A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization

TL;DR

This paper introduces AGRO, a novel deep generative approach using variational autoencoders to generate realistic, adversarial contingencies for two-stage adaptive robust optimization, reducing planning costs and improving decision robustness.

Contribution

The paper presents AGRO, a new algorithm that leverages VAEs and differentiable optimization to generate high-dimensional, realistic contingencies for robust optimization, outperforming standard methods.

Findings

AGRO reduces planning costs by up to 11.6% in power system expansion.

AGRO outperforms traditional algorithms by up to 1.8% in production-distribution planning.

Generated contingencies are more realistic and high-density, improving robustness.

Abstract

Two-stage adaptive robust optimization (ARO) is a powerful approach for planning under uncertainty, balancing first-stage decisions with recourse decisions made after uncertainty is realized. To account for uncertainty, modelers typically define a simple uncertainty set over which potential outcomes are considered. However, classical methods for defining these sets unintentionally capture a wide range of unrealistic outcomes, resulting in overly-conservative and costly planning in anticipation of unlikely contingencies. In this work, we introduce AGRO, a solution algorithm that performs adversarial generation for two-stage adaptive robust optimization using a variational autoencoder. AGRO generates high-dimensional contingencies that are simultaneously adversarial and realistic, improving the robustness of first-stage decisions at a lower planning cost than standard methods. To ensure generated contingencies lie in high-density regions of the uncertainty distribution, AGRO defines a tight uncertainty set as the image of "latent" uncertainty sets under the VAE decoding transformation. Projected gradient ascent is then used to maximize recourse costs over the latent uncertainty sets by leveraging differentiable optimization methods. We demonstrate the cost-efficiency of AGRO by applying it to both a synthetic production-distribution problem and a real-world power system expansion setting. We show that AGRO outperforms the standard column-and-constraint algorithm by up to 1.8% in production-distribution planning and up to 11.6% in power system expansion.