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

摘要-Sahinidad- 9704643 有两种方法来进行过程综合和优化-启发式和分析。 启发式提供快速的解决方案，但不能保证最优性。 分析整数规划方法提供了严格性，但遭受计算需求的组合爆炸（即，随着问题变得更大，解决方案对于大多数系统来说在计算上变得太大）。 该项目将追求分析研究作为一种理论手段，以表征算法和优化算法的行为，并产生一个框架，结合这两种方法的优点，同时消除它们的弱点。 初步结果表明，所提出的范例的背景下，多期的能力扩张问题的化工过程网络。 它的多周期方面使这个问题类似于离散时间调度。 同样的问题需要优化的超结构在综合问题。 这个问题的分析调查导致的启发式的发展，这被证明是渐近最优的标准假设下的问题参数。 在工艺合成和操作的更一般范围内，分析研究提供了大量的机会。 计划中的工作将明确地处理（I）多周期过程操作中的问题，（ii）热交换器网络的合成，和（iii）分离网络的合成。 PI的工作将致力于（1）确定这些问题的计算复杂性，（2）分析现有算法的最坏情况和预期行为，以及（3）开发新的、基于数学编程的多项式时间算法，这些算法在统计意义上是最优的。

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.