Distributed optimization using population dynamics with a local replicator equation

In distributed optimization problems, each agent can get information only from a neighborhood defined by a network topology to minimize a global objective function in a networked system. To solve this problem, we present a local strategy based on population dynamics, in order to perform a dynamic resource allocation in a system described by connected graph. The local replicator equation (LRE) is applied to a lighting control system to show that the achieved equilibrium point is an optimal solution to certain distributed optimization problems. We present some simulation results with different conditions, and a stability analysis to guarantee the convergence of the proposed algorithm.