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Large-scale LP problems from industry usually contain much redundancy thatseverely hurts the efficiency and reliability of solving LPs, making presolve(i.e., the problem simplification module) one of the most critical componentsin modern LP solvers. However, how to design high-quality presolve routines --that is, the program determining (P1) which presolvers to select, (P2) in whatorder to execute, and (P3) when to stop -- remains a highly challenging taskdue to the extensive requirements on expert knowledge and the large searchspace. Due to the sequential decision property of the task and the lack ofexpert demonstrations, we propose a simple and efficient reinforcement learning(RL) framework -- namely, reinforcement learning for presolve (RL4Presolve) --to tackle (P1)-(P3) simultaneously. Specifically, we formulate the routinedesign task as a Markov decision process and propose an RL framework withadaptive action sequences to generate high-quality presolve routinesefficiently. Note that adaptive action sequences help learn complex behaviorsefficiently and adapt to various benchmarks. Experiments on two solvers(open-source and commercial) and eight benchmarks (real-world and synthetic)demonstrate that RL4Presolve significantly and consistently improves theefficiency of solving large-scale LPs, especially on benchmarks from industry.Furthermore, we optimize the hard-coded presolve routines in LP solvers byextracting rules from learned policies for simple and efficient deployment toHuawei's supply chain. The results show encouraging economic and academicpotential for incorporating machine learning to modern solvers.

Accelerate Presolve in Large-Scale Linear Programming via Reinforcement Learning