An exact [epsilon]-constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits

Jean-François Bérubé, Michel Gendreau and Jean-Yves Potvin

European Journal of Operational Research, 2009, vol. 194, issue 1, 39-50

Abstract: This paper describes an exact [epsilon]-constraint method for bi-objective combinatorial optimization problems with integer objective values. This method tackles multi-objective optimization problems by solving a series of single objective subproblems, where all but one objectives are transformed into constraints. We show in this paper that the Pareto front of bi-objective problems can be efficiently generated with the [epsilon]-constraint method. Furthermore, we describe heuristics based on information gathered from previous subproblems that significantly speed up the method. This approach is used to find the exact Pareto front of the Traveling Salesman Problem with Profits, a variant of the Traveling Salesman Problem in which a profit or prize value is associated with each vertex. The goal here is to visit a subset of vertices while addressing two conflicting objectives: maximize the collected prize and minimize the travel costs. We report the first exact results for this problem on instances derived from classical Vehicle Routing and Traveling Salesman Problem instances with up to 150 vertices. Results on approximations of the Pareto front obtained from a variant of our exact algorithm are also reported.

Keywords: Bi-objective; combinatorial; optimization; [epsilon]-constraint; problem; Pareto; front; Branch-and-cut; Traveling; Salesman; Problem; with; Profits (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (62)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377-2217(07)01210-6
Full text for ScienceDirect subscribers only

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:eee:ejores:v:194:y:2009:i:1:p:39-50

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().