CAREER: Extensions of Stochastic Programming: Models, Algorithms, and Applications

该学院早期职业发展(CALEAR)奖是研究具有替代风险厌恶目标、主观概率和依赖于决策的不确定性的随机计划的新模型、算法和应用。虽然随机规划现在已经发展成为一种可行的不确定情况下的规划和决策范例，但这一领域的许多进展是以牺牲一些简化的假设为代价的。例如，传统的随机规划关注的是对期望目标函数进行优化。其他常见的假设包括对静态潜在概率分布的精确了解。然而，在许多实际应用中，这些忽略假设的风险可能是非常不可取的。不幸的是，这些概括通常会导致非凸优化模型。因此，传统的(凸)随机规划分解算法不再适用。该研究将研究分解原理在非凸优化算法中的集成，以攻击这些一般随机规划的大规模实例。开发的概念将应用于流程工业、工程设计和公用事业等重要经济部门的规划问题。这份职业发展计划的教育部分旨在将基于随机规划的规划和决策推广到工程教育和实践中。为了实现这一目标，将开发用户友好的随机规划建模和求解工具、电子教程和真实世界案例研究。运筹学研究社区认识到，随机规划是面对不确定性时决策支持的一种有价值的量化技术。然而，这一工具在实际规划和决策中并没有得到广泛的应用。造成这种情况的两个原因是：传统的随机规划模型对于现实生活中的应用往往过于简单化，以及在工程教育中缺乏对实际随机规划概念的接触。拟议的研究计划将扩展随机规划范式，超越一些传统的不切实际的假设。这些推广将需要开发全新的随机规划模型和算法，并将其应用于相关的实际问题。在教育方面，将开发用户友好的随机规划解算器、电子教程和工业案例研究，以促进在本科和研究生工程教育中引入应用随机规划的概念。

This Faculty Early Career Development (CAREER) award is to study new models, algorithms, and applications of stochastic programs with alternative risk-averse objectives, subjective probabilities, and decision-dependent uncertainties. Although stochastic programming has now evolved as a viable paradigm for planning and decision-making under uncertainty, much of the progress in this area has been made at the expense of some simplifying assumptions. For example, traditional stochastic programming is concerned with optimizing an expected objective function. Other common assumptions include precise knowledge of a static underlying probability distribution. However, these risk ignoring assumptions can be quite undesirable in many practical applications. Unfortunately, these generalizations typically lead to non-convex optimization models. Consequently, traditional decomposition algorithms for (convex) stochastic programs are inapplicable. The research will investigate the integration of decomposition principles within non-convex optimization algorithms in order to attack large-scale instances of these general stochastic programs. The developed concepts will be applied to planning problems in important economic sectors such as process industries, engineering design, and utility industries. The educational component of this career development plan is aimed at popularizing stochastic programming based planning and decision making in engineering education and practice. Towards this goal, user-friendly stochastic programming modeling and solver tools, electronic tutorials, and real world case studies will be developed.The operations research community recognizes Stochastic Programming as a valuable quantitative technique for decision support in the face of uncertainty. However, this tool has not achieved widespread use in practical planning and decision-making. Two reasons for this are: traditional stochastic programming models can often be overly simplistic for real-life applications and the lack of exposure to practical stochastic programming concepts in engineering education. The proposed research program will extend stochastic programming paradigm beyond some of the traditional impractical assumptions. These generalizations will require the development of entirely new stochastic programming models and algorithms, and their application to relevant practical problems. On the education side, user friendly stochastic programming solver, electronic tutorials, and industrial case-studies will be developed to facilitate the introduction of applied stochastic programming concepts in undergraduate and graduate engineering education.