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 (i.e., the local replicator equation (LRE)), to define functions and tasks assigned to each node in a system represented by a connected graph. To show the application of the proposed strategy, we implement the LRE to solve a problem of economic dispatch of distributed generators with some variations over the original framework. Finally, we present some simulation results obtained with different network topologies to illustrate the optimality and stability of the equilibrium points.