A loose Benders decomposition algorithm for approximating two-stage mixed-integer recourse models

We propose a new class of convex approximations for two-stage mixed-integer recourse models, the so-called generalized alpha-approximations. The advantage of these convex approximations over existing ones is that they are more suitable for efficient computations. Indeed, we construct a loose Benders decomposition algorithm that solves large problem instances in reasonable time. To guarantee the performance of the resulting solution, we derive corresponding error bounds that depend on the total variations of the probability density functions of the random variables in the model. The error bounds converge to zero if these total variations converge to zero. We empirically assess our solution method on several test instances, including the SIZES and SSLP instances from SIPLIB. We show that our method finds near-optimal solutions if the variability of the random parameters in the model is large. Moreover, our method outperforms existing methods in terms of computation time, especially for large problem instances.

Automated summary

The study introduces a new class of convex approximations, generalized alpha-approximations, which are more suitable for efficient computations than existing methods. By constructing a loose Benders decomposition algorithm, large problem instances can be solved in reasonable time.