An Empirical Study of Optimization for Maximizing Diffusion in Networks

We study the problem of maximizing the amount of stochastic diffusion in a network by acquiring nodes within a certain limited budget. We use a Sample Average Approximation (SAA) scheme to translate this stochastic problem into a simulation-based deterministic optimization problem, and present a detailed empirical study of three variants of the problem: where all purchases are made upfront, where the budget is split but one still commits to purchases from the outset, and where one has the ability to observe the stochastic outcome of the first stage in order to “re-plan” for the second stage. We apply this to a Red Cockaded Woodpecker conservation problem. Our results show interesting runtime distributions and objective value patterns, as well as a delicate trade-off between spending all budget upfront vs. saving part of it for later.