用生成模型设计更真实、低成本的不确定性场景,提升规划鲁棒性。
A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization
- 基于变分自编码器生成高维对抗性但真实的不确定性场景。
- 在生产-配送和电力系统扩展中,成本降低1.8%至11.6%。
- 适合需要平衡安全与成本的决策优化场景。
两阶段自适应鲁棒优化(ARO)是应对不确定性的强大规划方法,需在第一阶段决策后,根据实际不确定性情况做出补救决策。传统方法定义的不确定性集常包含大量不现实的情景,导致规划过度保守且成本过高。本文提出AGRO算法,利用变分自编码器(VAE)进行对抗性生成,构建同时具备对抗性和真实性的高维情景。AGRO通过将潜在空间中的不确定性集映射到高密度区域,确保生成情景分布合理;再结合可微优化的投影梯度上升法,在潜在空间最大化补救成本。在合成生产-配送问题和真实电力系统扩展案例中验证,相比标准列与约束算法,AGRO在生产-配送中提升1.8%,在电力系统扩展中提升11.6%,显著降低规划成本。
原文摘要 · Abstract (English)
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.
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