# Learning-Based Optimisation for Integrated Problems in
## 5 Discussion
### Future Perspectives on NCO  
Prediction and forecasting: In future logistics services, prediction and forecasting will play a critical role, especially for designing integrated AI-based decision supportsystems and smart digital twins. We particularly highlight the ability of GNNs and GANs to embed, process, and predict spatial and temporal information (e.g., vehicles, demand, delays). Today, Graph Attention Transformers (GATs) are already widely used in various forecasting scenarios such as traffic flow predictions [63; 64; 116; 139], stocks [140], and time-series [60; 66]. For future optimisation frameworks with NCO, GATs can be employed either as an upper policy in HRL or in a learn-to-configure setup, where the central agent predicts demand and parametrises the simulator for route planning based on the forecasts. Need for dynamic encoder-decoders: Current encoder-decoder architectures do not directly consider the transition function of the RL agents. In complex environments, each action in step \(t\) can implicitly modify other related state information in this environment. For example, after taking action \(a\) in step \(t\), the environment changes dynamically (e.g., the capacity, demand, and time windows of the customers reduce), but these dependencies are only reflected in the mask and additional context embeddings. Embedding the entire graph at the beginning of each episode may reduce solution quality [119; 141]. Additionally, once the state information has implicitly changed in state \(t+1\), the decoder should not rely on embeddings from the previous state \(t\). [PERSON] et al. [142] suggest that current decoders often overlook this dynamic context information and enhancing decoders will lead to better solution quality. Accelerating training and increasing solution diversity: Another key factor for achieving better NCO performance, and hence contributing to the development of smart decision support systems, is the training efficiency of the agents' policies [136]. [PERSON] et al. [141] state that, for most combinatorial problems, the diversity of solutions is critical for the overall performance. While some authors rely on parallel computing and fast matrix multiplication [137; 143], other scholars enhance NCO training by developing algorithms with a parallel local search that starts from multiple problem states simultaneously. Proximal Optimisation with Multiple Optima (POMO), proposed by [PERSON] et al. [144], enables policy training starting from multiple different nodes in parallel (learning on trajectories at each timestep), which effectively enhances the solution search (a Multi-Greedy decoding). However, this approach has only been validated on classical one-dimensional sequential decision problems, like sorting and routing problems, but it is potentially a suitable choice for advanced NCO frameworks with upper and lower policy training [136; 145]. Lack of safety, transparency and explainability: Although the majority of the reviewed studies advocate for achieving near-optimal solutions while significantly reducing computational time, a notable drawback of learning-based algorithms is the lack of safety, transparency, and explainability with respect to the decisions (actions) taken. Although building real-world safety-critical systems in the RL domain receives much attention [146; 147; 148], these efforts mostly address the selection of actions from a defined set of safe actions. In general, evaluating and proving the optimality of the learned policy is challenging, making the practical application of NCO techniques currently questionable. Among the reviewed literature, only [PERSON] et al. [83] address this issue by proposing decision trees to trace and evaluate actions. To this end, the practical application of NCO paradigms in intermodal scenarios appears limited. [PERSON] et al. [149] state that while NCO cannot currently compete with classical metaheuristics in terms of the solution quality and practicability, this is primarily linked to its early stage of development.