Variable Neighborhood Search Approach for Solving Roman and Weak Roman Domination Problems on Graphs

Authors

  • Marija Ivanović Faculty of Mathematics, University of Belgrade, 11 000 Belgrade, Serbia
  • Dragan Urošević Mathematical Institute SANU, 11 000 Belgrade, Serbia

DOI:

https://doi.org/10.31577/cai_2019_1_57

Keywords:

Roman domination in graphs, weak Roman domination in graphs, combinatorial optimization, metaheuristic, variable neighborhood search

Abstract

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.

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Published

2019-04-26

How to Cite

Ivanović, M., & Urošević, D. (2019). Variable Neighborhood Search Approach for Solving Roman and Weak Roman Domination Problems on Graphs. Computing and Informatics, 38(1), 57–84. https://doi.org/10.31577/cai_2019_1_57