Obtaining the Dominating Set in Graphs with the Invasive Weed Optimization Algorithm

The minimum dominant set problem in graphs is a well-known NP-hard problem that requires the use of heuristics to obtain approximate solutions due to its computational complexity. Among the many heuristic approaches found in the literature, the Invasive Weed Optimization (IWO) algorithm has been widely recognized due to its efficiency; however, its application areas are limited to traditional methods. So far, the binary form of this encoding has not been investigated and the IWO algorithm has not been applied to the dominant set problem. In this work, the gap in this field is addressed by applying the Invasive Weed Optimization algorithm to the minimum dominant set problem. The work leads to the development of a binary version of the IWO algorithm tailored to this problem, focusing specifically on determining the inclusion of nodes in the dominant set. This approach makes a significant contribution by extending the utility of the IWO algorithm and providing a promising new method for addressing binary optimization challenges in the context of graph theory.