An objective space cut and bound algorithm for convex multiplicative programmes

Authors:
Lizhen Shao;Matthias Ehrgott
Affiliations:
Key Laboratory of Advanced Control of Iron and Steel Process (Ministry of Education), School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China ...;Department of Management Science, Lanacaster University Management School, Bailrigg, Lancaster, UK LA1 4YX and Department of Engineering Science, The University of Auckland, Auckland, New Zealand ...
Venue:
Journal of Global Optimization
Year:
2014

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Abstract

Multiplicative programming problems are global optimisation problems known to be NP-hard. In this paper we propose an objective space cut and bound algorithm for approximately solving convex multiplicative programming problems. This method is based on an objective space approximation algorithm for convex multi-objective programming problems. We show that this multi-objective optimisation algorithm can be changed into a cut and bound algorithm to solve convex multiplicative programming problems. We use an illustrative example to demonstrate the working of the algorithm. Computational experiments illustrate the superior performance of our algorithm compared to other methods from the literature.