Generation techniques for linear and integer programming instances with controllable properties

This paper addresses the problem of generating synthetic test cases for experimentation in linear and mixed integer programming. We propose a generation framework to shift instance generation and search processes to an alternative encoded space. The framework is applied to produce 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 random generation and search algorithms in this framework generate only instances with this property. Our results demonstrate that controlled random generation and instance space search using this method achieves feature diversity more effectively than using a direct representation. Furthermore, local search algorithms in the encoded space are able to increase the difficulty of generated instances for linear programming algorithms. This research opens further questions as to the suitability of various search algorithms for targeted instance design, convergence of search algorithms in instance space, and appropriate predictive features for LP and MIP algorithm performance. ? Corresponding author. This research is funded by the Australian Research Council under Australian Laureate Fellowship FL140100012. S. Bowly · K. Smith-Miles · D. Baatar School of Mathematical Sciences Monash University, Clayton VIC 3800, Australia E-mail: simon.bowly@monash.edu K. Smith-Miles E-mail: kate.smith-miles@monash.edu D. Baatar E-mail: davaatseren.baatar@monash.edu H. Mittelmann School of Mathematical and Statistical Sciences Arizona State University, Tempe, AZ 85287-1804, U.S.A. E-mail: mittelmann@asu.edu