Abstract

Abstract
This work studies a two-echelon distribution system, in the context of city logistics, where storage is not permitted at intermediate transfer locations. Therefore, vehicles operating at both echelons need to be synchronised in time and space, allowing loads to be directly transferred from the first to the second echelon vehicles. Moreover, the problem considers that vehicles operating at the first echelon can perform direct deliveries to customers, that load transfers may occur at some customers' locations, and that vehicles operating at the second echelon are able to perform multiple trips before returning to the depot at the end of the day. To address this problem, we propose a novel mixed integer programming (MIP) model for the two-echelon, multi-trip vehicle routing problem with satellite synchronisation and direct deliveries (2E-MTVRPSS-DD). We tighten this formulation with several sets of valid inequalities, including symmetry breaking constraints based on lexicographical ordering, vehicle rounded capacity constraints, and satellite rounded capacity constraints. We test the model using a commercial solver with newly generated instances, and present computational results, as well as an evaluation of the performance of the proposed valid inequalities. The results show that for relatively small instances, the proposed model is able to solve the problem optimally, but in general, is unable to solve large instances in acceptable computational time, even when considering the proposed valid inequalities. Nevertheless, we show that adding these valid inequalities has a positive impact in improving the model's linear relaxation, with better lower and upper bounds, and ultimately in improving the MIP gaps. Moreover, we show that adding symmetry breaking constraints based on lexicographical ordering has a negative impact, in terms of computational time, for the solver to find a first upper bound, and that this issue may be overcome by warm-starting the MIP model.

Abstract
essential for achieving the Sustainable Development Goals (SDGs), particularly in regions aiming to balance energy efficiency, waste management, and urban development. This study explores the application of multicriteria decision-making and statistical techniques to evaluate municipal sustainability, with a focus on renewable energy, using the Alto Minho region of Portugal as a case study. The analysis incorporates 12 SDG indicators across ten municipalities, addressing energy consumption, urban renewal, and waste management. Cluster analysis revealed distinct groups of municipalities, highlighting disparities in sustainability performance. Municipalities such as Melgaco and Moncao excelled in energy-related metrics, while others showed strengths in waste management and urban renewal. The Analytic Hierarchy Process (AHP) emphasized the importance of renewable energy indicators, revealing notable changes in rankings when energy-related criteria were prioritized. Ponte de Lima and Melgaco ranked highest under energy-focused weighting schemes, showcasing their leadership in energy efficiency and renewable adoption. The findings underscore the need for targeted policies to enhance sustainability across municipalities, particularly in regions lagging in energy performance.

Abstract
Heterogeneous graphs can represent real-world problems in a way close to reality, supporting diverse types of vertices and edges. However, their inherent heterogeneity poses challenges in interpreting problem semantics. To address this, heterogeneous graph embedding, aiming to map graph elements to low-dimensional vectors, simplifies subsequent machine learning analysis. This approach has gained prominence in machine learning, fueling classification, recommendation, and similarity search applications. Embedding diverse data is essential for efficient data processing. Incorporating language models, like BERT, into heterogeneous graphs enhances semantic context capture, which is particularly useful when one vertex type represents text. Language models stand out in contextual representation, enriching graph vertex embeddings for various tasks. This paper proposes a novel approach to enhancing heterogeneous graph embeddings by combining language models and task class data. Our approach increases vector quality, accounting for graph structure, semantic textual information, and task labels. We compared our proposal with a language model in the aspect-based sentiment analysis task, demonstrating competitive results and, in some cases, a slight superiority. Furthermore, we explore applications of embeddings from auxiliary vertices in another task, highlighting another advantage of the approach over the language model.

Abstract
Sales forecasting in the presence of Missing Data poses significant challenges, particularly for short time series where limited observations amplify the impact of incomplete records. This study analyzes a real-world transactional dataset (2021-2024) to predict quantities and prices for 2025. We classify missingness patterns and mechanisms (MCAR, MAR, MNAR) to inform the selection of imputation strategies. We evaluate techniques including MICE, Mean, KNN, and Linear Regression under simulated missingness rates, with KNN emerging as the most robust for the MAR mechanism. Regarding very short-term series predictions, the naive forecast Max2 (maximum of the last two observed values) outperformed moving averages. The results highlight the importance of mechanismaware imputation and domain-tailored forecasting in sparse datasets. This work presents a practical framework for businesses to effectively utilize incomplete sales data.

Abstract
The development of computing paradigms alternative to von Neumann architectures has recently fueled significant progress in novel all-optical processing solutions. In this work, we investigate how the coherence properties can be exploited for computing by expanding information onto a higher-dimensional space in the photonic extreme learning machine framework. A theoretical framework is provided based on the transmission matrix formalism, mapping the input plane onto the output camera plane, resulting in the establishment of the connection with complex extreme learning machines and derivation of upper bounds for the hidden space dimensionality as well as the form of the activation functions. Experiments using free-space propagation through a diffusive medium, performed in low-dimensional input space regimes, validate the model and the proposed estimator for the dimensionality. Overall, the framework presented and the findings enclosed have the potential to foster further research in a multitude of directions, from the development of robust general-purpose all-optical hardware to a full-stack integration with optical sensing devices toward edge computing solutions.