A general framework for population-based distributed optimization over networks

This paper presents a population-based solution for the distributed optimization problem where the overall objective function is defined as an average of local cost functions corresponding to the nodes of a network. Populations are introduced for the nodes to cooperatively find the global optimum of the overall objective function. The main challenge is that each population cannot know the overall objective function and thus cannot directly evaluate the quality of their individuals in each iteration. To overcome this difficulty, we introduce consensus methods to design a message-passing protocol under which the local estimates can converge to the same value. We present a general framework that consists of consensus search, consensus evaluation, population evolution and local stopping steps. Compared with mathematical methods, this framework solves in-network distributed optimization problems without requiring a convexity assumption on the objective functions. The standard PSO and one of its variants, called MCO, are introduced for testing and comparison. Two simulated examples under different network topologies illustrate the feasibility of our approach.