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Generation techniques for linear programming instances with controllable properties

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Abstract

This paper addresses the problem of generating synthetic test cases for experimentation in linear programming. We propose a method which maps instance generation and instance space search to an alternative encoded space. This allows us to develop a generator for feasible bounded linear programming instances with controllable properties. We show that this method is capable of generating any feasible bounded linear program, and that parameterised generators and search algorithms using this approach generate only feasible bounded instances. Our results demonstrate that controlled generation and instance space search using this method achieves feature diversity more effectively than using a direct representation.

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Acknowledgements

The authors would like to thank the anonymous referees from Mathematical Programming Computation whose thorough comments significantly improved the focus and quality of this work.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3010, Australia

    Simon Bowly & Kate Smith-Miles

  2. School of Mathematical Sciences, Monash University, Clayton, VIC, 3800, Australia

    Davaatseren Baatar

  3. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA

    Hans Mittelmann

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  1. Simon Bowly
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  2. Kate Smith-Miles
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  3. Davaatseren Baatar
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  4. Hans Mittelmann
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Correspondence to Simon Bowly.

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This research is funded by the Australian Research Council under Australian Laureate Fellowship FL140100012.

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Bowly, S., Smith-Miles, K., Baatar, D. et al. Generation techniques for linear programming instances with controllable properties. Math. Prog. Comp. 12, 389–415 (2020). https://doi.org/10.1007/s12532-019-00170-6

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