Global optimization of mixed-integer nonlinear problems

C. S. Adjiman, I. P. Androulakis, C. A. Floudas

Research output: Contribution to journalReview article

204 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1769-1797
Number of pages29
JournalAIChE Journal
Volume46
Issue number9
DOIs
StatePublished - Sep 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Environmental Engineering
  • Chemical Engineering(all)

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