  Roman domination is a well researched topic in graph theory. Recently two new
variants of Roman domination, namely triple Roman domination and quadruple
Roman domination problems have been introduced, to provide better defense
strategies. However, triple Roman domination and quadruple Roman domination
problems are NP-hard. In this paper, we have provided genetic algorithm for
solving triple and quadruple Roman domination problems. Programming (ILP)
formulations for triple Roman domination and quadruple Roman domination
problems have been proposed. The proposed models are implemented using IBM
CPLEX 22.1 optimization solvers and obtained results for random graphs
generated using NetworkX Erdos-Renyi model.
