Stochastic shortest path problems with recourse

We consider shortest path problems defined on graphs with random arc costs. We assume that information on arc cost values is accumulated as the graph is being traversed. The objective is to devise a policy that leads from an origin to a destination node with minimal expected cost. We provide dynamic programming algorithms, estimates for their complexity, negative complexity results, and analysis of some possible heuristic algorithms.

[1]  H. Frank,et al.  Shortest Paths in Probabilistic Graphs , 1969, Oper. Res..

[2]  Pitu B. Mirchandani,et al.  Shortest distance and reliability of probabilistic networks , 1976, Comput. Oper. Res..

[3]  J. Croucher.  A note on the stochastic shortest‐route problem , 1978 .

[4]  Leslie G. Valiant,et al.  The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..

[5]  Richard C. Larson,et al.  Urban Operations Research , 1981 .

[6]  Christos H. Papadimitriou,et al.  Games against nature , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[7]  Hossein Soroush,et al.  Optimal paths in probabilistic networks: A case with temporary preferences , 1985, Comput. Oper. Res..

[8]  Refael Hassin,et al.  On Shortest Paths in Graphs with Random Weights , 1985, Math. Oper. Res..

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .

[10]  John N. Tsitsiklis,et al.  The Complexity of Markov Decision Processes , 1987, Math. Oper. Res..

[11]  Giovanni Andreatta,et al.  Stochastic shortest paths with recourse , 1988, Networks.

[12]  Mihalis Yannakakis,et al.  Shortest Paths Without a Map , 1989, ICALP.

[13]  Baruch Schieber,et al.  The Canadian Traveller Problem , 1991, SODA '91.

[14]  John N. Tsitsiklis,et al.  An Analysis of Stochastic Shortest Path Problems , 1991, Math. Oper. Res..

[15]  George H. Polychronopoulos.  Stochastic and dynamic shortest distance problems , 1992 .