Reduced Variable Neighbourhood Search for Pagenumber Minimization Problem

In this paper we apply reduced variable neighbourhood search (RVNS) to the page number minimization problem (PNP). In RVNS, random depth first search of the graph is used for placing the vertices on the spine and three edge embedding heuristics are used to distribute the edges on a minimal number of pages. The results show that the algorithm achieves the optimal page number for most of the standard graphs tested by us. RVNS performance is also compared with the genetic algorithm and hybrid evolutionary algorithm present in the literature on select instances of standard and random graphs. It is observed that RVNS gives better solutions for random instances. Extensive experiments were carried out on classes of graphs with known results/upper bounds. Optimal values were achieved by RVNS for all the graphs tested and substantially lower values were obtained for the graphs with known upper bounds of page number. The main contribution of the paper are some Harwell-Boeing Sparse Matrix Collection graphs and cartesian product of complete graphs with unknown page numbers.