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 ...

When investing in cyber security resources, information security managers have to follow effective decision-making strategies. We refer to this as the cyber security investment challenge. In this paper, we consider three possible decision-support methodologies for security managers to tackle this challenge. We consider methods based on game theory, combinatorial optimisation and a hybrid of the...

Integer programming-based local search (IPbLS) is a metaheuristic recently proposed for solving linear combinatorial optimization problems. IPbLS is basically the same as the first-choice hillclimbing except for using integer programming for neighbor generation. Meanwhile, the multidimensional knapsack problem (MKP) is one of the most well-known linear combinatorial optimization problems and ha...

Real-time multimedia applications such as video and audio streaming, video conferencing and online collaboration are becoming increasingly popular. In order to guarantee effective support of many of these applications, the Internet must provide absolute Quality of Service (QoS) guarantees for such parameters as network bandwidth and end-to-end delay by incorporating session admission control, s...

Cryptosystems based on the knapsack problem were among the first public-key systems to be invented. Their high encryption/ decryption rate attracted considerable interest until it was noticed that the underlying knapsacks often had a low density, which made them vulnerable to lattice attacks, both in theory and practice. To prevent low-density attacks, several designers found a subtle way to in...

Fitness landscape analysis techniques are used to better understand the influence of genetic representations and associated variation operators when solving a combinatorial optimization problem. Five representations are investigated for the Multidimensional Knapsack problem. Common mutation operators (like bit-flip mutation) and classic 1-point and uniform crossover are employed to generate fit...

The need of totally secure online auction has led to the invention of many auction protocols. But as new attacks are developed, auction protocols also require corresponding strengthening. We analyze the auction protocol based on the well-known mathematical public-key knapsack problem for the design of asymmetric public-key knapsack trapdoor cryptosystem. Even though the knapsack system is not c...

We address in this paper the problem of modifying both profits and costs of a fractional knapsack problem optimally such that a prespectified solution becomes an optimal solution with prespect to new parameters. This problem is called the inverse fractional knapsack problem. Concerning the l1-norm, we first prove that the problem is NP -hard. The problem can be however solved in quadratic time ...

It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of th...

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...