Hybridizing simulated annealing with variable neighborhood search for bipartite graph crossing minimization

Gintaras Palubeckis, Arūnas Tomkevičius and Armantas Ostreika

Applied Mathematics and Computation, 2019, vol. 348, issue C, 84-101

Abstract: Given a bipartite graph, the problem we address, called the bipartite graph crossing minimization problem (BGCMP), is to find an embedding the parts of the graph along two parallel lines so that the number of edge crossings is minimized. It is assumed that each edge is drawn as a straight line segment and edges sharing an end vertex do not cross. We propose an approach for the BGCMP, which combines a simulated annealing (SA) method with a variable neighborhood search (VNS) scheme. These two algorithms are executed iteratively. At each iteration, the solution produced by SA is submitted as input to the VNS component of the approach. Our VNS algorithm uses a local search technique which is based on a fast insertion neighborhood exploration procedure. We show that the time complexity of this procedure is O(n2), where n is the order of the graph. Another fast procedure is proposed for computing the gain in the objective function value obtained by swapping positions of two vertices. We experimentally compare our algorithm (called SA-VNS) against the tabu search algorithm as well as GRASP approach from the literature. Computational results are reported on four sets of bipartite graphs. The results demonstrate the superiority of SA-VNS over the state-of-the-art methods. The source code implementing SA-VNS is made publicly available as a benchmark for future comparisons.

Keywords: Graphs; Edge crossing minimization; Combinatorial optimization; Simulated annealing; Variable neighborhood search (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318310257
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:apmaco:v:348:y:2019:i:c:p:84-101

DOI: 10.1016/j.amc.2018.11.051

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().