We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0–1 knapsack set, the mixed 0–1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a common presentation of the inequalities based on covers and packs and highlight the connections among them. The focus of the paper is on recent re...

The 0/1 Knapsack Problem is an optimization problem solved using various soft computing methods. The solution to the 0/1 Knapsack Problem (KP) can be viewed as the result of a sequence of decisions. Simple Genetic Algorithm (SGA) effectively solves knapsack problem for large data set. But it has problems like premature convergence and population diversity. Dual Population Genetic Algorithm (DPG...

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 problem called the temporal knapsack problem, presents several algorithms for solving it, and compares their performance. The temporal knapsack problem is a generalisation of the knapsack problem and specialisation of the multidimensional (or multiconstraint) knapsack problem. It arises naturally in applications such as allocating communication bandwidth or CPUs in a mul...

Knapsack constraints are a key modeling structure in discrete optimization and form the core of many real-life problem formulations. Only recently, a cost-based filtering algorithm for Knapsack constraints was published that is based on some previously developed approximation algorithms for the Knapsack problem. In this paper, we provide an empirical evaluation of approximated consistency for K...

The widening gap between processors and memory necessitates the development of novel memory hierarchies: hierarchies that can possibly service memory references at register speeds, since service at cache speeds may not be adequate. We consider the design of a novel memory hierarchy component, a knapsack, whose purpose is to provide (very) fast access to frequently-used data objects. Software al...

In the classical deterministic knapsack problem, a knapsack of capacity C is given, together with K classes of objects. For every k = 1, . . . ,K, each object of the class k has a size bk and an associated reward rk. The objects can be placed into the knapsack as long as the sum of their sizes does not exceed the capacity C. The problem consists in placing the objects inside the knapsack so as ...

One of the combinatorial optimization problems is Knapsack problem, which aims to maximize benefit objects whose weight not exceeding capacity knapsack. This paper introduces artificial bee colony algorithm select a subset project and represented by knapsack problem put best investment plan achieve highest profits within determined costs, this one applications financial field. The result from p...

Window functions are used in the estimation of power spectra, [1] and bispectra [2] in order to ensure the consistency of the periodogram and the Fourier type bispectrum estimation methods. In this paper, a three dimensional optimum bias lag window function is introduced in the estimation of the fourth order cumulant spectrum, also called trispectrum, which is estimated from the three dimesiona...