Learning Warm Starts for the Simplex Method from Measured Solver Cost

Key points

• Prior work has shown that starting bases predicted by graph neural networks can sharply reduce iteration counts, but the time saved may fall well short of the iterations saved.1
• On 25 classes of linear programs (LPs), we find that a strong supervised basis predictor removes two thirds of the dual simplex's iterations but only a third of its time.1
• We introduce CostStart, which uses supervised prediction for the basis and trains a small policy on measured instruction counts to choose, per LP, how many predicted columns to use, which algorithm and pricing rule to run, and whether to warm-start at all.1
• On unseen LPs of the training classes, including LPs four times the training size, CostStart roughly halves the solve time relative to the solver's default start and is 1.4 to 2.2 times as fast as two published methods retrained on the same data.1

Sources (1)

• [1]Learning Warm Starts for the Simplex Method from Measured Solver Cost
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 08:19 PM

  Learned warm starts for the simplex method build starting bases using predictions of which variables will be basic at optimality.

  Prior work has shown that starting bases predicted by graph neural networks can sharply reduce iteration counts, but the time saved may fall well short of the iterations saved.

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