Accelerating Benders decomposition for solving a sequence of sample average approximation replications

TL;DR

This paper develops techniques to speed up solving multiple sample average approximation replications of stochastic programs by exploiting similarities across replications using Benders decomposition, significantly reducing solution times.

Contribution

It introduces methods to leverage information from previous replications to accelerate solving sequential SAA problems with Benders decomposition.

Findings

Significant reduction in solution time for later replications.

Effective use of problem structure similarities across replications.

Empirical validation through extensive computational experiments.

Abstract

Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from solving an SAA is random, statistical estimates on the optimal value of the true problem can be obtained by solving multiple SAA replications with independent samples. We study techniques to accelerate the solution of this set of SAA replications, when solving them sequentially via Benders decomposition. We investigate how to exploit similarities in the problem structure, as the replications just differ in the realizations of the random samples. Our extensive computational experiments provide empirical evidence that our techniques for using information from solving previous replications can significantly reduce the solution time of later replications.