The knapsack problem with disjoint multiple‐choice constraints

Vijay Aggarwal, Narsingh Deo, Dilip Sarkar

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this article we consider the binary knapsack problem under disjoint multiple‐choice constraints. We propose a two‐stage algorithm based on Lagrangian relaxation. The first stage determines in polynomial time an optimal Lagrange multiplier value, which is then used within a branch‐and‐bound scheme to rank‐order the solutions, leading to an optimal solution in a relatively low depth of search. The validity of the algorithm is established, a numerical example is included, and computational experience is described.

Original languageEnglish (US)
Pages (from-to)213-227
Number of pages15
JournalNaval Research Logistics (NRL)
Volume39
Issue number2
DOIs
StatePublished - Jan 1 1992

Fingerprint

Knapsack Problem
Disjoint
Lagrangian Relaxation
Lagrange multipliers
Polynomial time
Optimal Solution
Polynomials
Binary
Numerical Examples
Knapsack problem
Experience
Optimal solution
Lagrangian relaxation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research

Cite this

The knapsack problem with disjoint multiple‐choice constraints. / Aggarwal, Vijay; Deo, Narsingh; Sarkar, Dilip.

In: Naval Research Logistics (NRL), Vol. 39, No. 2, 01.01.1992, p. 213-227.

Research output: Contribution to journalArticle

Aggarwal, Vijay ; Deo, Narsingh ; Sarkar, Dilip. / The knapsack problem with disjoint multiple‐choice constraints. In: Naval Research Logistics (NRL). 1992 ; Vol. 39, No. 2. pp. 213-227.
@article{72388efc3ed5407b82fdee84de8eb703,
title = "The knapsack problem with disjoint multiple‐choice constraints",
abstract = "In this article we consider the binary knapsack problem under disjoint multiple‐choice constraints. We propose a two‐stage algorithm based on Lagrangian relaxation. The first stage determines in polynomial time an optimal Lagrange multiplier value, which is then used within a branch‐and‐bound scheme to rank‐order the solutions, leading to an optimal solution in a relatively low depth of search. The validity of the algorithm is established, a numerical example is included, and computational experience is described.",
author = "Vijay Aggarwal and Narsingh Deo and Dilip Sarkar",
year = "1992",
month = "1",
day = "1",
doi = "10.1002/nav.3220390206",
language = "English (US)",
volume = "39",
pages = "213--227",
journal = "Naval Research Logistics Quarterly",
issn = "0028-1441",
publisher = "John Wiley and Sons Inc.",
number = "2",

}

TY - JOUR

T1 - The knapsack problem with disjoint multiple‐choice constraints

AU - Aggarwal, Vijay

AU - Deo, Narsingh

AU - Sarkar, Dilip

PY - 1992/1/1

Y1 - 1992/1/1

N2 - In this article we consider the binary knapsack problem under disjoint multiple‐choice constraints. We propose a two‐stage algorithm based on Lagrangian relaxation. The first stage determines in polynomial time an optimal Lagrange multiplier value, which is then used within a branch‐and‐bound scheme to rank‐order the solutions, leading to an optimal solution in a relatively low depth of search. The validity of the algorithm is established, a numerical example is included, and computational experience is described.

AB - In this article we consider the binary knapsack problem under disjoint multiple‐choice constraints. We propose a two‐stage algorithm based on Lagrangian relaxation. The first stage determines in polynomial time an optimal Lagrange multiplier value, which is then used within a branch‐and‐bound scheme to rank‐order the solutions, leading to an optimal solution in a relatively low depth of search. The validity of the algorithm is established, a numerical example is included, and computational experience is described.

UR - http://www.scopus.com/inward/record.url?scp=84989675145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989675145&partnerID=8YFLogxK

U2 - 10.1002/nav.3220390206

DO - 10.1002/nav.3220390206

M3 - Article

AN - SCOPUS:84989675145

VL - 39

SP - 213

EP - 227

JO - Naval Research Logistics Quarterly

JF - Naval Research Logistics Quarterly

SN - 0028-1441

IS - 2

ER -