A branch & bound algorithm for the 0-1 mixed integer knapsack problem with linear multiple choice constraints

Authors:
George Kozanidis;Emanuel Melachrinoudis
Affiliations:
Department of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, 334 Snell Engineering Center Boston, MA;Department of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, 334 Snell Engineering Center Boston, MA
Venue:
Computers and Operations Research
Year:
2004

Citing 3
Cited 1

An O(n) algorithm for the linear multiple choice knapsack problem and related problems

Information Processing Letters
Introduction to algorithms

Introduction to algorithms
A computational study of a multiple-choice knapsack algorithm

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Solving the linear multiple choice knapsack problem with two objectives: profit and equity

Computational Optimization and Applications

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Abstract

This paper presents a branch and bound (B&B) algorithm for the 0-1 mixed integer knapsack problem with linear multiple choice constraints. The formulation arose in an application to transportation management for allocating funds to highway improvements. Several model properties are developed and utilized to design a B&B solution algorithm. The algorithm solves at each node of the B&B tree a linear relaxation using an adaptation of an existing algorithm for the linear multiple choice knapsack problem. The special relationship between the parent and children subproblems is exploited by the algorithm. This results in high efficiency and low storage space requirements. The worst case complexity of the algorithm is analyzed and computational results that demonstrate its efficiency in the average case are reported.