Constraint Programming to Discover One-Flip Local Optima of Quadratic Unconstrained Binary Optimization Problems

Verma, Amit; Lewis, Mark A.

doi:10.48550/arxiv.2104.01709

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2021

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“…Extensive computational tests indicate that the approach is viable for Max 3-SAT using a generic metaheuristic designed for the QUBO framework. Further improvement in computational performance could be achieved by utilizing the techniques proposed in [23,25].…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Efficient QUBO transformation for Higher Degree Pseudo Boolean Functions

Verma¹,

Lewis²,

Kochenberger³

2021

Preprint

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Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is useful to have a method for transforming higher degree pseudo-Boolean problems to QUBO format. The standard transformation approach requires additional auxiliary variables supported by penalty terms for each higher degree term. This paper improves on the existing cubicto-quadratic transformation approach by minimizing the number of additional variables as well as penalty coefficient. Extensive experimental testing on Max 3-SAT modeled as QUBO shows a near 100% reduction in the subproblem size used for minimization of the number of auxiliary variables.

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Section: Conclusion and Future Researchmentioning

confidence: 99%