In this paper we study and solve two different variants of static knapsack problems with random weights: The stochastic knapsack problem with simple recourse as well the stochastic knapsack problem with probabilistic constraint. Special regard is given the corresponding continuous problems and three different problem solving methods are presented. The resolution of the continuous problems serve...

The basic Merkle-Hellman additive trapdoor knapsack public-key cryptosystem was recently shown to be insecure, and attacks have also been developed on stronger variants of it, such as the Graham-Shamir system and the iterated knapsack cryptosystem. This paper shows that some simple variants of another Merkle-Hellman system, the multiplicative knapsack cryptosystem, are insecure. It is also show...

We study the Knapsack Problem with Conflict Graph (KPCG), an extension of the 0-1 Knapsack Problem, in which a conflict graph describing incompatibilities between items is given. The goal of the KPCG is to select the maximum profit set of compatible items while satisfying the knapsack capacity constraint. We present a new Branch-and-Bound approach to derive optimal solutions to the KPCG in shor...

We consider the distributed version of the Multiple Knapsack Problem (MKP), wherem items are to be distributed amongst n processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff between time and message complexities. The algorithms are based on the greedy approach of assigning the best item to the knapsack with the largest capacity. These algor...

In this paper we study an exact separation algorithm for mixed knapsack sets with the aim of evaluating its effectiveness in a cutting plane algorithm for Mixed-Integer Programming. First proposed by Boyd in the 90’s, exact knapsack separation has recently found renewed interest. In this paper we present a “lightweight” exact separation procedure for mixed knapsack sets and perform a computatio...

This paper considers knapsack problem with fuzzy weights, says fuzzy knapsack problem (FKP). Here we introduce possibility index which gives the possibility of choosing the items with fuzzy weights for knapsack with crisp capacity. In this paper a dynamic programming technique has been introduced to optimize the utility value of objective function. An algorithm has been proposed which gives the...

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 ...

Mathematical models of biogeography inspired the development of the biogeography-based optimization algorithm. In this article we propose a binary version of biogeography-based optimization (BBO) for the Knapsack Problem. Two new mutation operators are proposed to extend the biogeography-based optimization algorithm to binary optimization problems. We also demonstrate the performance of the res...

The Three-Dimensional Knapsack Packing Problem consists of finding the maximum profit for packing a subset of boxes in a larger box (packing box). The boxes to pack are rectangular but of different sizes. This problem is a variant of the Knapsack Problem and therefore its computational complexity is NP-Complete. This article shows a parallel genetic algorithm based on the Island Model and the N...

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation...