Large-scale global optimization through consensus of opinions over complex networks

Abstract

Purpose: Large-scale optimization tasks have many applications in science and engineering. There are many algorithms to perform such optimization tasks. In this manuscript, we aim at using consensus in multi-agent systems as a tool for solving large-scale optimization tasks. Method: The model is based on consensus of opinions among agents interacting over a complex networked structure. For each optimization task, a number of agents are considered, each with an opinion value. These agents interact over a networked structure and update their opinions based on their best-matching neighbor in the network. A neighbor with the best value of the objective function (of the optimization task) is referred to as the best-matching neighbor for an agent. We use structures such as pure random, small-world and scale-free networks as interaction graph. The optimization algorithm is applied on a number of benchmark problems and its performance is compared with a number of classic methods including genetic algorithms, differential evolution and particle swarm optimization. Results: We show that the agents could solve various large-scale optimization tasks through collaborating with each other and getting into consensus in their opinions. Furthermore, we find pure random topology better than small-world and scale-free topologies in that it leads to faster convergence to the optimal solution. Our experiments show that the proposed consensus-based optimization method outperforms the classic optimization algorithms. Conclusion: Consensus in multi-agents systems can be efficiently used for large-scale optimization problems. Connectivity structure of the consensus network is effective in the convergence to the optimum solution where random structures show better performance as compared to heterogeneous networks. AMS subject classification: 15A04, 54A20, 60J20, 92D25