Lightweight agents distributed in space have the potential to solve many complex problems. In this paper, we examine a model where agents represent individuals in a genetic algorithm (GA) solving a shared problem. We examine two questions: (1) How does the network density of connections between agents affect the performance of the systems? (2) How does the interaction topology affect the performance of the system? In our model, agents exist in either a random network topology with long-distance communication, or a location-based topology, where agents only communicate with near neighbors. We examine both fixed and dynamic networks. Within the context of our investigation, our initial results indicate that relatively low network density achieves the same results as a panmictic, or fully connected, population. Additionally, we find that dynamic networks outperform fixed networks, and that random network topologies outperform proximity-based network topologies. We conclude by showing how this model can be useful not only for multi-agent learning, but also for genetic algorithms, agentbased simulation and models of diffusion of innovation.

Pair approximations have often been used to predict equilibrium conditions in spatially-explicit epidemiological and ecological systems. In this work, we investigate whether this method can be used to approximate takeover dynamics in spatially structured evolutionary algorithms. Our results show that the pair approximation, as originally formulated, is insufficient for approximating pre-equibilibrium dynamics, since it does not properly account for the interaction between the size and shape of the local neighborhood and the population size. After parameterizing the pair approximation to account for these influences, we demonstrate that the resulting system of differential equations can serve as a general and rapid approximator for takeover dynamics on a variety of spatially-explicit regular interaction topologies with varying population sizes. Strengths, limitations, and potential applications of the pair approximation to evolutionary computation are discussed.