Learning to select cuts for efficient mixed-integer programming

Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions the early stage, thus largely reducing computational burden without hurting solution accuracy. However, major cut approaches heavily rely on heuristics, which strongly depend specific problem at hand and limit their generalization capability. In this paper, we propose data-driven generalizable approach, named Cut Ranking, settings multiple instance learning. To measure quality candidate cuts, scoring function, takes instance-specific features as inputs, is trained applied ranking selection. order to evaluate our method, conduct extensive experiments both synthetic datasets real-world datasets. Compared with commonly used heuristics selection, learning-based policy has shown be more effective, capable generalizing over problems different properties. Ranking been deployed an industrial solver large-scale MIPs. online A/B testing product planning than 107 variables constraints daily, achieved average speedup ratio 12.42% production any accuracy loss solution.