Advanced Computational Models for Multistage Stochastic Optimization of Process Systems with Renewable Resources

摘要：Ignacio E. Grossmann机构：卡内基梅隆大学项目编号：0521769题目：可再生资源过程系统多阶段随机优化的先进计算模型处理多周期运行过程系统设计中的不确定性已成为一个日益重要的问题，特别是在处理诸如生物过程等系统时，其中在原料的可用性和质量以及过程单元的产量方面存在显著的不确定性。该项目的一个主要目标是为涉及外生和内生不确定性的过程系统的随机优化开发新的计算模型。前者的例子包括需要量或进料组成，而后者的例子包括产量或其他工艺参数。该研究的具体目标是开发多阶段随机优化的新模型和有效的求解方法，其中场景树的结构是给定内源性不确定性的设计决策的函数。为了克服计算上具有挑战性的计算，PI打算研究一种新的析取规划公式，该公式以封闭的形式表示场景树与设计决策的依赖性。在此基础上，他打算研究求解线性随机问题的拉格朗日分支割法的计算过程。该方法将依赖于网格计算的使用，使用主工作算法来开发可以作为分解的一部分独立解决的子问题。本文还将研究这种计算方法在双线性模型中的推广。这种计算技术将应用于两个问题。第一个问题涉及生物精炼厂（生物质转化系统）的设计，其中食品残渣（原料）的可用性和质量以及所涉及的各种过程的转化产量都存在不确定性。第二个应用涉及综合工艺水系统，其中污染物的浓度和处理装置的回收率存在不确定性。第一个应用将被建模为一个线性随机规划问题，而第二个应用是一个涉及双线性的非线性随机问题。更广泛的影响：这项研究不仅有可能扩大随机优化的范围和意义，而且还可以大大改进生物工艺和工艺水系统的设计。研究结果和计算工具将通过互联网提供。项目负责人还打算编制两份设计案例研究，将通过工艺设计中心分发给工艺设计教员。他认为，这些案例研究将对本科教育产生重大影响，因为它们将使学生接触到生物炼制、工艺水系统和处理不确定性的技术。最后，为了提高高中学生对应用数学和基于可再生资源的过程的兴趣，他计划通过卡内基梅隆大学的施泰因布伦纳环境教育研究所开展推广活动，让学生们接触到简化版本的案例研究。

ABSTRACTPI: Ignacio E. Grossmann Institution: Carnegie Mellon UniversityProposal Number: 0521769Title: Advanced Computational Models for Multistage Stochastic Optimization of Process Systems with Renewable ResourcesHandling uncertainties in the design of process systems under multiperiod operation is becoming an increasingly important issue, particularly when dealing with systems such as bioprocesses where there are significant uncertainties in the availability and quality of the feedstocks and in the yields of the process units. A major objective of this project is to develop novel computational models for the stochastic optimization of process systems that involve exogenous and endogenous uncertainties. Examples of the former include demands or feed compositions, whereas examples of the latter include yields or other process parameters. The specific goal of the research is to develop novel models and effective solution methods for multistage stochastic optimization where the structure of scenario trees are functions of design decisions given endogenous uncertainties. To overcome the computationally challenging computations the PI intends to investigate a novel disjunctive programming formulation that expresses in closed form the dependency of the scenario tree with the design decisions. Based on that model, he intends to investigate a computational procedure based on a Lagrangean branch and cut method for solving linear stochastic problems. The method will rely on the use of grid computing using master-worker algorithms to exploit the subproblems that can be solved independently as part of the decomposition. The extension of this computational method to bilinear models will also be investigated.This computational technique will be applied to two problems. The first one deals with the design of biorefineries (biomass conversion systems) in which there are uncertainties in the availability and quality of food residues (raw materials) and in the yields of conversion in the various processes that are involved. The second application deals with the synthesis of integrated process water systems in which there are uncertainties in the concentration of contaminants and in the recoveries of treatment units. The first application will be modeled as a linear stochastic programming problem, while the second one is a nonlinear stochastic problem that involves bilinearities.Broader impact:This research has the potential not only of expanding the scope and significance of stochastic optimization, but also for greatly improving the design of bioprocesses and process water systems. The research results and computational tools will be made available through the internet. The PI also intends to develop two design case studies that will be disseminated to process design instructors through CACHE. He believes that these case studies will have significant impact in undergraduate education as they will expose the students to biorefineries, process water systems and techniques for handling uncertainties. Finally, in order to promote interest in high schools in applied mathematics and processes based on renewable resources, he plans to perform outreach activities through the Steinbrenner Institute for Environmental Education at Carnegie Mellon where students can be exposed to simplified versions of the case studies.