An integer programming column generation principle for heuristic search methods

There is an increasing interest in integrating column generation and heuristic approaches to efficiently solve large‐scale discrete optimisation problems. We contribute in this direction. Based on the insights from Lagrangian duality theory, we present an auxiliary problem that can be used for findi...

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Bibliographic Details
Published inInternational transactions in operational research Vol. 27; no. 1; pp. 665 - 695
Main Authors Zhao, Yixin, Larsson, Torbjörn, Rönnberg, Elina
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.01.2020
Subjects
column generation
Columnar structure
Heuristic
Heuristic methods
Integer programming
large neighbourhood search
Mathematical models
matheuristics
metaheuristics
Operations research
Optimization
Production scheduling
Resource allocation
Search methods
Transportation problem
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Summary:There is an increasing interest in integrating column generation and heuristic approaches to efficiently solve large‐scale discrete optimisation problems. We contribute in this direction. Based on the insights from Lagrangian duality theory, we present an auxiliary problem that can be used for finding near‐optimal solutions to a discrete column‐oriented model. The structure of this auxiliary problem makes it suitable for being addressed with a heuristic search method involving column generation. To this end, we suggest a large neighbourhood search strategy where the repair step is to solve a column generation type subproblem. The suggested search strategy and mathematical models involved need to be tailored to the problem structure. To illustrate important design options and computational behaviour, four applications are studied: bin packing, generalised assignment, a resource allocation problem and the fixed‐charge transportation problem.
ISSN:0969-6016
1475-3995
DOI:10.1111/itor.12521