用生成模型构建可表达复杂依赖的不确定性集,提升优化鲁棒性。
Generative Robust Optimisation

- 用神经网络解码器生成不确定性集,自动捕捉非线性相关与多模态特征。
- 在6种分布和6种架构下验证,兼具表达力、校准性和计算可解性。
- 适合需要高精度鲁棒优化的工业场景,如生产计划与设施选址。
传统鲁棒优化中的不确定性集采用固定几何形状,难以刻画真实数据中的复杂依赖关系。本文提出生成式鲁棒优化(Generative Robust Optimisation, GRO),其中深度生成模型通过神经网络解码器在标定的潜在空间上定义不确定性集,自然适应非线性相关性、不对称性和多模态结构。我们构建了一个五维评估框架(重建保真度、分布匹配、潜在空间规整性、鲁棒相关性、计算可处理性),为基于神经网络的不确定性集提供系统化、模型无关的评估标准。通过引入基于高斯混合模型引导训练的Wasserstein对抗自编码器,并结合约束一致性正则化以确保鲁棒相关性,同时将解码器限制为ReLU激活,实现通过混合整数规划嵌入进行精确最坏情况验证。在六种不确定性分布和六种生成架构下的生产计划问题,以及多周期设施选址研究中进行了广泛实验,结果表明,对五项指标的系统关注可使不确定性集同时具备强表达能力、良好校准性和优化可处理性。
原文摘要 · Abstract (English)
Classical uncertainty sets for robust optimisation impose fixed geometric shapes that cannot represent the complex dependencies present in real-world data. We propose Generative Robust Optimisation (GRO), a framework in which a deep generative model defines the uncertainty set as the image of a neural network decoder over a calibrated latent set, naturally accommodating nonlinear correlations, asymmetry, and multimodality. A five-point evaluation framework (reconstruction fidelity, distribution matching, latent regularity, robust relevance, and computational tractability) provides systematic, model-agnostic criteria for assessing any neural network-based uncertainty set. We instantiate this framework with a Wasserstein Adversarial Autoencoder employing Gaussian mixture model-guided training for latent regularity and constraint-consistency regularisation for robust relevance. Restricting the decoder to ReLU activations enables exact worst-case verification through mixed-integer programming embedding. Extensive experiments on a production planning problem across six uncertainty distributions and six generative architectures, together with a multi-period facility location study, validate the framework and demonstrate that systematic attention to all five criteria yields uncertainty sets that are simultaneously expressive, well-calibrated, and optimisation-tractable.
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