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

该学院早期职业发展（CAREER）资助正在开发理论，方法和算法，用于在使用基于计算机的模拟建模的复杂系统中进行不确定性决策。该speci #64257;c的重点将是开发可实现的算法，确定最佳决策方面的多个性能指标。这样的问题经常出现在各种应用中，包括运输、能源、运输、设施定位、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很慢，不精确或不准确。开发解决此类问题的方法，并在速度、精度和准确性方面提供可证明的保证，将使决策者能够在各个学科中做出更好、及时的决策。社会将从以提高效率和降低成本为特征的改进系统中受益。本项目还支持PI的教育目标，即在概率和优化的界面上传播清晰和引人入胜的教育材料，以招募，培养和留住下一代在不确定性下做出决策的专业人员。本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。通过模拟的多目标优化问题是非线性多目标优化问题，其中每个目标只能通过蒙特卡洛模拟的输出误差来观察;该问题的解决方案是非支配（帕累托）集。尽管它的流行和成熟的发展，在类似的确定性背景下，多目标优化通过仿真问题已经看到了相对较少的理论和算法的发展，通过仿真文献的优化。这些问题是困难的fi由于它们的复杂性，目标函数只能通过潜在昂贵的蒙特卡罗模拟来估计，并且帕累托集通常会随着目标的数量而增长。该研究将为随机背景下的帕累托集估计提供理论基础。规格fi最后，所提出的理论和方法包括降维尺度、渐近逼近、快速收敛的优化框架和并行实现。这样的理解将导致新的算法方法，最佳地演变在一个可证明的意义和可实现的，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.