Genetic Algorithm Based Coordination and Optimization Model for Generation Grid Load Storage in Active Distribution Networks

The increasing uncertainty from flexible demand and renewable generation has made distributionally robust optimization (DRO) an important tool for robust power system dispatch. DRO relies on forecast scenarios to construct ambiguity sets, but conventional scenario generation pipelines are often trained in an accuracy-oriented manner and may neglect spatial correlations among uncertainties. This mismatch can produce ambiguity sets that are statistically plausible but suboptimal for downstream operation. This work proposes a decision-focused generative framework for correlated scenario generation in DRO-based dispatch. Instead of training generative models solely to fit the historical uncertainty distribution, the proposed framework optimizes generated scenarios according to their induced downstream operational cost. The proposed framework is tailored to mainstream generative models, including variational autoencoders, generative adversarial networks, and diffusion models, while capturing the joint distribution of uncertainties across buses. To improve computational tractability, we further develop a differentiable scenario selector that selects decision-relevant scenarios from a generated pool and can be trained within the same decision-focused pipeline. Case studies demonstrate that the proposed framework effectively reduces 0.80%-2.02% operational cost across different generative models compared to accuracy-oriented methods.

Inventory and distribution planning in Physical Internet networks requires coordinating factory-hub assignments, factory supply, lateral transshipment among collaborative hubs, retailer deliveries, and shortages. The problem combines discrete assignment decisions with interdependent continuous flows, while uncertain operating costs make robust planning more difficult. This study formulates deterministic and min-max regret models for a three-echelon network of factories, hubs, and retailers and develops a graph neural network-guided genetic algorithm (GNN-GA) for the assignment decisions. The GNN estimates hub-specific factory-selection probabilities that are used to construct the initial GA population and adapt mutation according to prediction uncertainty. Each previously unseen candidate assignment is evaluated by solving the remaining continuous-flow problem to LP optimality. Simulated annealing, a standard GA, and GNN-GA are compared on 15 instances using matched random seeds and fixed limits on distinct assignment evaluations. Because the evaluation budgets for test Instances 13-15 are smaller than the nominal population size, these experiments primarily assess the quality of learned initialization rather than multi-generation evolutionary search. A separate 400-evaluation experiment on exact test Instance 13 permits three complete offspring generations and a partial fourth pass, with GNN-GA outperforming GA in all 10 matched runs. Three independently generated exact-solvable instances provide a separate test of transfer. Ablation results show that learned initialization provides most of the improvement, while entropy-guided mutation has a smaller, instance-dependent effect. Per-instance solution times include GNN inference and search but exclude model training and one-time model setup.

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.