Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex mixed‐integer nonlinear optimization

Large‐scale strongly nonlinear and nonconvex mixed‐integer nonlinear programming (MINLP) models frequently appear in optimization‐based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within acceptable time. In...

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Bibliographic Details
Published in:AIChE journal Vol. 68; no. 6
Main Authors: Ma, Yingjie, Li, Jie
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.06.2022
American Institute of Chemical Engineers
Subjects:
Algorithms
branch and bound
Branch and bound methods
Computational efficiency
Computer applications
Continuation methods
homotopy continuation
Integers
MINLP
Nonlinear programming
Optimization
Process control
Process controls
process synthesis
rigorous models
Synthesis
ISSN:0001-1541, 1547-5905
Online Access:Get full text
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Summary:Large‐scale strongly nonlinear and nonconvex mixed‐integer nonlinear programming (MINLP) models frequently appear in optimization‐based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within acceptable time. In this study, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB‐FP and HCBB‐RB) where the homotopy continuation method is employed to gradually approach the optimum of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results from solving four existing process synthesis problems demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB‐RB is superior to HCBB‐FP due to much lower computational effort required for the same locally optimal solution.
Bibliography:Funding information
China Scholarship Council ‐ The University of Manchester Joint Scholarship, Grant/Award Number: 201809120005
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ISSN:0001-1541
1547-5905
DOI:10.1002/aic.17629