Feasible solutions are crucial for Integer Programming (IP) since they can substantially speed up the solving process. In many applications, similar IP instances often exhibit similar structures and shared solution distributions, which can be potentially modeled by deep learning methods. Unfortunately, existing deep-learning-based algorithms, such as Neural Diving [21] and Predict-and-search framework [8], are limited to generating only partial feasible solutions, and they must rely on solvers like SCIP and Gurobi to complete the solutions for a given IP problem. In this paper, we propose a novel framework that generates complete feasible solutions end-to-end. Our framework leverages contrastive learning to characterize the relationship between IP instances and solutions, and learns latent embeddings for both IP instances and their solutions. Further, the framework employs diffusion models to learn the distribution of solution embeddings conditioned on IP representations, with a dedicated guided sampling strategy that accounts for both constraints and objectives. We empirically evaluate our framework on four typical datasets of IP problems, and show that it effectively generates complete feasible solutions with a high probability (> 89.7 %) without the reliance of Solvers and the quality of solutions is comparable to the best heuristic solutions from Gurobi. Furthermore, by integrating our method's sampled partial solutions with the CompleteSol heuristic from SCIP [19], the resulting feasible solutions outperform those from state-of-the-art methods across all datasets, exhibiting a 3.7 to 33.7% improvement in the gap to optimal values, and maintaining a feasible ratio of over 99.7% for all datasets.

Inbound parcel volume forecasting problem (IPVFP) plays an important role in the logistics system as it can facilitate various downstream applications. Despite the fact that a number of time series forecasting techniques have been developed, existing approaches fail to explicitly consider intrinsic characteristics of the logistics system, e.g., parcel transport patterns, operation patterns, and their spatial-temporal dependencies. To this end, we propose a novel hybrid inbound parcel volume forecasting model to analyze the logistic spatial-temporal graph that is constructed based on logistics data and the physical location of logistics stations. The graph includes engineered features such as the transition matrix and modified Dynamic Time Warping (DTW) distance matrix, which accurately depicts the parcel transfer patterns within the system. In addition, it incorporates a dedicated attention mechanism that introduces a novel bit-embedding representation method for integer tokens, enabling to capture of dynamic correlations among different timestamps. Finally, a collaborative module comprising dilated convolution layers and Gated Recurrent Units (GRU) is integrated to capture long-term dependencies. Extensive experiments on real-world data evaluate the effectiveness of the proposed graph and model, demonstrating its superiority over 16 other advanced baseline models. We release our code and data at https://github.com/YelsAlyssa/IPVFP.