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The graph coloring problem (GCP) is a well-known classical combinatorial optimization problem in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. This article proposes a modified binary crow search algorithm (MBCSA) to solve the graph coloring problem. First, the binary crow search algorithm is obtained from the original crow search algorithm using the V-shaped transfer function and the discretization method. Second, we use chaotic maps to choose the right values of the flight length (FL) and the awareness probability (AP). Third, we adopt the Gaussian distribution method to replace the random variables used for updating the position of the crows. The aim of these contributions is to avoid the premature convergence to local optima and ensure the diversity of the solutions. To evaluate the performance of our algorithm, we use the well-known DIMACS benchmark graph coloring instances. The simulation results reveal the efficiency of our proposed algorithm in comparison with other existing algorithms in the literature.

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In recent years, we are witnessing the spread of many and various modern real-time applications implemented on computer networks such as video conferencing, distance education, online games, and video streaming. These applications require the high quality of different network resources such as bandwidth, delay, jitter, and packet loss rate. In this paper, we propose an improved quantum chaotic animal migration optimization algorithm to solve the multicast routing problem(Multi-Constrained Least Cost MCLC). We used a quantum representation of the solutions that allow the use of the original AMO version without discretization, as well as improving AMO by introducing chaotic map to determine the random numbers. These two contributions improve the diversification and intensification of the algorithm. The simulation results show that our proposed algorithm has a good scalability and efficiency compared with other existing algorithms in the literature.