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An integer programming column generation principle for heuristic search methods
Author(s) -
Zhao Yixin,
Larsson Torbjörn,
Rönnberg Elina
Publication year - 2020
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12521
Subject(s) - column generation , mathematical optimization , heuristic , column (typography) , bin packing problem , integer programming , computer science , local search (optimization) , duality (order theory) , mathematics , algorithm , bin , telecommunications , frame (networking) , discrete mathematics
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.