Shane G. Henderson: A Tutorial and Perspectives on Monte Carlo Simulation Optimization

Abstract: I provide a tutorial and some perspectives on simulation optimization, in which one wishes to minimize an objective function that can only be evaluated with noise through a stochastic computer simulation. First, I'll give a few examples and intuitively explain some central issues in the area. Second, I'll explain why so-called sample-path functions can exhibit extremely complex behavior that is well worth understanding. Third, I'll argue that more attention should be devoted to the finite-time performance of solvers than on ensuring convergence properties that may only arise in asymptotic time scales that may never be reached in practice. I'll outline an approach for obtaining such results analytically (through Lyapunov functions) and introduce a framework and code for computational experiments that can further this goal. Fourth (if time permits, though I doubt it will), I'll advocate the use of a layered approach to formulating and solving optimization problems, whereby a sequence of models are built and optimized, rather than first building a simulation model and only later “bolting on” optimization, partly through an example of my work involving bike sharing with the organization Citi Bike in New York city.