Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Towards Stochastic Constraint Programming: A Study of Online Multi-choice Knapsack with Deadlines
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows
Transportation Science
Regrets only! online stochastic optimization under time constraints
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Online stochastic and robust optimization
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Online stochastic optimization in the large: application to kidney exchange
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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This paper considers online stochastic reservation problems, where requests come online and must be dynamically allocated to limited resources in order to maximize profit. Multi-knapsack problems with or without overbooking are examples of such online stochastic reservations. The paper studies how to adapt the online stochastic framework and the consensus and regret algorithms proposed earlier to online stochastic reservation systems. On the theoretical side, it presents a constant sub-optimality approximation of multi-knapsack problems, leading to a regret algorithm that evaluates each scenario with a single mathematical programming optimization followed by a small number of dynamic programs for one-dimensional knapsacks. On the experimental side, the paper demonstrates the effectiveness of the regret algorithm on multi-knapsack problems (with and without overloading) based on the benchmarks proposed earlier.