We study the deterministic global optimization of the K-Medoids clustering problem. This work proposes a branch and bound (BB) scheme, in which a tailored Lagrangian relaxation method proposed in the 1970s is used to provide a lower bound at each BB node. The lower bounding method already guarantees the maximum gap at the root node. A closed-form solution to the lower bound can be derived analytically without explicitly solving any optimization problems, and its computation can be easily parallelized. Moreover, with this lower bounding method, finite convergence to the global optimal solution can be guaranteed by branching only on the regions of medoids. We also present several tailored bound tightening techniques to reduce the search space and computational cost. Extensive computational studies on 28 machine learning datasets demonstrate that our algorithm can provide a provable global optimal solution with an optimality gap of 0.1% within 4 hours on datasets with up to one million samples. Besides, our algorithm can obtain better or equal objective values than the heuristic method. A theoretical proof of global convergence for our algorithm is also presented.

However, achieving such an assumption is non-trivial, leading to the following two aspects of challenges. On the one hand, it is challenging to design a model with enough capacity with limited computational resources, andexisting models areusually tailored forspecific problems which require heavytrailand-error [25,57,59].

Graph Neural Networks (GNNs) have been widely applied to various fields for learning over graph-structured data.

Graph Neural Networks (GNNs) have been widely applied to various fields for learning over graph-structured data. They have shown significant improvements over traditional heuristic methods in various tasks such as node classification and graph classification. However, since GNNs heavily rely on smoothed node features rather than graph structure, they often show poor performance than simple heuristic methods in link prediction where the structural information, e.g., overlapped neighborhoods, degrees, and shortest paths, is crucial. To address this limitation, we propose Neighborhood Overlap-aware Graph Neural Networks (Neo-GNNs) that learn useful structural features from an adjacency matrix and estimate overlapped neighborhoods for link prediction. Our Neo-GNNs generalize neighborhood overlap-based heuristic methods and handle overlapped multi-hop neighborhoods. Our extensive experiments on Open Graph Benchmark datasets (OGB) demonstrate that Neo-GNNs consistently achieve state-of-the-art performance in link prediction.

Large Language Diffusion Models (LLDMs) benefit from a flexible decoding mechanism that enables parallelized inference and controllable generations over autoregressive models. Yet such flexibility introduces a critical challenge: inference performance becomes highly sensitive to the decoding order of tokens. Existing heuristic methods, however, focus mainly on local effects while overlooking long-term impacts. To address this limitation, we propose the Foreseeing Decoding Method (FDM), a novel approach that integrates both local and global considerations to unlock the full potential, employing a search-based strategy to enable effective optimization in discrete spaces. Furthermore, by analyzing the consistency of chosen tokens in the full decoding process, we develop a variant, FDM with Acceleration (FDM-A), which restricts deep exploration to critical steps identified as the exploration and balance circumantences. Extensive experiments across diverse benchmarks and model architectures validate the scalability of FDM and demonstrate the superior efficiency-performance trade-off achieved by FDM-A. Our work might potentially provide a principled step toward more powerful decoding methods for LLDMs.

THIS WORK HAS BEEN SUBMITTED TO THE IEEE FOR POSSIBLE PUBLICA TION. Abstract--The capacitated location-routing problems (CLRPs) are classical problems in combinatorial optimization, which require simultaneously making location and routing decisions. In CLRPs, the complex constraints and the intricate relationships between various decisions make the problem challenging to solve. With the emergence of deep reinforcement learning (DRL), it has been extensively applied to address the vehicle routing problem and its variants, while the research related to CLRPs still needs to be explored. In this paper, we propose the DRL with heterogeneous query (DRLHQ) to solve CLRP and open CLRP (OCLRP), respectively. We are the first to propose an end-to-end learning approach for CLRPs, following the encoder-decoder structure. In particular, we reformulate the CLRPs as a markov decision process tailored to various decisions, a general modeling framework that can be adapted to other DRL-based methods. T o better handle the interdependency across location and routing decisions, we also introduce a novel heterogeneous querying attention mechanism designed to adapt dynamically to various decision-making stages. Experimental results on both synthetic and benchmark datasets demonstrate superior solution quality and better generalization performance of our proposed approach over representative traditional and DRL-based baselines in solving both CLRP and OCLRP . HE facility location problem (FLP) and vehicle routing problem (VRP) are two critical combinatorial optimization problems (COPs) in transportation and logistics, which are traditionally addressed sequentially. However, planning the routes after facility location may lead to suboptimal solutions due to the interdependencies across various decisions [1], [2]. Therefore, the capacitated location-routing problems (CLRPs) [3] are proposed to simultaneously make location and routing decisions. The CLRPs are one of the most classical topics in the community of operations research and have extensive applications such as supply-chain management [4], emergency management [5], and disaster relief [6]. This work was supported by the National Key Research and Development Program of China No.2022ZD0119703; in part by the National Natural Science Foundations of China (NSFC) under Grant 62273044 and 62022015; in part by the National Natural Science Foundation of China National Science Fund for Distinguished Y oung Scholars under Grant 62025301; in part by the National Natural Science Foundation of China Basic Science Center Program under Grant 62088101. In CLRPs, depots and vehicles are subject to the maximum capacity constraints, and the depots are considered heterogeneous due to distinct capacities and opening costs. Meanwhile, we also study the open CLRP (OCLRP) [7], a variant of CLRP, by considering open-ended routes.

Abstract--This paper explores the application of machine learning (ML) techniques in predicting the QPU processing time of quantum jobs. By leveraging ML algorithms, this study introduces predictive models that are designed to enhance operational efficiency in quantum computing systems. Using a dataset of about 150,000 jobs that follow the IBM Quantum schema, we employ ML methods based on Gradient-Boosting (LightGBM) to predict the QPU processing times, incorporating data preprocessing methods to improve model accuracy. The results demonstrate the effectiveness of ML in forecasting quantum jobs. This improvement can have implications on improving resource management and scheduling within quantum computing frameworks. This research not only highlights the potential of ML in refining quantum job predictions but also sets a foundation for integrating AI-driven tools in advanced quantum computing operations. The nature of quantum computing becomes increasingly relevant in the core of data-center operations due to a paradigm shift in computational processing, prioritization, and execution.