Title: A partitioning algorithm for the mixed integer nonlinear programming problem

Authors: Biket Ergüneş; Linet Özdamar; Onur Demir; Nur Gülcan

Addresses: Department of Systems Engineering, Yeditepe University, Kayisdagi Cad., 34755 Kadıkoy, Istanbul, Turkey ' Department of Systems Engineering, Yeditepe University, Kayisdagi Cad., 34755 Kadıkoy, Istanbul, Turkey ' Department of Computer Engineering, Yeditepe University, Kayisdagi Cad., 34755 Kadıkoy, Istanbul, Turkey ' Department of Systems Engineering, Yeditepe University, Kayisdagi Cad., 34755 Kadıkoy, Istanbul, Turkey

Abstract: An interval partitioning method (IPM) is proposed to solve the (non-convex) mixed integer nonlinear programming problem (MINLP). The MINLP is encountered in many application areas and solving this problem bears practical importance. This paper proposes an IPM where two tree search strategies (breadth first and mixed breadth/depth first) and three variable subdivision methods are implemented. Two proposed variable subdivision methods are novel and they prioritise variables hierarchically according to several features. The IPM is implemented on a set of non-convex MINLP instances extracted from the MINLP benchmarks and numerical results show that its performance is quite promising.

Keywords: mixed integer nonlinear programming; MINLP; interval partitioning; global optimisation; variable subdivision rules; tree search.

DOI: 10.1504/IJOR.2017.081469

International Journal of Operational Research, 2017 Vol.28 No.2, pp.201 - 215

Received: 30 Sep 2014
Accepted: 29 Nov 2014

Published online: 02 Jan 2017 *

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