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

• Published in: Journal of global optimization Vol. 77; no. 1; pp. 75 - 96
• Main Authors: Muts, Pavlo, Nowak, Ivo, Hendrix, Eligius M. T
• Format: Journal Article
• Language: English
• Published: New York, NY Springer US 01.05.2020; Springer; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computer Science; Convex MINLP; DECOA; Decomposition; Decomposition method; Global optimization; Hyperplanes; Integer programming; Linear programming; Mathematics; Mathematics and Statistics; Mixed integer; Nonlinear programming; Operations Research/Decision Theory; Optimization; Outer approximation; Real Functions; Global optimization; DECOA; Convex MINLP; Outer approximation; Decomposition method
• ISSN: 1573-2916; 0925-5001; 1573-2916
• DOI: 10.1007/s10898-020-00888-x

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.