research-article

An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating

Author:

David BergmanAuthors Info & Claims

INFORMS Journal on Computing, Volume 31, Issue 3

Pages 477 - 492

https://doi.org/10.1287/ijoc.2018.0840

Published: 01 July 2019 Publication History

Abstract

Knapsack problems play a pivotal role in the operations research literature, with various generalizations proposed and studied over the last century. Of recent interest is the quadratic multiknapsack problem (QMKP). Despite a plethora of heuristics, no exact methods for the QMKP have been published in the literature. This paper presents an exact branch-and-price algorithm for the QMKP. Experimental results indicate that the proposed algorithm is far superior, both in terms of solution times and objective function bounds, to state-of-the-art optimization technology solving a standard encoding of the problem. In addition to the algorithmic contribution, this paper studies the optimization problem of seating attendees at events, an operational challenge faced by event organizers. An optimization model for table event seating is shown to be closely related to the QMKP, and computational testing indicates that the proposed algorithm is particularly well suited for this application.

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Cited By

Mehrani SCardonha CBergman D(2022)Models and Algorithms for the Bin-Packing Problem with Minimum Color FragmentationINFORMS Journal on Computing10.1287/ijoc.2021.112034:2(1070-1085)Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1287/ijoc.2021.1120
Berktaş NYaman H(2021)A Branch-and-Bound Algorithm for Team Formation on Social NetworksINFORMS Journal on Computing10.1287/ijoc.2020.100033:3(1162-1176)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1287/ijoc.2020.1000

Index Terms

An Exact Algorithm for the Quadratic Multiknapsack Problem with an Application to Event Seating
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

Index terms have been assigned to the content through auto-classification.

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Published In

cover image INFORMS Journal on Computing

INFORMS Journal on Computing Volume 31, Issue 3

Summer 2019

222 pages

ISSN:1526-5528

DOI:10.1287/ijoc.2019.31.issue-3

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Copyright © 2019, INFORMS.

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 July 2019

Accepted: 21 May 2018

Received: 20 November 2016

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Cited By

Mehrani SCardonha CBergman D(2022)Models and Algorithms for the Bin-Packing Problem with Minimum Color FragmentationINFORMS Journal on Computing10.1287/ijoc.2021.112034:2(1070-1085)Online publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1287/ijoc.2021.1120
Berktaş NYaman H(2021)A Branch-and-Bound Algorithm for Team Formation on Social NetworksINFORMS Journal on Computing10.1287/ijoc.2020.100033:3(1162-1176)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1287/ijoc.2020.1000

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