Distributed optimization with population dynamics

Abstract

Distributed optimization problems are generally described as the minimization of a global objective function in a system, where each agent can get information only from a neighborhood defined by a network topology. To solve this problem, we present a local strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the local replicator equation (LRE) converges to an optimal global outcome by means of the local-information exchange subject to the topological constraints of the graph. To show the application of the proposed strategy, we implement the LRE to solve both an economic dispatch and a distributed lighting control problem, requiring variations of the original framework. Finally, we present some simulation and implementation results that illustrate the theoretic optimality and stability of the equilibrium points.