# Benchmarks

### Convex MINLP

Here is a solution profile from the benchmark in the paper:

Lundell, A. Kronqvist, J. and Westerlund, T. *The Supporting Hyperplane Optimization Toolkit: A Polyhedral Outer Approximation Based Convex MINLP Solver Utilizing a Single Branching Tree Approach* (2018). <http://www.optimization-online.org/DB_FILE/2018/06/6680.pdf>

where some commercial and noncommercial solvers were tested on 406 convex MINLP instances from [MINLPLib](http://www.minlplib.org). The commercial version of SHOT uses CPLEX and CONOPT as subsolvers, while the noncommercial version uses Cbc and IPOPT.

<div align="left"><img src="/files/-M9U_xHR7VAQnrdjmAoK" alt=""></div>

Some benchmarks (for an older version of SHOT 0.9.2) is available in the open-access journal paper:&#x20;

Kronqvist, J., Bernal, D.E, Lundell, A. and Grossmann, I.E. T. *A review and comparison of solvers for convex MINLP*. Optimization and Engineering 20(2), pp. 397-455 (2018). <https://link.springer.com/article/10.1007/s11081-018-9411-8>.

The files for the benchmarks are also available at: <https://andreaslundell.github.io/minlpbenchmarks/>.

### Nonconvex MINLP

Benchmarks for SHOT 1.0 on a test set of 326 nonconvex MINLP and MIQCQP problems are available in the preprint:

Lundell, A. and Kronqvist, J., *Polyhedral Approximation Strategies in Nonconvex Mixed-Integer Nonlinear Programming.* Optimization Online (2020). <http://www.optimization-online.org/DB_HTML/2020/03/7691.html>


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