In this paper Roman and weak Roman domination problems on graphs are considered. Given that both problems are NP hard, a new heuristic approach, based on a Variable Neighborhood Search (VNS), is presented. The presented algorithm is tested on instances known from the literature, with up to 600 vertices. The VNS approach is justified since it was able to achieve an optimal solution value on the majority of instances where the optimal solution value is known. Also, for the majority of instances where optimization solvers found a solution value but were unable to prove it to be optimal, the VNS algorithm achieves an even better solution value.
Publié le : 2019-04-26
Classification:
Software Engineering; Integer programming;,
Roman domination in graphs, weak Roman domination in graphs, combinatorial optimization, metaheuristic, variable neighborhood search,
05C69, 05C85, 90C10
@article{cai2019_1_57,
author = {Marija Ivanovi\'c; Faculty of Mathematics, University of Belgrade and Dragan Uro\v sevi\'c; Mathematical Institute SANU, Belgrade},
title = {Variable Neighborhood Search Approach for Solving Roman and Weak Roman Domination Problems on Graphs},
journal = {Computing and Informatics},
volume = {37},
number = {6},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/cai2019_1_57}
}
Marija Ivanović; Faculty of Mathematics, University of Belgrade; Dragan Urošević; Mathematical Institute SANU, Belgrade. Variable Neighborhood Search Approach for Solving Roman and Weak Roman Domination Problems on Graphs. Computing and Informatics, Tome 37 (2019) no. 6, . http://gdmltest.u-ga.fr/item/cai2019_1_57/