In a multi-agent framework, distributed optimization problems are generally described as the minimization of a global objective function, where each agent can get information only from a neighborhood defined by a network topology. To solve the problem, this work presents an information-constrained strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the so-called distributed replicator equation (DRE) 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 DRE to solve an economic dispatch problem with distributed generation. We also present some simulation results to illustrate the theoretic optimality and stability of the equilibrium points and the effects of typical network topologies on the convergence rate of the algorithm.
In a multi-agent framework, distributed optimization problems are generally described as the minimization of a global objective function, where each agent can get information only from a neighborhood defined by a network topology. To solve the problem, this work presents an information-constrained strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the so-called distributed replicator equation (DRE) 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 DRE to solve an economic dispatch problem with distributed generation. We also present some simulation results to illustrate the theoretic optimality and stability of the equilibrium points and the effects of typical network topologies on the convergence rate of the algorithm.En un marco multiagente, los problemas de optimización distribuida generalmente se describen como la minimización de una función de objetivo global, donde cada agente puede obtener información sólo de un vecindario definido por una topología de red. Para resolver este problema, se presenta una estrategia de información limitada basada en dinámicas de población, donde las funciones y tareas de pago se asignan a cada nodo en un grafo conectado. Probamos que la llamada ecuación de replicador distribuido (DRE por sus siglas en inglés) converge a un resultado global óptimo mediante el intercambio de información local sujeto a las restricciones topológicas del grafo. Para mostrar la aplicación de la estrategia propuesta, implementamos la DRE para resolver un problema de despacho económico. También presentamos algunos resultados de simulación para ilustrar la optimalidad teórica y la estabilidad de los puntos de equilibrio y los efectos de las topologías de red típicas en la tasa de convergencia del algoritmo.
