General Knapsack Problems in a Dynamic Setting.

The world is dynamic and changes over time, thus any optimization problems used to model real life problems must address this dynamic nature. Otherwise, ignoring the dynamicity of the problem will result in locally optimal solutions on the one hand, but inadequate on the other hand. The multistage model was introduced with this goal in mind. In the multistage model we are given a series of instance of an optimization problem, and a solution is provided for each instance. The strive for continuous and similar solutions over time are quantified and integrated into the objective function. In this paper we consider the Generalized Multistage $d$-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem as well as the $d$-Dimensional Knapsack problem. We present a PTAS for Generalized Multistage $d$-Knapsack.