Multimodal freight transportation is essential for enhancing logistics efficiency and reducing costs, with route optimization as its core component. However, uncertainties are prevalent in multimodal systems, posing challenges for the construction and validation of simulation models. Furthermore, the involvement of multiple stakeholders introduces conflicting optimization objectives. Effectively balancing these objectives to maximize overall benefits has become a critical issue that requires resolution. For the multimodal transport route optimization problem in hybrid uncertainty environments (e.g., there are uncertainties in transportation demand, transportation time, and transfer time), this study constructs a multiobjective optimization model based on fuzzy numbers. The complexity of the model is reduced by introducing the chance-constrained programming theory. To solve the model, a data-driven multi-objective evolutionary algorithm is designed, integrating Monte Carlo simulation with surrogate models to effectively reduce the computational cost of uncertainty estimation. Furthermore, a constraint prioritization strategy is developed to handle multiple conflict objectives, and complex constraints efficiently. Simulation results demonstrate that the proposed algorithm exhibits excellent performance across networks of varying scales, providing robust decision support for multimodal transportation decision-making.

Mixed-integer linear programming (MILP) is a cornerstone of optimization with applications across numerous domains. However, the development and evaluation of MILP-solving algorithms are hindered by existing benchmark datasets, which are often limited in scale, lack diversity, and are poorly structured, making them inadequate for systematic testing across different solving approaches, especially for machine learning (ML)-based methods. To address these issues, we introduce MILPBench, a large-scale benchmark suite comprising 100,000 MILP instances organized into 60 well-categorized classes. Using structural properties and embedding similarity metrics, we developed a novel classification framework to ensure both intra-class homogeneity and inter-class diversity. In addition to the dataset, MILPBench includes a comprehensive baseline library featuring 15 mainstream solving methods, spanning traditional solvers, heuristic algorithms, and ML-based approaches. This design enables rigorous and standardized evaluation of MILP-solving algorithms under diverse conditions. Extensive benchmarking demonstrates the utility of MILPBench as a scalable and versatile testbed for advancing MILP research, fostering innovation in solver development, and bridging the gap between optimization and machine learning.

Recent decomposition-based neural multi-objective combinatorial optimization (MOCO) methods struggle to achieve desirable performance. Even equipped with complex learning techniques, they often suffer from significant optimality gaps in weight-specific subproblems. To address this challenge, we propose a neat weight embedding method to learn weight-specific representations, which captures weight-instance interaction for the subproblems and was overlooked by most current methods. We demonstrate the potentials of our method in two instantiations. First, we introduce a succinct addition model to learn weight-specific node embeddings, which surpassed most existing neural methods. Second, we design an enhanced conditional attention model to simultaneously learn the weight embedding and node embeddings, which yielded new state-of-the-art performance. Experimental results on classic MOCO problems verified the superiority of our method. Remarkably, our method also exhibits favorable generalization performance across problem sizes, even outperforming the neural method specialized for boosting size generalization.

We propose a novel algorithm for online resource allocation with non-stationary customer arrivals and unknown click-through rates. We assume multiple types of customers arriving in a nonstationary stochastic fashion, with unknown arrival rates in each period. Additionally, customers’ click-through rates are assumed to be unknown and only learnable online. By leveraging results from the stochastic contextual bandit with knapsack and online matching with adversarial arrivals, we develop an online scheme to allocate the resources to nonstationary customers. We prove that under mild conditions, our scheme achieves a “best-of-both-world” result: the scheme has a sublinear regret when the customer arrivals are near-stationary, and enjoys an optimal competitive ratio under general (non-stationary) customer arrival distributions. Finally, we conduct extensive numerical experiments to show our approach generates near-optimal revenues for all different customer scenarios.