The primary trade-off faced in public transport planning and design is between the level of service experienced by users and the costs borne by the operators. It has been shown that these latter weigh more when imposing self-financing policies at the expense of the relevance of users’ costs (their time), inducing smaller than optimal fleets of larger than optimal vehicles. This study analyzes the effects of ignoring user costs (UC) in the strategic design of public transport systems from a structural perspective, with a particular focus on spatial design. The problem is addressed using three simplified networks (cross-shaped, triangular, and Y-shaped), over which traditional line structures are compared: Feeder-Trunk, Hub-and-Spoke, Direct (avoiding transfers), and Exclusive (avoiding transfers and intermediate stops). For each network and line structure, operational variables —frequencies and bus sizes— are optimized under two objectives: minimizing operator cost (OC) and minimizing OC + UC. Four elements stand out in the analysis: transfers, idle capacity, excess distance traveled, and stopped utilization. The main result is that the optimal structure varies with the level and distribution of demand when OC + UC are minimized, but when UC is omitted, the structure that generally dominates is the Exclusive one, always operating with an undersized fleet of oversized buses running at lower frequencies than those of the OC + UC optimum. Differences with what is reported in the literature are discussed, motivating further analysis in more complex networks.
We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations. The method combines a Gaussian Nadaraya–Watson kernel interpolant with a Voronoi-adaptive bandwidth determined entirely by the geometry of the sampled data, yielding an explicit closed-form construction that requires neither training, iterative optimization, preprocessing, nor parameter tuning.The proposed interpolant satisfies several theoretical properties. It reproduces the observed data exactly, enforces a vanishing intrinsic gradient at every sample point, and, in the dense-sampling limit, attenuates high-frequency oscillatory components through the geometric regularization induced by the adaptive bandwidth. Furthermore, the construction admits an interpretation in terms of minimizing a discrete total variation–type functional, establishing a natural connection with compressed sensing and sparsity-promoting regularization.Unlike classical kernel interpolation methods employing a fixed global bandwidth, the proposed adaptive strategy automatically adjusts to the local sampling geometry through the Voronoi tessellation while preserving an explicit analytical formulation. Because the interpolant is available in closed form, the overall computational cost is entirely determined by the inference stage: evaluating the interpolant at a query point requires only the computation of Gaussian kernel weights and their weighted combination, resulting in linear complexity with respect to the number of sample points. In contrast to many data-driven interpolation approaches, no additional offline computational stage is required before inference.Finally, we demonstrate the practical performance of the proposed methodology in sparse-angle computed tomography reconstruction, where interpolation of the sinogram prior to filtered back-projection produces accurate reconstructions while substantially reducing the overall computational time compared with standard total variation–based reconstruction methods.
We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations. The method combines a Gaussian Nadaraya-Watson kernel interpolant with a Voronoi-adaptive bandwidth determined entirely by the geometry of the sampled data, yielding an explicit closed-form construction that requires neither training, iterative optimization, preprocessing, nor parameter tuning. The proposed interpolant satisfies several theoretical properties. It reproduces the observed data exactly, enforces a vanishing intrinsic gradient at every sample point, and, in the dense-sampling limit, attenuates high-frequency oscillatory components through the geometric regularization induced by the adaptive bandwidth. Furthermore, the construction admits an interpretation in terms of minimizing a discrete total variation-type functional, establishing a natural connection with compressed sensing and sparsity-promoting regularization. Unlike classical kernel interpolation methods employing a fixed global bandwidth, the proposed adaptive strategy automatically adjusts to the local sampling geometry through the Voronoi tessellation while preserving an explicit analytical formulation. Because the interpolant is available in closed form, the overall computational cost is entirely determined by the inference stage: evaluating the interpolant at a query point requires only the computation of Gaussian kernel weights and their weighted combination, resulting in linear complexity with respect to the number of sample points. In contrast to many data-driven interpolation approaches, no additional offline computational stage is required before inference. Finally, we demonstrate the practical performance of the proposed methodology in sparse-angle computed tomography reconstruction, where interpolation of the sinogram prior to filtered back-projection produces accurate reconstructions while substantially reducing the overall computational time compared with standard total variation-based reconstruction methods.
Public transport network design lies at the intersection of strategic theory and algorithmic complexity. While strategic models offer general insights using simplified representations, and algorithmic approaches solve large-scale problems via heuristics, these two perspectives have largely evolved in isolation. This paper bridges the gap by enhancing a state-of-the-art genetic algorithm with a theoretically grounded decision rule: the Divisibility Index introduced by Gomez et al. (2026), a strategic quantity that determines whether a public transport line should be split into two. This index is integrated into a genetic algorithm, potentially splitting the candidate lines in every iteration when convenient. This enhanced method is tested on a stylised city under four distinct demand scenarios, each favouring a different network topology: hub-and-spoke, feeder-trunk, direct-based, and exclusivebased. In all cases, this seemingly minor (yet strategic) tweak leads to significant performance gains: the modified algorithm consistently finds better solutions in a single iteration than the original version does in fourteen. Notably, the resulting networks match expected topologies for each demand pattern. Similar results arise in adapted real-city representations. Those results highlight the potential of combining strategic public transport analysis and complex algorithms not only to improve solution quality and speed, but also to reveal new strategic insights.
Transmission expansion planning (TEP) plays a critical role in ensuring power system reliability and facilitating the integration of renewable energy resources. However, this process requires planners to constantly deal with significant uncertainty. While multistage stochastic TEP models provide a robust framework for identifying investment plans under uncertainty, the rapid growth in problem size hinders their computational tractability. To address this challenge, this paper develops a hybrid machine learning-optimisation framework for stochastic TEP. The proposed approach uses investment decisions and uncertainty scenarios as input features to train surrogate neural networks, which are then reformulated as mixed-integer linear constraints and embedded within an optimisation model. The surrogate model approximates expected operational costs to inform TEP decisions, reducing the burden arising from large operational problems. Case study applications on IEEE test systems demonstrate that, after training, the proposed approach achieves near-optimal investment costs while reducing total computational time by up to a factor of around 13 compared to a single full-optimisation stochastic formulation. This enables performing extensive multi-scenario analysis and stress testing that would otherwise be computationally prohibitive at scale.
