Becu, B., Dey, S. S., Qiu, F., & Xavier, Á. S. (2024). Approximating the Gomory Mixed-Integer Cut Closure Using Historical Data. arXiv preprint arXiv:2411.15090.
This paper investigates the potential of using historical data to generate effective cutting planes for families of similar mixed-integer linear programming (MILP) instances, aiming to improve solver performance.
The authors propose a learning heuristic inspired by their theoretical finding that a finite set of constraint aggregation multipliers can generate the Gomory Mixed-Integer Cut (GMIC) closure for an infinite family of MILPs with the same constraint matrix and right-hand-sides belonging to a lattice. The heuristic involves collecting GMIC cuts from multiple tableau bases of training instances and reusing these multipliers to generate cuts for new test instances. They evaluate different cut selection strategies based on instance similarity and varying numbers of training instances.
The study demonstrates the effectiveness of using historical data for generating strong cutting planes and improving MILP solver performance. The proposed learning heuristic, despite its simplicity, shows promising results and opens up new avenues for data-driven optimization.
This research contributes to the growing field of data-driven optimization by providing both theoretical insights and practical methods for leveraging historical data to enhance MILP solution processes.
The authors acknowledge limitations in their cut generation implementation and suggest exploring more sophisticated expert methods and handling more dramatic changes in problem data as future research directions. Further theoretical investigation into generalizing the finite multiplier result for broader families of cuts is also encouraged.
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