CAREER: Multi-Objective Optimization via Simulation: Theory, Methods, and Parallel Computation

学院早期职业发展(Career)助学金正在开发理论、方法和算法，用于复杂系统中的不确定情况下的决策，这些系统使用基于计算机的模拟来建模。具体的重点将是开发可实现的算法，以识别关于多个性能指标的最优决策。这类问题经常出现在各种应用中，包括南希、能源、交通、设施选址、供应链管理、电信和医疗保健管理。虽然这些问题普遍存在，但研究不足，目前的解决方法可能缓慢、不精确或不准确。开发解决此类问题的方法，并在速度、精确度和准确性方面提供可证明的保证，将使决策者能够在各种学科中做出更好、更及时的决策。社会将受益于以提高效率和降低成本为特征的改进的系统。这个项目还支持了PI的教育目标，即在概率和优化的界面上传播清晰和吸引人的教育材料，以招募、培养和留住在不确定情况下做出决策的下一代专业人员。这项研究将开发通过模拟问题解决多目标优化的理论、方法和并行算法。基于仿真的多目标优化问题是一类非线性多目标优化问题，其中每个目标只能作为蒙特卡罗模拟的输出带误差观测；该问题的解是一个非支配(Pareto)集。尽管多目标优化问题在类似确定性的背景下得到了广泛的应用和成熟的发展，但基于模拟问题的多目标优化在理论和算法方面的发展相对较少。由于它们的复杂性，这些问题很难解决：目标函数只能通过潜在昂贵的蒙特卡罗模拟来估计，而且帕累托集往往会随着目标数量的增加而产生误差。这项研究将为在随机环境下估计帕累托集奠定理论基础。具体地说，提出的理论和方法包括用于降维的缩放、渐近逼近、获得快速收敛速度的优化框架和并行实现。这样的理解将导致新的算法方法在可证明的意义上最优地发展，并导致可实现的、有效的并行算法来解决这些困难的问题。

This Faculty Early Career Development (CAREER) grant is developing theory, methods, and algorithms for decision-making under uncertainty in complex systems that are modeled using computer-based simulations. The specific focus will be on developing implementable algorithms that identify optimal decisions with respect to multiple performance measures. Such problems arise frequently in a variety of applications including finance, energy, transportation, facility location, supply chain management, telecommunication, and healthcare management. Though widespread, these problems are under-studied, and current solution methods may be slow, imprecise, or inaccurate. Developing methods to solve such problems with provable guarantees on speed, precision, and accuracy will enable decision-makers to make better, timely decisions across a variety of disciplines. Society will benefit from improved systems, characterized by increased efficiency and reduced cost. This project also supports the PI's educational goal of disseminating clear and engaging educational materials at the interface of probability and optimization that recruit, train, and retain the next generation of professionals who make decisions under uncertainty.This research will develop theory, methods, and parallel algorithms for solving multi-objective optimization via simulation problems. Multi-objective optimization via simulation problems are nonlinear multi-objective optimization problems in which each objective can only be observed with error as output from a Monte Carlo simulation; a solution to this problem is a non-dominated (Pareto) set. Despite its prevalence and mature development in the analogous deterministic context, multi-objective optimization via simulation problems have seen relatively little theoretical and algorithmic development in the optimization via simulation literature. These problems are difficult to solve because of their complexity: the objective functions can only be estimated with error through potentially expensive Monte Carlo simulation, and the Pareto set often grows in the number of objectives. The proposed research will develop the theoretical underpinnings of estimating Pareto sets in the stochastic context. Specifically, the proposed theory and methods include scaling for dimension reduction, asymptotic approximation, optimization frameworks that retrieve fast convergence rates, and parallel implementation. Such understanding will lead to new algorithmic methods that evolve optimally in a provable sense and to implementable, efficient parallel algorithms for solving these difficult problems.