A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs

TL;DR

This paper introduces a supervised learning method to efficiently identify representative scenarios in two-stage stochastic integer programs, enabling near-optimal solutions with reduced computation time.

Contribution

It presents a novel learning-based approach that predicts representative scenarios to quickly obtain high-quality primal solutions for 2SIP problems, ensuring feasibility and efficiency.

Findings

Consistently finds near-optimal solutions in facility location problems.

Achieves computational times comparable to general-purpose solvers.

Guarantees first-stage feasibility through scenario prediction.

Abstract

We propose a novel approach using supervised learning to obtain near-optimal primal solutions for two-stage stochastic integer programming (2SIP) problems with constraints in the first and second stages. The goal of the algorithm is to predict a "representative scenario" (RS) for the problem such that, deterministically solving the 2SIP with the random realization equal to the RS, gives a near-optimal solution to the original 2SIP. Predicting an RS, instead of directly predicting a solution ensures first-stage feasibility of the solution. If the problem is known to have complete recourse, second-stage feasibility is also guaranteed. For computational testing, we learn to find an RS for a two-stage stochastic facility location problem with integer variables and linear constraints in both stages and consistently provide near-optimal solutions. Our computing times are very competitive with those of general-purpose integer programming solvers to achieve a similar solution quality.