Dynamic programming approaches for the temporal knapsack problem

François Clautiaux (1) , Boris Detienne (1) , Gaël Guillot (1)

1 Realopt - Reformulations based algorithms for Combinatorial Optimization

In this paper, we address a problem called temporal knapsack problem. In this generalization of the classical knapsack problem, selected items enter and leave the knapsack at fixed dates. We model this problem as an exponential size dynamic program, which is solved using a method called Successive Sublimation Dynamic Programming (SSDP), proposed by Ibaraki. This method starts by relaxing a set of constraints from the initial problem, and iteratively reintroduces them when needed. We show that a direct application of SSDP to the temporal knapsack problem does not lead to an efficient method. Several techniques are developed to solve difficult instances from the literature: detecting unnecessary states at early stages, choosing the right dimensions to use, partial enumeration in the dynamic program, among others. Using these different refinements, our method is able to improve the best results from the literature on classical benchmarks.

Domaines: Optimisation et contrôle [math.OC]

François Clautiaux, Boris Detienne, Gaël Guillot. Dynamic programming approaches for the temporal knapsack problem. 2019. ⟨hal-02044832v1⟩