Simultaneous optimization and sampling of agent trajectories over a network

Abstract

We study the problem of optimizing the trajectories of agents moving over a network given their preferences over which nodes to visit subject to operational constraints on the network. In our running example, a theme park manager optimizes which attractions to include in a day-pass to maximize the pass’s appeal to visitors while keeping operational costs within budget. The first challenge in this combinatorial optimization problem is that it involves quantities (expected visit frequencies of each attraction) that cannot be expressed analytically, for which we use the Sample Average Approximation. The second challenge is that while sampling is typically done prior to optimization, the dependence of our sampling distribution on decision variables couples optimization and sampling. Our main contribution is a mathematical program that simultaneously optimizes decision variables and implements inverse transform sampling from the distribution they induce. The third challenge is the limited scalability of the monolithic mathematical program. We present a dual decomposition approach that exploits independence among samples and demonstrate better scalability compared to the monolithic formulation in different settings.