Abstract
In this chapter, we discuss instances of QUBO where the input data is random. Such random instances are often analyzed within the topic of “probabilistic combinatorial optimization” and the goal is to study the behavior of the distribution of the optimal value and the distribution of the optimal solution. The introduction of randomness makes the problem more challenging from a computational perspective. We discuss a probabilistic model with dependent random variables where it is possible to extend many of the known computational results from deterministic QUBO to random QUBO. We also review an interesting asymptotic characterization of the random optimal value under independent and identically distributed random variables.
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Acknowledgements
We would like to thanks Dongjian Shi and Toh Kim Chuan for their significant contributions to the work discussed in this chapter. This work was done as part of the PhD thesis titled “Regret models and preprocessing techniques for combinatorial optimization under uncertainty” by Dongjian Shi at the National University of Singapore. The author of this chapter and Toh Kim Chuan were his doctoral advisors.
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Natarajan, K. (2022). The Random QUBO. In: Punnen, A.P. (eds) The Quadratic Unconstrained Binary Optimization Problem. Springer, Cham. https://doi.org/10.1007/978-3-031-04520-2_7
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DOI: https://doi.org/10.1007/978-3-031-04520-2_7
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