The decomposition-based outer approximation algorithm for convex mixed-integer nonlinear programming

Pavlo Muts (), Ivo Nowak () and Eligius M. T. Hendrix ()
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Pavlo Muts: Hamburg University of Applied Sciences
Ivo Nowak: Hamburg University of Applied Sciences
Eligius M. T. Hendrix: University of Málaga

Journal of Global Optimization, 2020, vol. 77, issue 1, No 5, 75-96

Abstract: Abstract This paper presents a new two-phase method for solving convex mixed-integer nonlinear programming (MINLP) problems, called Decomposition-based Outer Approximation Algorithm (DECOA). In the first phase, a sequence of linear integer relaxed sub-problems (LP phase) is solved in order to rapidly generate a good linear relaxation of the original MINLP problem. In the second phase, the algorithm solves a sequence of mixed integer linear programming sub-problems (MIP phase). In both phases the outer approximation is improved iteratively by adding new supporting hyperplanes by solving many easier sub-problems in parallel. DECOA is implemented as a part of Decogo (Decomposition-based Global Optimizer), a parallel decomposition-based MINLP solver implemented in Python and Pyomo. Preliminary numerical results based on 70 convex MINLP instances up to 2700 variables show that due to the generated cuts in the LP phase, on average only 2–3 MIP problems have to be solved in the MIP phase.

Keywords: Global optimization; Decomposition method; Convex MINLP; Outer approximation; DECOA (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10898-020-00888-x

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