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This paper addresses the broader topic of using game theoretical learning mechanisms to efficiently and effectively identify relevant (e.g., optimal and non-mixed) solutions to large scale optimization problems. The longer-term goal is for the proposed MCFP-variants to become established methods for finding pure Nash equilibria and global optima of large-scale problems. 

The objective is to understand the role of emerging variants, vaccination, and NPI policies on COVID-19 infections and deaths. We aim to identify scenarios in which COVID-19 can be managed such that the death rate from COVID-19 becomes comparable with the combined annual mortality rate from influenza and pneumonia. As a case study for a large urban area, we simulate COVID-19 transmission in King County, Washington, (greater Seattle) using an agent- based simulation model. Calibrated to local epidemiological data, our study uses detailed synthetic population data and includes interactions between vaccination and specific NPIs while considering waning immunity and emergence of variants. Virus mutation scenarios include 12 combinations of infectivity, disease severity, and immune evasiveness. A highly effective pancoronavirus vaccine that works against all strains is considered an optimistic scenario. Our findings highlight the potential benefits of pancoronavirus vaccines that offer enhanced and longer-lasting immunity. We emphasize the crucial role of nonpharmaceutical interventions in reducing COVID-19 deaths regardless of virus mutation scenarios. Owing to highly immune evasive and contagious SARS-CoV-2 variants, most scenarios in this study fail to reduce the mortality of COVID-19 to the level of influenza and pneumonia. However, our findings indicate that periodic vaccinations and a threshold nonpharmaceutical intervention policy may succeed in achieving this goal. This indicates the need for caution and vigilance in managing a continuing COVID-19 epidemic. 

Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that the objective function can be observed directly. We consider the case where the objective function must be estimated, often using a noisy function, as in simulation. We present a finite-time analysis of algorithm performance that combines estimation with a sampling distribution. We present a framework called Hesitant Adaptive Search with Estimation, and derive an upper bound on function evaluations that is cubic in dimension, under certain conditions. We extend the framework to Quantile Adaptive Search with Estimation, which focuses sampling points from a series of nested quantile level sets. The analyses suggest that computational effort is better expended on sampling improving points than refining estimates of objective function values during the progress of an adaptive search algorithm. 

The outbreak of seasonal flu costs billions of dollars in health care utilization and lost productivity. Despite the effectiveness of vaccination and antiviral medications to prevent serious flu-related complications and slow down the spread of an influenza epidemic, only 52% of the U.S. population aged 6 months and older received flu vaccines in the 2019-20 flu season. In addition, a costly out-of-pocket expense results in fewer patients seeking treatment, leading to potential hospitalizations and even flu-related deaths. In this study, we develop an integrated healthcare insurance mechanism that optimizes two incentive policies, vaccination reward and cost-sharing, to alleviate the medical cost and disease burden while preventing the outbreak of seasonal influenza. We model the dynamic interaction between a single insurer and multiple insureds as a Stackelberg vaccination game; we then embed the game into an agent-based simulation to model the spread of flu in a population under different policies. Finally, we apply machine learning and simulation optimization to optimize healthcare incentive policies in a large-scale flu transmission simulation. Simulation results indicate that the proposed methodology efficiently identifies a set of good incentive policies under different scenarios of flu vaccine efficacy and reproduction numbers. 

Water Distribution Networks are a particularly critical infrastructure for the high energy costs and frequent failures. Variable Speed Pumps have been introduced to improve the regulation of water pumps, a key for the overall infrastructure performance. This paper addresses the problem of analyzing the effect of the VSPs regulation on the pressure distribution of a WDN, which is highly correlated to leakages and energy costs. Due to the fact that water network behavior can only be simulated, we formulate the problem as a black box feasibility determination, which we solve with a novel stochastic partitioning algorithm, the Feasibility Set Approximation Probabilistic Branch and Bound, that extends the algorithm previously proposed by two of the authors. We use, as black box, EPANet, a widely adopted hydraulic simulator. The preliminary results, over theoretical functions as well as a water distribution network benchmark case, show the viability and advantages of the proposed approach. 

Optimizing the performance of complex systems modeled by stochastic computer simulations is a challenging task, partly because of the lack of structural properties (e.g., convexity). This challenge is magnified by the presence of random error whereby an adaptive algorithm searching for better designs can at times mistakenly accept an inferior design. In contrast to performing multiple simulations at a design point to estimate the performance of the design, we propose a framework for adaptive search algorithms that executes a single simulation for each design point encountered. Here the estimation errors are reduced by averaging the performances from previously evaluated designs drawn from a shrinking ball around the current design point. We show under mild regularity conditions for continuous design spaces that the accumulated errors, although dependent, form a martingale process, and hence, by the strong law of large numbers for martingales, the average errors converge to zero as the algorithm proceeds. This class of algorithms is shown to converge to a global optimum with probability one. By employing a shrinking ball approach with single observations, an adaptive search algorithm can simultaneously improve the estimates of performance while exploring new and potentially better design points. Numerical experiments offer empirical support for this paradigm of single observation simulation optimization.