EconPapers    
Economics at your fingertips  
 

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

Christian Artigues, Nicolas Jozefowiez (nicolas.jozefowiez@univ-lorraine.fr) and Boadu M. Sarpong
Additional contact information
Christian Artigues: Université de Toulouse
Nicolas Jozefowiez: Université de Lorraine
Boadu M. Sarpong: Université de Toulouse

EURO Journal on Computational Optimization, 2018, vol. 6, issue 2, No 1, 117-142

Abstract: Abstract 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 $$\varepsilon $$ 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 $$\varepsilon $$ ε -constraint presented is also better than a standard $$\varepsilon $$ ε -constraint method in terms of the quality of the bound sets.

Keywords: Column generation; Multi-objective optimization; Bound sets; Vehicle routing problems; 90-08; 90C10; 90C29; 90C27 (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s13675-017-0090-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurjco:v:6:y:2018:i:2:d:10.1007_s13675-017-0090-6

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/13675

DOI: 10.1007/s13675-017-0090-6

Access Statistics for this article

EURO Journal on Computational Optimization is currently edited by Martine C. Labbé

More articles in EURO Journal on Computational Optimization from Springer, EURO - The Association of European Operational Research Societies
Bibliographic data for series maintained by Sonal Shukla (sonal.shukla@springer.com) and Springer Nature Abstracting and Indexing (indexing@springernature.com).

 
Page updated 2024-12-29
Handle: RePEc:spr:eurjco:v:6:y:2018:i:2:d:10.1007_s13675-017-0090-6