it is well suited for applications that are embedded in dynamic and stochastic environments. The computational performance of the approach is investigated with applications to two stochastic routing problems. The dynamic version of the heuristic appears to be the first algorithm available in the literature to approximately solve a variant of one of these problems.
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References
Barr, S., B.L. Golden, J.P. Kelly, M.G.C. Resende, and W.R. Stewart. (1995). “Designing and Reporting on Computational Experiments with Heuristic Methods.” Journal of Heuristics 1, 9–32.
Bertsekas, D.P. (1995). Dynamic Programming and Optimal Control. Vols. I and II Belmont: Athena Scientific.
Bertsekas, D.P. (1998). Network Optimization: Continuous and Discrete Models. Belmont: Athena Scientific.
Bertsekas, D.P. and D.A. Castanon. (1998). “Rollout Algorithms for Stochastic Scheduling Problems.” Journal of Heuristics 5, 89–108.
Bertsekas, D.P. and J.N. Tsitsiklis. (1996). Neuro-Dynamic Programming. Belmont: Athena Scientific.
Bertsekas, D.P., J.N. Tsitsiklis, and C. Wu. (1997). “Rollout Algorithms for Combinatorial Optimization.” Journal of Heuristics 3, 245–262.
Bertsimas, D.J. (1992). “AVehicle Routing Problem with Stochastic Demands.” Operations Research 40, 574–585.
Bertsimas, D.J., P. Chervi, and M. Peterson. (1995). “Computational Approaches to Stochastic Vehicle Routing Problems.” Transportation Science 29, 342–252.
Bertsimas, D.J. and R. Demir. (2002). “An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems.” Management Science 48, 550–565.
Bertsimas, D.J., P. Jaillet, and A. Odoni. (1990). “A Priori Optimization.” Operations Research 38, 1019–1033.
Bertsimas, D.J. and I. Popescu. (2000). “Revenue Management in a Dynamic Network Environment.” Forthcoming in Transportation Science.
Bertsimas, D.J. and D. Simchi-Levi. (1996). “A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty.” Operations Research 44, 216–304.
Bertsimas, D.J., C.P. Teo, and R. Vohra. (1998). “Greedy, Randomized and Approximate Dynamic Programming Algorithms for Facility Location Problems.” Technical Report, MIT, Cambridge, MA.
Fisher, M. (1995). “Vehicle Routing.” In M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (eds.), Network Routing,Vol.8 of Handbooks in Operations Research and Management Science. Amsterdam: Elsevier.
Garey, M.R. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: Freeman.
Gendreau, M., G. Laporte, and R. Séguin. (1995). “An Exact Algorithm for the Vehicle Routing Problem with Stochastic Demands and Customers.” Transportation Science 29, 143–155.
Gendreau, M., G. Laporte, and R. Séguin. (1996). “Stochastic Vehicle Routing.” European Journal of Operational Research 88, 3–12.
Glover, F. (1998a). Personal Communication.
Glover, F. (1998b). “A Template for Scatter Search and Path Relinking.” In J.-K. Hao, E. Lutton, E. Ronald, M. Schoenauer, and D. Snyers (eds.), Artificial Evolution, Lecture Notes In Computer Science, 1363. Berlin: Springer-Verlag.
Glover, F. and M. Laguna. (1997). Tabu Search. Boston: Kluwer.
Golden, B.L. and A.A. Assad (eds.). (1988). Vehicle Routing: Methods and Studies. Amsterdam: North-Holland.
Haimovich, M. and A.H.G. Rinnooy Kan. (1985). “Bounds and Heuristics for Capacitated Routing Problems.” Mathematics of Operations Research 10, 527–542.
Held, M. and R.M. Karp. (1962). “A Dynamic Programming Approach to Sequencing Problems.” Journal of the Society for Industrial and Applied Mathematics 10, 225–248.
Jayawardena, T. and S. Yakowitz. (1996). “Methodology for Stochastic Graph Completion-Time Problems.” INFORMS Journal on Computing 8, 331–343.
Kao, E.P.C. (1978). “A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem.” Operations Research 26, 1033–1045.
Laporte, G. (1992). “The Vehicle Routing Problem: An Overview of Exact and Approximate Algorithms.” European Journal of Operational Research 59, 345–358.
Lawler, E.L., J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys (eds.). (1985). The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Chichester: Wiley.
McGovern, A. and E. Moss. (1999). “Scheduling Straight-Line Code Using Reinforcement Learning and Rollouts.” Advances in Neural Information Processing Systems 11, 903–909.
Nemhauser, G.L. and L.A. Wolsey. (1988). Integer and Combinatorial Optimization. New York: Wiley.
Powell, W.B., P. Jaillet, and A. Odoni. (1995). “Stochastic and Dynamic Networks and Routing.” In M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (eds.), Network Routing, Vol. 8 of Handbooks in Operations Research and Management Science. Amsterdam: Elsevier.
Psaraftis, H.N. (1995). “Dynamic Vehicle Routing.” Annals of Operations Research 61, 143–164.
Savelsbergh, M.W.P. and M. Goetschalckx. (1995). “A Comparison of the Efficiency of Fixed versus Variable Vehicle Routes.” Journal of Business Logistics 16, 163–187.
Secomandi, N. (1998). “Exact and Heuristic Dynamic Programming Algorithms for the Vehicle Routing Problem with Stochastic Demands.” Ph.D. Thesis, University of Houston, Houston, TX.
Secomandi, N. (2000). “Comparing Neuro-Dynamic Programming Algorithms for the Vehicle Routing Problem with Stochastic Demands.” Computers and Operations Research 27, 1201–1225.
Secomandi, N. (2001). “A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands.” Operations Research 49, 796–802.
Stewart, W.R. and B.L. Golden. (1983). “Stochastic Vehicle Routing: A Comprehensive Approach.” European Journal of Operational Research 14, 371–385.
Sutton, R. and A.S. Barto. (1998). Reinforcement Learning. Cambridge: MIT Press.
Tesauro, G. and G.R. Galperin. (1997). “On-Line Policy Improvement Using Monte Carlo Search.” Advances in Neural Information Processing Systems 9, 1068–1074.
Yang, W.H., K. Mathur, and R.H. Ballou. (2000). “Stochastic Vehicle Routing with Restocking.” Transportation Science 34, 99–112.
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Secomandi, N. Analysis of a Rollout Approach to Sequencing Problems with Stochastic Routing Applications. Journal of Heuristics 9, 321–352 (2003). https://doi.org/10.1023/A:1025605803490
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DOI: https://doi.org/10.1023/A:1025605803490