"Combining Gradient and Adaptive Search in Simulation Optimization"
This research project aims to make significant theoretical and practical advances in simulation optimization. Specifically, we plan on doing the following: (i) develop new simulation optimization algorithms based on different sequences of the so-called ``reference distributions" in a recently developed approach called model reference adaptive search, and new hybrid global-local search algorithms integrating local gradient search and problem structure; and (ii) conduct rigorous theoretical analysis of the resulting algorithms, both finite-time behavior using an adaptive search framework and asymptotic behavior using a novel connection to stochastic approximation methods. We will also develop efficient computational selection methods for implementing these algorithms in simulation optimization, where the objective function requires multiple simulation replications, which are computationally expensive, in order to estimate system performance. A wide variety of applications from supply chain management to financial engineering will be tested for the purposes of investigating specific gradient search algorithms and problem structure, and evaluating the effectiveness in terms of empirical behavior.
Simulation is used throughout the US industry, so if successful, the resulting optimization algorithms will have broad practical applicability. To attack difficult problems arising from large, complex stochastic discrete-event simulation models will require significant new methodologies, leading to research advances in both algorithmic development and convergence analysis. In terms of theory, the rigorous analysis will explore connections to a rich body of results in stochastic approximation and stochastic adaptive research that have never been employed in this manner before, yielding new insights into both finite-time performance and asymptotic rates of convergence. In terms of practice, this line of research fills an important part of the "analytics" computational tool kit that has led to increased competitiveness for US businesses from manufacturers and retailers with global supply chains to financial services managing complex risk factors.
