Abstract
Quantified mixed integer linear programs (QMIPs) are mixed integer linear programs (MIPs) with variables being either existentially or universally quantified. They can be interpreted as two-person zero-sum games between an existential and a universal player on the one side, or multistage optimization problems under uncertainty on the other side. Solutions of QMIPs are so-called winning strategies for the existential player that specify how to react on moves—certain fixations of universally quantified variables—of the universal player to certainly win the game. In order to solve the QMIP optimization problem, where the task is to find an especially attractive winning strategy, we examine the problem’s hybrid nature and present the open source solver Yasol that combines linear programming techniques with solution techniques from game-tree search.
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Notes
- 1.
For brevity, we use “he” and “his” whenever “he or she” and “his or her” are meant.
- 2.
The sources and an installation guide can be found on http://www.q-mip.org.
- 3.
Also see http://www.q-mip.org for more detail.
- 4.
For further information see miplib.zib.de.
- 5.
For further information see lonsing.github.io/depqbf.
- 6.
The used instances can be found on http://q-mip.org/index.php?id=3.
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Ederer, T., Hartisch, M., Lorenz, U., Opfer, T., Wolf, J. (2017). Yasol: An Open Source Solver for Quantified Mixed Integer Programs. In: Winands, M., van den Herik, H., Kosters, W. (eds) Advances in Computer Games. ACG 2017. Lecture Notes in Computer Science(), vol 10664. Springer, Cham. https://doi.org/10.1007/978-3-319-71649-7_19
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