A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic Mixed-Integer Problems

TL;DR

This paper introduces TULIP, a two-step method that efficiently solves large-scale two-stage stochastic mixed-integer programs by reducing scenarios and accelerating the solution process, demonstrated on benchmark problems.

Contribution

The paper proposes the TULIP algorithm, a novel two-step approach that improves computational efficiency for large-scale stochastic mixed-integer problems by scenario reduction and constraint acceleration.

Findings

TULIP significantly reduces computation time compared to traditional methods.

The method is effective on benchmark problems like vehicle routing and Steiner forest.

Numerical experiments confirm the generic effectiveness of TULIP.

Abstract

Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm ("Two-step warm start method Used for solving Large-scale stochastic mixed-Integer Problems"), a two-step approach for solving two-stage stochastic (mixed) integer linear programs with an exponential number of constraints. In this approach, we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of TULIP on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. The results of our extensive numerical experiments show that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut.