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Global mixed-integer dynamic optimization

Authors

  • Benoît Chachuat,

    1. Process Systems Engineering Laboratory, Dept. of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
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  • Adam B. Singer,

    1. Process Systems Engineering Laboratory, Dept. of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
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  • Paul I. Barton

    Corresponding author
    1. Process Systems Engineering Laboratory, Dept. of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
    • Process Systems Engineering Laboratory, Dept. of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

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. © 2005 American Institute of Chemical Engineers AIChE J, 2005

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