One way, used in [1], is use this heuristic: Solve the problem in continuous space. Conduct a bi-dimensional search for the nearest valid (discrete) values. If there were N parameters, there would be at most 2^N possible options. Apply the same utility function or a different one to find the best option.
Another way, used in [2], is a branch and bound algorithm [3] that uses heuristic evaluation, which allows to optimise over a discrete data set in linear time. In [2], the utilized two versions (Promote and Boost), but the results were similar.
References
[1] Mu, Mu, et al. "User-level fairness delivered: network resource allocation for adaptive video streaming." 2015 IEEE 23rd International Symposium on Quality of Service (IWQoS). IEEE, 2015.
[2] Georgopoulos, Panagiotis, et al. "Towards network-wide QoE fairness using openflow-assisted adaptive video streaming." Proceedings of the 2013 ACM SIGCOMM workshop on Future human-centric multimedia networking. ACM, 2013.
[3] R. J. Dakin. A Tree-search Algorithm for Mixed Integer Programming Problems. Comput. J., 8(3):250{255, 1965.
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