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 present an approach to connection admission control in single-hop multiservice wireless networks with quality of service (QoS) requirements. The approach consists of two steps: 1) the specification of an admission region that captures the QoS requirements and 2) the formulation of a generalized knapsack problem that captures the connection admission control. To illustrate approach 1), we det...

Motivated by a food promotion problem, we introduce the Knapsack Problem for Perishable Items (KPPI) to address a dynamic problem of optimally filling a knapsack with items that disappear randomly. The KPPI naturally bridges the gap and elucidates the relation between the pspace-hard restless bandit problem and the np-hard knapsack problem. Our main result is a problem decomposition method resu...

A new repair method based on QEA for 0/1 knapsack problems is proposed. In this approach, the qubit chromosome is used as heuristic knowledge to evaluate each element for the knapsack. The main idea is to delete the knapsack elements in the ascending order of qubit chromosome’s probability value whilst avoid violating the constraints on its capacity. To minimize the influence of initialization,...

We examine a situation in which a decision-maker executes a sequence of resource allocation decisions over time, but the availability of the indivisible resources at future epochs is uncertain due to actions of competitors. We cast this problem as a specialized type of stochastic knapsack problem in which the uncertainty of item (resource) availability is induced by competitors concurrently fil...

We present an algorithm for the penalized multiple choice knapsack problem (PMCKP), a combination of the more common penalized knapsack problem (PKP) and multiple choice knapsack problem (MCKP). Our approach is to converts a PMCKP into a PKP using a previously known transformation between MCKP and KP, and then solve the PKP greedily. For PMCKPs with well-behaved penalty functions, our algorithm...

A necessary and sufficient condition for the identification of dominated terms in a general knapsack problem is derived. By general we mean a knapsack problem which is unbounded, equality constrained and which has a parametric right hand side. The given condition yields published results in the literature. A report on computational experiments for large scale knapsack problems, demonstrating th...

This paper considers the application of Bayesian optimisation to well-known multidimensional knapsack problem which is strongly NP-hard. For with a large number items and constraints, two-level formulation presented take advantage global capability approach, efficiency integer programming solvers on small problems. The first level makes decisions about optimal allocation capacities different it...

We propose a new hybrid approach to solve the unbounded integer knapsack problem (UKP), where valid inequalities are generated based on intermediate solutions of an equivalent forward dynamic programming formulation. These inequalities help tighten the initial LP relaxation of the UKP, and therefore improve the overall computational efficiency. We also extended this approach to solve the multi-...