An iterative dynamic programming approach 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 the temporal knapsack problem (TKP). In this generalization of the classical knapsack problem, selected items enter and leave the knapsack at fixed dates. We solve the TKP with a dynamic program of exponential size, which is solved using a method called Successive Sublimation Dynamic Programming (SSDP). 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 effective method, and that several improvements are needed to compete with the best results from the literature.

Mots clés: Temporal knapsack; Exact algorithm; Lagrangian Relaxation; Successive Sublimation Dynamic Programming method

Domaines: Optimisation et contrôle [math.OC]

François Clautiaux, Boris Detienne, Gaël Guillot. An iterative dynamic programming approach for the temporal knapsack problem. European Journal of Operational Research, 2021, 293 (2), ⟨10.1016/j.ejor.2020.12.036⟩. ⟨hal-02044832v3⟩