Global mixed-integer dynamic optimization

TitleGlobal mixed-integer dynamic optimization
Publication TypeJournal Article
Year of Publication2005
AuthorsChachuat B, Singer AB, Barton PI
JournalAIChE Journal

Recent advances in process synthesis, design, operations, and control have created an increasing demand for efficient numerical algorithms for optimizing a dynamic system coupled with discrete decisions; these problems are termed mixed-integer dynamic optimization (MIDO). In this communication, we develop a decomposition approach for a quite general class of MIDO problems that is capable of guaranteeing finding a global solution despite the nonconvexities inherent in the dynamic optimization subproblems. Two distinct algorithms are considered. On finite termination, the first algorithm guarantees finding a global solution of the MIDO within nonzero tolerance; the second algorithm finds rigorous bounds bracketing the global solution value, with a substantial reduction in computational expense relative to the first algorithm. A case study is presented in connection with the optimal design and operation of a batch process consisting of a series reaction followed by a separation with no intermediate storage. The developed algorithms demonstrate efficiency and applicability in solving this problem. Several heuristics are tested to enhance convergence of the algorithms; in particular, the use of bounds tightening techniques and the addition of cuts resulting from a screening model of the batch process are considered.