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

摘要：伊格纳西奥E.格罗斯曼研究所：卡内基梅隆大学提案编号：0521769标题：可再生资源过程系统多阶段随机优化的高级计算模型处理多周期运行过程系统设计中的不确定性正成为一个越来越重要的问题，特别是当处理诸如生物过程的系统时，其中在原料的可获得性和质量以及过程单位。 这个项目的一个主要目标是开发新的计算模型的过程系统，涉及外源性和内源性的不确定性的随机优化。前者的例子包括需求或进料组成，而后者的例子包括产率或其他工艺参数。研究的具体目标是开发新的模型和有效的解决方法，多阶段随机优化的结构的情况下，树的功能的设计决策给定的内生不确定性。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编程公式，以封闭的形式表达的依赖关系的场景树的设计决策。基于该模型，他打算研究一个计算程序的基础上拉格朗日分支和削减方法解决线性随机问题。 该方法将依赖于使用网格计算，使用主-工人算法，利用子问题，可以独立解决的分解的一部分。 本文还将研究这种计算方法在双线性模型中的推广。这种计算方法将应用于两个问题。第一个涉及生物精炼厂（生物质转化系统）的设计，其中食物残渣（原材料）的可得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。第二个应用程序涉及综合工艺用水系统，其中有不确定性的污染物的浓度和处理单元的回收率。第一个应用程序将被建模为一个线性随机规划问题，而第二个是一个非线性随机问题，涉及bilinearities.Broader影响：这项研究不仅有可能扩大随机优化的范围和意义，而且大大提高了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。PI还打算开发两个设计案例研究，通过CACHE传播给流程设计讲师。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，工艺用水系统和处理不确定性的技术。最后，为了促进高中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Steinbrenner环境教育研究所开展外联活动，学生可以接触到案例研究的简化版本。

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.