Bridging The Gap Between Heuristic and Exact Approaches in Process Systems Engineering via Analytical Investigations

摘要：工艺综合与优化有两种方法：启发式方法和解析式方法。启发式提供快速解决方案，但不能保证最优性。分析型整数规划方法提供了严谨性，但会遭受计算需求的组合爆炸（即，随着问题变得更大，解决方案对大多数系统来说计算量太大）。该项目将进行分析调查，作为一种理论手段来表征启发式和优化算法的行为，并产生一个框架，结合两种方法的优点，同时消除它们的缺点。初步结果表明，该模型适用于化工过程网络的多周期产能扩张问题。它的多周期特性使得这个问题类似于离散时间调度。与综合问题一样，同样的问题需要优化上层结构。对该问题的分析研究导致了一个启发式的发展，该启发式在关于问题参数的标准假设下是渐近最优的。在更一般的过程综合和操作范围内，分析性调查提供了大量的机会。计划的工作将明确处理以下问题：(1)多周期工艺操作，(2)热交换器网络的综合，以及(3)分离网络的综合。PI的工作将指向(1)确定这些问题的计算复杂性，(2)分析现有启发式的最坏情况和预期行为，以及(3)开发新的、基于数学规划的、在统计意义上最优的多项式时间启发式。

Abstract - Sahinidis - 9704643 There are two approaches to process synthesis and optimization - heuristic and analytical. Heuristics offer fast solutions but do not guarantee optimality. Analytical integer programming approaches offer rigor but suffer combinatorial explosion of computational requirements (i.e. as the problems become larger, the solutions become computationally too large for most systems). This project will pursue analytical investigations as a theoretical means to characterize the behavior of heuristics and optimization algorithms and produce a framework that combines the strengths of the two approaches while eliminating their weaknesses. Preliminary results demonstrate the proposed paradigm in the context of the multi-period capacity expansion problem for chemical process networks. The multi-period aspects of it makes this problem similar to discrete-time scheduling. The same problem requires optimizing a superstructure as in synthesis problems. Analytical investigations for this problem lead to the development of a heuristic which is proved to be asymptotically optimal under standard assumptions about the problem parameters. In the more general scope of process synthesis and operations, analytical investigations present a large array of opportunities. The work planned will deal explicitly with problems in (I) multi-period process operations, (ii) synthesis of heat exchanger networks, and (iii) synthesis of separation networks. The PI's efforts will be directed towards (1) determining the computational complexity of these problems, (2) analyzing the worst case and expected behavior of existing heuristics, and (3) developing new, mathematical programming-based, polynomial time heuristics that are optimal in a statistical sense.