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The Capacitated Vehicle Routing Problem (CVRP) is a central challenge in combinatorial optimization, with critical applications in logistics and transportation. Traditional methods struggle with large-scale instances, due to the computational demands, while learned construction models often suffer from degraded solution quality and constraint violations. This work proposes SPORL, a Scalable Partitioning and Optimization via Reinforcement Learning framework for large-scale CVRPs. SPORL decomposes the problem using a learned partitioning strategy, followed by parallel subproblem solving, and employs a greedy decoding scheme at inference to ensure scalability for instances with up to 1000 customers. A key innovation is a context-based attention mechanism that incorporates sub-route embeddings, enabling more informed and constraint-aware partitioning decisions. Extensive experiments on benchmark datasets with up to 1000 customers demonstrated that SPORL consistently outperformed state-of-the-art learning-based baselines (e.g., AM, POMO) and achieved competitive performance relative to strong heuristics such as LKH3, while reducing inference time from hours to seconds. Ablation studies confirmed the critical role of the proposed context embedding and decoding strategy in achieving high solution quality.

A (0, 2)-graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of (0, λ)-graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free (0, 2)-graph. (0, 2)-graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in (0, λ)-graphs and more specifically in (0, 2)-graphs, leading to new characterizations of rectagraphs and hypercubes.

Learning concepts from examples presented in user’s query and infer the other items that belong to this query is still a significant challenge for images retrieval systems. Existing models from cognitive science namely Bayesian models of generalization mainly focus on this challenge where they remarkably succeed at explaining how to generalize from few examples in a wide range of domains. However their success largely depends on the validity of examples. They require that each example is a good representative, which is not always the case in the context of images retrieval. In this paper, we will extend the Bayesian models of generalization to identify the appropriate level of generalization for a given query in the context of query by semantic example systems. Our model uses an ontology as the basis of its hypothesis space which allows us to take advantages of its semantic richness and inference capacity. Experimental study using the ImageNet benchmark verifies the efficiency of our model in comparison to the state-of-the-art models of generalization.

Multi-variate time-series (MTS) forecasting is the prediction of future for a sequence of data. The process of analysing obtained data can benefit the community financially and securely, for instance observing stock exchange trends and predicting malicious attacks whenabout. MTS forecasting models face many problems including data and model complexity, energy constraints and computational cost. These problems could affect budget allocation, latency and carbon emission. Recurrent neural networks are one of these models, which are known for their computational complexity due to slow learning process which requires more energy to train. Contributing to green AI, in this paper, we propose a competitive and energy-efficient lightweight recurrent neural network based on a hybrid neural architecture that combines Random Neural Network (RaNN) and Simple Recurrent Network (SRN), namely Random Simple Recurrent Network (RSRN). We consider RaNN for its distinctive probabilistic properties and SRN for adding lightweight recurrent ability to the RaNN to process sequential data. The paper shows how RSRN is trained using adapted and optimised versions of back propagation (BP), back propagation through time (BPTT) and truncated BPTT (TBPTT). The latter two algorithms use penalised gradient descent to prevent gradient explosion problems by employing the average of total gradient over time. Evaluated on several datasets, RSRN achieves best performance when using TBPTT. Moreover, we performed a comparative study against well-known recurrent models showing its superiority compared to the state-of-the-art models, while requiring much less computational time and training parameters. In addition, we investigated the multi-layer architecture and its properties.