Global optimization of mixed-integer nonlinear problems

Authors

  • C. S. Adjiman,

    1. Dept. of Chemical Engineering, Princeton University, Princeton, NJ 08544
    Current affiliation:
    1. Center for Process Systems Engineering, Imperial Colleg of Science, Technology and Medicine, Prince Consort Road, London SW7 2BY, UK: I. P. AndroulakisCC, Exxon Research and Development, Annandale, NJ
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  • I. P. Androulakis,

    1. Dept. of Chemical Engineering, Princeton University, Princeton, NJ 08544
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  • C. A. Floudas

    Corresponding author
    1. Dept. of Chemical Engineering, Princeton University, Princeton, NJ 08544
    • Dept. of Chemical Engineering, Princeton University, Princeton, NJ 08544
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Abstract

Two novel deterministic global optimization algorithms for nonconvex mixed-integer problems (MINLPs) are proposed, using the advances of the αBB algorithm for nonconvex NLPs of Adjiman et al. The special structure mixed-integer αBB algorithm (SMIN-αBB) addresses problems with nonconvexities in the continuous variables and linear and mixed-bilinear participation of the binary variables. The general structure mixed-integer αBB algorithm (GMIN-αBB) is applicable to a very general class of problems for which the continuous relaxation is twice continuously differentiable. Both algorithms are developed using the concepts of branch-and-bound, but they differ in their approach to each of the required steps. The SMIN-αBB algorithm is based on the convex underestimation of the continuous functions, while the GMIN-αBB algorithm is centered around the convex relaxation of the entire problem. Both algorithms rely on optimization or interval-based variable-bound updates to enhance efficiency. A series of medium-size engineering applications demonstrates the performance of the algorithms. Finally, a comparison of the two algorithms on the same problems highlights the value of algorithms that can handle binary or integer variables without reformulation.

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