Abstract: Modeling of network security is useful approach to comprehend the status. In this paper, network is modeled in a graph. Security problem is solved in graph as Graph Coloring Problem (GCP). In GCP, two adjacent nodes must have different colors. Thus GCP provides the security in the network. One objective in GCP is chromatic number and another objective is total price. We present a multi-objective problem for GCP in this paper. Defined problem is solved with multi-objective simulated annealing and multi-objective imperialist competitive algorithm.
DOI: *As the DOI is a unique identifier, it is already available in the pdf version. **The DOI link will be activated in the first midst of January 2026.