Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models
Computational & Mathematical Organization Theory
Resource Constrained Shortest Paths
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Multi-objective and multi-constrained non-additive shortest path problems
Computers and Operations Research
Computers and Operations Research
Route finder: efficiently finding k shortest paths using constraint programming
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Using dominators for solving constrained path problems
PADL'06 Proceedings of the 8th international conference on Practical Aspects of Declarative Languages
Shorter path constraints for the resource constrained shortest path problem
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Constraint-Based local search for constrained optimum paths problems
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
An overview of constraint-based path selection algorithms for QoS routing
IEEE Communications Magazine
Performance evaluation of constraint-based path selection algorithms
IEEE Network: The Magazine of Global Internetworking
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We present an exact solution approach to the constrained shortest path problem with a super additive objective function. This problem generalizes the resource constrained shortest path problem by considering a cost function c(·) such that, given two consecutive paths P1 and P2, c(P1∪P2)≥c(P1)+c(P2). Since super additivity invalidates the Bellman optimality conditions, known resource constrained shortest path algorithms must be revisited. Our exact solution algorithm is based on a two stage approach: first, the size of the input graph is reduced as much as possible using resource, cost, and Lagrangian reduced-cost filtering algorithms that account for the super additive cost function. Then, since the Lagrangian relaxation provides a tight lower bound, the optimal solution is computed using a near-shortest path enumerative algorithm that exploits the lower bound. The behavior of the different filtering procedures are compared, in terms of computation time, reduction of the input graph, and solution quality, considering two classes of graphs deriving from real applications.