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An objective space cut and bound algorithm for convex multiplicative programmes

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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.

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Authors and Affiliations

  1. 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, 100083, China

    Lizhen Shao

  2. Department of Management Science, Lanacaster University Management School, Bailrigg, Lancaster, LA1 4YX, UK

    Matthias Ehrgott

  3. Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Matthias Ehrgott

Authors
  1. Lizhen Shao
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  2. Matthias Ehrgott
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Corresponding author

Correspondence to Lizhen Shao.

Additional information

This work has been partially supported by the National Natural Science Foundation of China (No. 81000650), the Ph.D. Programs Foundation of Ministry of Education of China (No. 20100006120016), Beijing Key Discipline Development Program (No. XK100080537) and National High-tech Research Development Program of China (863 Program) (No. 2013AA040705).

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Shao, L., Ehrgott, M. An objective space cut and bound algorithm for convex multiplicative programmes. J Glob Optim 58, 711–728 (2014). https://doi.org/10.1007/s10898-013-0102-x

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