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Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs

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Abstract

We present a parallel large neighborhood search framework for finding high quality primal solutions for general mixed-integer programs (MIPs). The approach simultaneously solves a large number of sub-MIPs with the dual objective of reducing infeasibility and optimizing with respect to the original objective. Both goals are achieved by solving restricted versions of two auxiliary MIPs, where subsets of the variables are fixed. In contrast to prior approaches, ours does not require a feasible starting solution. We leverage parallelism to perform multiple searches simultaneously, with the objective of increasing the effectiveness of our heuristic. We computationally compare the proposed framework with a state-of-the-art MIP solver in terms of solution quality, scalability, reproducibility, and parallel efficiency. Results show the efficacy of our approach in finding high quality solutions quickly both as a standalone primal heuristic and when used in conjunction with an exact algorithm.

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Acknowledgements

We wish to thank the referees, whose comments led to an improved version of the paper.

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Correspondence to Lluís-Miquel Munguía.

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This research has been supported in part by ExxonMobil Upstream Research Company, the National Science Foundation, the Office of Naval Research and the Air Force Office of Scientific Research.

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Munguía, LM., Ahmed, S., Bader, D.A. et al. Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs. Comput Optim Appl 69, 1–24 (2018). https://doi.org/10.1007/s10589-017-9934-5

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