Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective

Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective

Many practical combinatorial optimization problems can be described by integer linear programs having an exponential number of variables, and they are efficiently solved by column generation algorithms. For these problems, column generation is used to compute good dual bounds that can be incorporate...

Full description

Saved in:
Bibliographic Details
Published in:EURO journal on computational optimization Vol. 6; no. 2; pp. 117 - 142
Main Authors: Artigues, Christian, Jozefowiez, Nicolas, Sarpong, BoaduM
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Elsevier Ltd 01-06-2018
Springer Berlin Heidelberg
Springer Nature B.V
Springer
Elsevier
Subjects:
90-08
90C10
90C27
90C29
Algorithms
Bound sets
Business and Management
Column generation
Combinatorial analysis
Computer Science
Constraint modelling
Integer programming
Linear programming
Management Science
Multi-objective optimization
Multiple objective analysis
Operations Management
Operations Research
Operations Research/Decision Theory
Optimization
Original Paper
Routing
Studies
Upper bounds
Vehicle routing problems
90C10
Column generation
Vehicle routing problems
90-08
90C29
Multi-objective optimization
90C27
Bound sets
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Many practical combinatorial optimization problems can be described by integer linear programs having an exponential number of variables, and they are efficiently solved by column generation algorithms. For these problems, column generation is used to compute good dual bounds that can be incorporated in branch-and-price algorithms. Recent research has concentrated on describing lower and upper bounds of bi-objective and general multi-objective problems with sets of points (bound sets). An important issue to address when computing a bound set by column generation is how to efficiently search for columns corresponding to each point of the bound set. In this work, we propose a generalized column generation scheme to compute bound sets for bi-objective combinatorial optimization problems. We present specific implementations of the generalized scheme for the case where one objective is a min–max function by using a variant of the ε-constraint method to efficiently model these problems. The proposed strategies are applied to a bi-objective extension of the multi-vehicle covering tour problem, and their relative performances based on different criteria are compared. The results show that good bound sets can be obtained in reasonable times if columns are efficiently managed. The variant of the ε-constraint presented is also better than a standard ε-constraint method in terms of the quality of the bound sets.
ISSN:2192-4406
2192-4414
DOI:10.1007/s13675-017-0090-6