This paper is dedicated to a study of different extensions of the classical knapsack problem to the case when different elements of the problem formulation are subject to a degree of uncertainty described by random variables. This brings the knapsack problem into the realm of stochastic programming. Two different model formulations are proposed, based on the introduction of probability constrai...

The knapsack problems are a classic NP-hard problem in the combinational optimization. Inspired by the conclusion of the cognitive psychology about the human memory system, a Tabu Search method based on Double Tabu-List (DTL-TS) has been proposed to solve it. With the addition of the search strategy of intensification and diversification, the excellent experiment results have been gotten. Compa...

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Besides being important in its own right, the semi-continuous knapsack problem arises in a number of other contexts, e.g. it is a relaxation of general mixed-integer programming. We show how strong inequalities valid for the semi-continuous knapsack ...

The knapsack problem and the minimum spanning tree problem are both fundamental in operations research and computer science. We are concerned with a combination of these two problems. That is, we are given a knapsack of a fixed capacity, as well as an undirected graph where each edge is associated with profit and weight. The problem is to fill the knapsack with a feasible spanning tree such tha...

In this note we study packing or covering integer programs with at most k constraints, which are also known as k-dimensional knapsack problems. For integer k > 0 and real ǫ > 0, we observe there is a polynomial-sized LP for the k-dimensional knapsack problem with integrality gap at most 1+ ǫ. The variables may be unbounded or have arbitrary upper bounds. In the (classical) packing case, we can ...

The Temporal Knapsack Problem (TKP) is a generalization of the standard Knapsack Problem where a time horizon is considered, and each item consumes the knapsack capacity during a limited time interval only. In this paper we solve the TKP using what we call a Recursive Dantzig-Wolfe Reformulation (DWR) method. The generic idea of Recursive DWR is to solve a Mixed Integer Program (MIP) by recursi...