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...

This paper considers a distributionally robust version of a quadratic knapsack problem. In this model, a subsets of items is selected to maximizes the total profit while requiring that a set of knapsack constraints be satisfied with high probability. In contrast to the stochastic programming version of this problem, we assume that only part of information on random data is known, i.e., the firs...

Abstract The 0-1 quadratic knapsack problem consists of maximizing a quadratic objective function subject to a linear capacity constraint. To exactly solve large instances of this problem with a tree search algorithm (e.g., a branch and bound method), the knowledge of good lower and upper bounds is crucial for pruning the tree but also for fixing as many variables as possible in a preprocessing...

The maximum profit twoor three-dimensional knapsack packing problem asks to pack a maximum profit subset of some given rectangles or boxes into a larger rectangle or box of fixed dimensions. Items must be orthogonally packed, but no other restrictions are imposed to the problem. The problem could also be considered as a knapsack problem generalized to two or three dimensions. In this paper we p...

In this paper we consider the Knapsack Problem under Uncertainty (KPu). Given a container, the knapsack, characterized by a maximum weight that can be accommodated into and a set of items with given weight and random profit, KPu aims to define the subset of items that can be accommodated into the knapsack such that the sum of the weights of the loaded items does not exceed the knapsack maximum ...

Constraints exist in almost every optimization problem. Different constraint handling techniques have been incorporated with genetic algorithms (GAs), however most of current studies are based on computer experiments. An example is Michalewicz’s comparison among GAs using different constraint handling techniques on the 0-1 knapsack problem. The following phenomena are observed in experiments: 1...

There are many applications of the classical knapsack problem in which the weight of the items being considered for the knapsack are identical, e.g., selecting successful applicants for grants, awarding scholarships to students, etc. Often there are multiple criteria for selecting items to be placed in the knapsack. This paper presents two new algorithms for finding efficient bi-criteria knapsa...

The expected utility knapsack problem is to pick a set of items whose values are described by random variables so as to maximize the expected utility of the total value of the items picked while satisfying a constraint on the total weight of items picked. We consider the following solution approach for this problem: (i) use the sample average approximation framework to approximate the stochasti...

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...