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

摘要-萨希尼迪斯-9704643有两种方法来进行过程综合和优化--启发式和解析式。启发式方法提供了快速的解决方案，但不能保证最优性。分析整数规划方法提供了严密性，但遭受了计算需求的组合爆炸(即，随着问题变得更大，解对大多数系统来说变得太大)。这个项目将进行分析调查，作为描述启发式和优化算法行为的一种理论手段，并产生一个框架，结合这两种方法的优点，同时消除它们的缺点。初步结果表明，在化工过程网络的多周期能力扩展问题的背景下，所提出的范例是可行的。它的多周期特性使得该问题类似于离散时间调度问题。与综合问题一样，同样的问题也需要优化上层建筑。通过对该问题的分析研究，提出了一种启发式算法，证明了该算法在关于问题参数的标准假设下是渐近最优的。在更广泛的过程综合和操作范围内，分析调查提供了大量的机会。计划的工作将明确地处理(I)多周期过程操作、(Ii)换热网络的合成和(Iii)分离网络的合成中的问题。PI的工作将针对(1)确定这些问题的计算复杂性，(2)分析现有启发式算法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算法。

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.