Exact algorithms on reliable routing problems under uncertain topology using aggregation techniques for exponentially many scenarios

• Published in: Annals of operations research Vol. 249; no. 1-2; pp. 141 - 162
• Main Authors: Huang, Zhouchun, Zheng, Qipeng P., Pasiliao, Eduardo L., Simmons, Daniel
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2017; Springer; Springer Nature B.V
• Subjects: Algorithms; Approximation; Benders decomposition; Business and Management; Combinatorics; Computer networks; Costs; Dynamic programming; Failure; Mathematical models; Network management systems; Network topologies; Networks; Operations research; Operations Research/Decision Theory; Optimization; Routing; Routing (telecommunications); S.I.: Pardalos60; Shortest path algorithms; Studies; Theory of Computation; Topology; Travel; Traveling salesman problem; Shortest path problem; Traveling salesman problem; Benders decomposition; Reliable routing; Arc failures; Compact formulation
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-016-2244-y

Network routing problems are often modeled with the assumption that the network structure is deterministic, though they are often subject to uncertainty in many real-life scenarios. In this paper, we study the traveling salesman and the shortest path problems with uncertain topologies modeled by arc failures. We present the formulations that incorporate chance constraints to ensure reliability of the selected route considering all arc failure scenarios. Due to the computational complexity and large scales of these stochastic network optimization problems, we consider two cutting plane methods and a Benders decomposition algorithm to respectively solve them. We also consider to solve the reformulations of the problems obtained by taking the logarithm transformation of the chance constraints. Numerical experiments are performed to obtain results for comparisons among these proposed methods.