In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operator...

In this paper we introduce a new Packing problem, the Three-Dimensional Knapsack Problem with Balancing Constraints (3BKP), the extension of the ThreeDimensional Knapsack Problem (3KP) where additional constraints related to the packing center of mass are given. The 3BKP consists in orthogonally packing a subset of threedimensional weighted items into a knapsack in order to maximize the total p...

A lot of current research in DNA computing has been directed towards solving hard combinatorial problems. Among them Knapsack problem is one of the most common problems which have been studied intensively in the last decade attracting both theorists and practicians. Fractional Knapsack Problem is easily solvable by greedy strategy, but 0/1 Knapsack Problem is not possible to solve in this metho...

I cannot help but start this review with an analogy between the knapsack problem and the traveling salesman problem (TSP), the two most studied problems of combinatorial optimization. Both problems are easy to explain even to a stranger, both are hard to solve. Each of these problems is important in its own right as well as due to numerous applications. Each of the two problems forms an excelle...

Merkle and Hellman proposed a first knapsack cryptosystem. However, it was broken because the density is not sufficiently high. In this paper, we propose a a new trapdoor in modular knapsack PKC. Proposed scheme can use the message encoding. This method can use the method of enlarging messages over a finite field in order to realize a high density over 1. Keywords— Knapsack public-key cryptosys...

This paper introduces a framework for screening cargo containers for nuclear material at security stations throughout the United States using knapsack problem, reliability, and Bayesian probability models. The approach investigates how to define a system alarm given a set of screening devices, and hence, designs and analyzes next-generation security system architectures. Containers that yield a...

We call any (m+2)-tuple (n, r, r1, . . . , rm) satisfying this equation a binomial knapsack. The problem first came to the authors’ attention when considering a problem on symmetric functions, but the name is derived from the connection to knapsacktype problems. This article considers the simplest case of this problem. That is, we consider the problem of determining all 4-tuples (n, r, s, t) sa...