Research
Publications
The methods in SHOT are described in peer-reviewed papers. If you use SHOT in your research, please cite it.
Cite SHOT
The SHOT papers
Please cite these papers if you use SHOT in your research. The first describes the solver; the second describes its features for nonconvex problems.
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2022
The supporting hyperplane optimization toolkit for convex MINLP
Journal of Global Optimization, 84(1), 1–41
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2022
Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT
Journal of Global Optimization, 82(4), 863–896
@article{Lundell2022SHOT,
author = {Lundell, Andreas and Kronqvist, Jan and Westerlund, Tapio},
title = {The supporting hyperplane optimization toolkit for convex {MINLP}},
journal = {Journal of Global Optimization},
volume = {84},
number = {1},
pages = {1--41},
year = {2022},
doi = {10.1007/s10898-022-01128-0}
}
@article{Lundell2022Nonconvex,
author = {Lundell, Andreas and Kronqvist, Jan},
title = {Polyhedral approximation strategies for nonconvex mixed-integer
nonlinear programming in {SHOT}},
journal = {Journal of Global Optimization},
volume = {82},
number = {4},
pages = {863--896},
year = {2022},
doi = {10.1007/s10898-021-01006-1}
}Both papers in BibTeX, ready for your bibliography. Both are open access.
Methods
SHOT and its algorithms
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2019
A center-cut algorithm for quickly obtaining feasible solutions and solving convex MINLP problems
Computers & Chemical Engineering, 122, 105–113
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2019
AIP Conference Proceedings, 2070, 020012
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2019
On solving nonconvex MINLP problems with SHOT
Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019), Advances in Intelligent Systems and Computing, 991, 448–457
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2019
Convex MINLP – an efficient tool for design and optimization tasks?
Computer Aided Chemical Engineering, 47, 245–250
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2018
Reformulations for utilizing separability when solving convex MINLP problems
Journal of Global Optimization, 71(3), 571–592
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2017
SHOT – a global solver for convex MINLP in Wolfram Mathematica
Computer Aided Chemical Engineering, 40, 2137–2142
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2017
A center-cut algorithm for solving convex mixed-integer nonlinear programming problems
Computer Aided Chemical Engineering, 40, 2131–2136
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2016
The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming
Journal of Global Optimization, 64(2), 249–272
Workshops
Workshop papers
Short papers from the Global Optimization Workshop series (GOW, HUGO and STOGO).
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2025
Stockholm Global Optimization Workshop (STOGO 2025), 129–132
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2025
Improved bounding techniques for nonconvex MINLP in SHOT
Stockholm Global Optimization Workshop (STOGO 2025), 133–136
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2025
A parallel framework for primal heuristics in SHOT
Stockholm Global Optimization Workshop (STOGO 2025), 137–140
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2025
Separating hyperplanes for mixed-integer polynomial optimization problems
Stockholm Global Optimization Workshop (STOGO 2025), 199–202
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2022
Eigendecomposition-based reformulations for convex MINLP in the SHOT solver
Hungarian Global Optimization Workshop (HUGO 2022), 107–110
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2022
On solving MINLP problems with nonconvex signomials in SHOT
Hungarian Global Optimization Workshop (HUGO 2022), 129–132
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2016
Improvements to the supporting hyperplane optimization toolkit solver for convex MINLP
XIII Global Optimization Workshop (GOW’16), 101–104
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2016
Lifted polyhedral approximations in convex mixed integer nonlinear programming
XIII Global Optimization Workshop (GOW’16), 117–120
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2014
An extended supporting hyperplane algorithm for convex MINLP problems
XII Global Optimization Workshop (GOW’14), 21–24
Preprints
Recent preprints
Work that is part of, or builds on, SHOT 2.0.
- 2026
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2026
Separating hyperplanes for mixed-integer polynomial optimization problems
Optimization Online
Global optimization
Reformulations and global optimization
Earlier research by the team on global optimization of nonconvex MINLP problems, in particular signomial transformations and reformulations, which also underlies SHOT’s reformulation engine.
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2018
Solving global optimization problems using reformulations and signomial transformations
Computers & Chemical Engineering, 116, 122–134
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2016
Global optimisation of a portfolio adjustment problem under credibility measures
International Journal of Operational Research, 25(4), 464–474
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2015
Computer Aided Chemical Engineering, 37, 833–838
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2013
A reformulation framework for global optimization
Journal of Global Optimization, 57(1), 115–141
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2013
Computer Aided Chemical Engineering, 32, 529–534
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2013
The reformulation-based αGO algorithm for solving nonconvex MINLP problems – some improvements
Chemical Engineering Transactions, 32, 1321–1326
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2013
Improved discrete reformulations for the quadratic assignment problem
Lecture Notes in Computer Science, 7874, 193–203
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2012
Finding an optimized set of transformations for convexifying nonconvex MINLP problems
Computer Aided Chemical Engineering, 31, 1497–1501
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2011
Global optimization of mixed-integer signomial programming problems
Mixed Integer Nonlinear Programming, The IMA Volumes in Mathematics and its Applications, 154, 349–369
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2011
Some notes on convex relaxations
AIDIC Conference Series, 10, 383–392
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2011
Global optimization with C2 constraints by convex reformulations
Chemical Engineering Transactions, 24, 373–378
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2011
On convex relaxations in nonconvex optimization
Chemical Engineering Transactions, 24, 331–336
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2010
Global optimization of signomial programming problems
Workshop on Mixed Integer Nonlinear Programming
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2009
Convex underestimation strategies for signomial functions
Optimization Methods & Software, 24(4–5), 505–522
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2009
Some transformation techniques with applications in global optimization
Journal of Global Optimization, 43(2–3), 391–405
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2009
Implementation of a convexification technique for signomial functions
Computer Aided Chemical Engineering, 26, 579–583
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2009
Computer Aided Chemical Engineering, 27, 231–236
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2009
On the relationship between power and exponential transformations for positive signomial functions
Chemical Engineering Transactions, 17, 1287–1292
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2009
On the relationship between some transformations for positive signomial terms
AIDIC Conference Series, 9, 187–196
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2009
Transformation techniques for signomial functions in global optimization
PhD thesis, Åbo Akademi University
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2008
Exponential and power transformations for convexifying signomial terms in MINLP problems
Proceedings of the 27th IASTED International Conference on Modelling, Identification and Control, 154–159
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2007
Optimization of power transformations in global optimization
Chemical Engineering Transactions, 11, 95–100
Benchmarks
Solver comparisons
A comparison of SHOT with other convex MINLP solvers on the convex instances in MINLPLib. Note that the paper is from 2019 and used an older version of SHOT (0.9.2); SHOT has changed considerably since.
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2019
A review and comparison of solvers for convex MINLP
Optimization and Engineering, 20(2), 397–455
Theses
Theses on SHOT
Master’s theses at Åbo Akademi University that have contributed to SHOT.
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2025
Developing a Python interface utilizing pybind11 for SHOT
Master’s thesis, Åbo Akademi University
Contribution: The initial Python interface
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2025
Enhancements for nonconvex MINLP in SHOT
Master’s thesis, Åbo Akademi University
Contribution: Nonconvex MINLP
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2024
Automated release management and testing for SHOT
Master’s thesis, Åbo Akademi University
Contribution: Release management and testing with GitHub
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2024
Implementation of a distributed benchmarking system for optimization solvers
Master’s thesis, Åbo Akademi University
Contribution: The benchmark system
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2023
Master’s thesis, Åbo Akademi University
Contribution: VIVA, for analyzing and visualizing benchmark results