| Issue |
RAIRO-Oper. Res.
Volume 50, Number 4-5, October-December 2016
Special issue - Advanced Optimization Approaches and Modern OR-Applications
|
|
|---|---|---|
| Page(s) | 857 - 867 | |
| DOI | https://doi.org/10.1051/ro/2016060 | |
| Published online | 03 November 2016 | |
An exact method to generate all nondominated spanning trees
Faculty of Mathematics, USTHB, RECITS Laboratory, O2M team, Algiers, Algeria.
aboumesbah@usthb.dz; boumesbah-asma@hotmail.fr; mchergui@usthb.dz;
mohamedelaminec@yahoo.com
Received:
21
November
2015
Accepted:
30
August
2016
We describe an exact method to generate the nondominated set of the minimum spanning tree problem with at least two criteria. It is a separation and construction based method whose branching process is done with respect to edges belonging to at least two cycles of a given graph, inducing a step of constructing linear constraints that progressively break cycles while respecting the connectivity of the resulting graph. This has the effect of partitioning the initial graph into subgraphs, each of which corresponds to a discrete multi-objective linear program allowing to find the nondominated set of spanning trees. Randomly generated instances with more than two criteria are provided that show the efficiency of the method.
Mathematics Subject Classification: 90C10 / 90C27 / 90C29
Key words: Minimum spanning tree / integer linear programming / multiple objective linear optimization / combinatorial optimization / branch and bound method
© EDP Sciences, ROADEF, SMAI 2016
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