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.

Keywords

MSC

05C69, 05C85, 90C10

Cite this article

@article{cai-3596,
  author  = {Marija Ivanović and Dragan Urošević},
  title   = {Variable Neighborhood Search Approach for Solving Roman and Weak Roman Domination Problems on Graphs},
  journal = {Computing and Informatics},
  volume  = {38},
  number  = {1},
  pages   = {57--84},
  year    = {2019},
  issn    = {1335-9150},
  doi     = {10.31577/cai_2019_1_57}
}
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