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.

翻译：罗马支配是图论中一个研究较深入的课题。近期，为了提供更优的防御策略，研究人员引入了罗马支配的两种新变体，即三重罗马支配问题和四重罗马支配问题。然而，三重罗马支配和四重罗马支配问题属于NP难问题。本文针对三重和四重罗马支配问题，给出了遗传算法解决方案。提出了三重罗马支配和四重罗马支配问题的整数线性规划形式。采用IBM CPLEX 22.1优化求解器对提出的模型进行了实现，并针对使用NetworkX Erdos-Renyi模型生成的随机图获得了结果。