Point cloud registration based on correspondences computes the rigid transformation that maximizes the number of inliers constrained within the noise threshold. Current state-of-the-art (SOTA) methods employing spatial compatibility graphs or branch-and-bound (BnB) search mainly focus on registration under high outlier ratios. However, graph-based methods require at least quadratic space and time complexity for graph construction, while multi-stage BnB search methods often suffer from inaccuracy due to local optima between decomposed stages. This paper proposes a geometric maximum overlapping registration framework via rotation-only BnB search. The rigid transformation is decomposed using Chasles' theorem into a translation along rotation axis and a 2D rigid transformation. The optimal rotation axis and angle are searched via BnB, with residual parameters formulated as range maximum query (RMQ) problems. Firstly, the top-k candidate rotation axes are searched within a hemisphere parameterized by cube mapping, and the translation along each axis is estimated through interval stabbing of the correspondences projected onto that axis. Secondly, the 2D registration is relaxed to 1D rotation angle search with 2D RMQ of geometric overlapping for axis-aligned rectangles, which is solved deterministically in polynomial time using sweep line algorithm with segment tree. Experimental results on 3DMatch, 3DLoMatch, and KITTI datasets demonstrate superior accuracy and efficiency over SOTA methods, while the time complexity is polynomial and the space complexity increases linearly with the number of points, even in the worst case.

This paper develops a novel COllaborative-Online-Learning (COOL)-enabled motion control framework for multi-robot systems to avoid collision amid randomly moving obstacles whose motion distributions are partially observable through decentralized data streams. To address the notable challenge of data acquisition due to occlusion, a COOL approach based on the Dirichlet process mixture model is proposed to efficiently extract motion distribution information by exchanging among robots selected learning structures. By leveraging the fine-grained local-moment information learned through COOL, a data-stream-driven ambiguity set for obstacle motion is constructed. We then introduce a novel ambiguity set propagation method, which theoretically admits the derivation of the ambiguity sets for obstacle positions over the entire prediction horizon by utilizing obstacle current positions and the ambiguity set for obstacle motion. Additionally, we develop a compression scheme with its safety guarantee to automatically adjust the complexity and granularity of the ambiguity set by aggregating basic ambiguity sets that are close in a measure space, thereby striking an attractive trade-off between control performance and computation time. Then the probabilistic collision-free trajectories are generated through distributionally robust optimization problems. The distributionally robust obstacle avoidance constraints based on the compressed ambiguity set are equivalently reformulated by deriving separating hyperplanes through tractable semi-definite programming. Finally, we establish the probabilistic collision avoidance guarantee and the long-term tracking performance guarantee for the proposed framework. The numerical simulations are used to demonstrate the efficacy and superiority of the proposed approach compared with state-of-the-art methods.

The Vision Transformer (ViT) architecture has become widely recognized in computer vision, leveraging its self-attention mechanism to achieve remarkable success across various tasks. Despite its strengths, ViT's optimization remains confined to modeling local relationships within individual images, limiting its ability to capture the global geometric relationships between data points. To address this limitation, this paper proposes a novel framework that integrates ViT with the proximal tools, enabling a unified geometric optimization approach to enhance feature representation and classification performance. In this framework, ViT constructs the tangent bundle of the manifold through its self-attention mechanism, where each attention head corresponds to a tangent space, offering geometric representations from diverse local perspectives. Proximal iterations are then introduced to define sections within the tangent bundle and project data from tangent spaces onto the base space, achieving global feature alignment and optimization. Experimental results confirm that the proposed method outperforms traditional ViT in terms of classification accuracy and data distribution.

Rigid registration, aiming to estimate a rigid transformation to align source and target data, play a crucial role in applications such as SLAM and 3D reconstruction. However, noisy, partially overlapping data and the need for real-time processing pose major challenges for rigid registration. Considering that feature-based matching can handle large transformation differences but suffers from limited accuracy, while local geometry-based matching can achieve fine-grained local alignment but relies heavily on a good initial transformation, we propose a novel dual-space paradigm to fully leverage the strengths of both approaches. First, we introduce an efficient filtering mechanism that incorporates a computationally lightweight single-point RANSAC algorithm followed by a refinement module to eliminate unreliable feature-based correspondences. Subsequently, we treat filtered correspondences as anchor points, extract geometric proxies, and formulates an effective objective function with a tailored solver to estimate the transformation. Experiments verify our method's effectiveness, as shown by achieving up to a 32x CPU-time speedup over MAC on KITTI with comparable accuracy.

Handling data staleness remains a significant challenge in federated learning with highly time-sensitive tasks, where data is generated continuously and data staleness largely affects model performance. Although recent works attempt to optimize data staleness by determining local data update frequency or client selection strategy, none of them explore taking both data staleness and data volume into consideration. In this paper, we propose DUFL( D ata U pdating in F ederated L earning), an incentive mechanism featuring an innovative local data update scheme manipulated by three knobs: the server's payment, outdated data conservation rate, and clients' fresh data collection volume, to coordinate staleness and volume of local data for best utilities. To this end, we introduce a novel metric called DoS(the D egree o f S taleness) to quantify data staleness and conduct a theoretic analysis illustrating the quantitative relationship between DoS and model performance. We model DUFL as a two-stage Stack-elberg game with dynamic constraint, deriving the optimal local data update strategy for each client in closed-form and the approximately optimal strategy for the server. Experimental results on real-world datasets demonstrate the significant performance of our approach.

Deformable retinal image registration is notoriously difficult due to large homogeneous regions and sparse but critical vascular features, which cause limited gradient signals in standard learning-based frameworks. In this paper, we introduce Gaussian Primitive Optimization (GPO), a novel iterative framework that performs structured message passing to overcome these challenges. After an initial coarse alignment, we extract keypoints at salient anatomical structures (e.g., major vessels) to serve as a minimal set of descriptor-based control nodes (DCN). Each node is modelled as a Gaussian primitive with trainable position, displacement, and radius, thus adapting its spatial influence to local deformation scales. A K-Nearest Neighbors (KNN) Gaussian interpolation then blends and propagates displacement signals from these information-rich nodes to construct a globally coherent displacement field; focusing interpolation on the top (K) neighbors reduces computational overhead while preserving local detail. By strategically anchoring nodes in high-gradient regions, GPO ensures robust gradient flow, mitigating vanishing gradient signal in textureless areas. The framework is optimized end-to-end via a multi-term loss that enforces both keypoint consistency and intensity alignment. Experiments on the FIRE dataset show that GPO reduces the target registration error from 6.2\,px to ~2.4\,px and increases the AUC at 25\,px from 0.770 to 0.938, substantially outperforming existing methods. The source code can be accessed via https://github.com/xintian-99/GPOreg.

Urban land-use allocation represents a complex multi-objective optimization problem critical for sustainable urban development policy. This paper presents novel computational intelligence approaches for optimizing land-use allocation in mixed-use areas, addressing inherent trade-offs between land-use compatibility and economic objectives. We develop multiple optimization algorithms, including custom variants integrating differential evolution with multi-objective genetic algorithms. Key contributions include: (1) CR+DES algorithm leveraging scaled difference vectors for enhanced exploration, (2) systematic constraint relaxation strategy improving solution quality while maintaining feasibility, and (3) statistical validation using Kruskal-Wallis tests with compact letter displays. Applied to a real-world case study with 1,290 plots, CR+DES achieves 3.16\% improvement in land-use compatibility compared to state-of-the-art methods, while MSBX+MO excels in price optimization with 3.3\% improvement. Statistical analysis confirms algorithms incorporating difference vectors significantly outperform traditional approaches across multiple metrics. The constraint relaxation technique enables broader solution space exploration while maintaining practical constraints. These findings provide urban planners and policymakers with evidence-based computational tools for balancing competing objectives in land-use allocation, supporting more effective urban development policies in rapidly urbanizing regions.

E-graphs have attracted growing interest in many fields, particularly in logic synthesis and formal verification. E-graph extraction is a challenging NP-hard combinatorial optimization problem. It requires identifying optimal terms from exponentially many equivalent expressions, serving as the primary performance bottleneck in e-graph based optimization tasks. However, traditional extraction methods face a critical trade-off: heuristic approaches offer speed but sacrifice optimality, while exact methods provide optimal solutions but face prohibitive computational costs on practical problems. We present e-boost, a novel framework that bridges this gap through three key innovations: (1) parallelized heuristic extraction that leverages weak data dependence to compute DAG costs concurrently, enabling efficient multi-threaded performance without sacrificing extraction quality; (2) adaptive search space pruning that employs a parameterized threshold mechanism to retain only promising candidates, dramatically reducing the solution space while preserving near-optimal solutions; and (3) initialized exact solving that formulates the reduced problem as an Integer Linear Program with warm-start capabilities, guiding solvers toward high-quality solutions faster. Across the diverse benchmarks in formal verification and logic synthesis fields, e-boost demonstrates 558x runtime speedup over traditional exact approaches (ILP) and 19.04% performance improvement over the state-of-the-art extraction framework (SmoothE). In realistic logic synthesis tasks, e-boost produces 7.6% and 8.1% area improvements compared to conventional synthesis tools with two different technology mapping libraries. e-boost is available at https://github.com/Yu-Maryland/e-boost.

Preference-based Pure Exploration (PrePEx) aims to identify with a given confidence level the set of Pareto optimal arms in a vector-valued (aka multi-objective) bandit, where the reward vectors are ordered via a (given) preference cone $\mathcal{C}$. Though PrePEx and its variants are well-studied, there does not exist a computationally efficient algorithm that can optimally track the existing lower bound for arbitrary preference cones. We successfully fill this gap by efficiently solving the minimisation and maximisation problems in the lower bound. First, we derive three structural properties of the lower bound that yield a computationally tractable reduction of the minimisation problem. Then, we deploy a Frank-Wolfe optimiser to accelerate the maximisation problem in the lower bound. Together, these techniques solve the maxmin optimisation problem in $\mathcal{O}(KL^{2})$ time for a bandit instance with $K$ arms and $L$ dimensional reward, which is a significant acceleration over the literature. We further prove that our proposed PrePEx algorithm, FraPPE, asymptotically achieves the optimal sample complexity. Finally, we perform numerical experiments across synthetic and real datasets demonstrating that FraPPE achieves the lowest sample complexities to identify the exact Pareto set among the existing algorithms.

Multi-objective Bayesian optimization (MOBO) struggles with sparse (non-space-filling), scarce (limited observations) datasets affected by experimental uncertainty, where identical inputs can yield varying outputs. These challenges are common in physical and simulation experiments (e.g., randomized medical trials and, molecular dynamics simulations) and are therefore incompatible with conventional MOBO methods. As a result, experimental resources are inefficiently allocated, leading to subop-timal designs. To address this challenge, we introduce NOSTRA (Noisy and Sparse Data Trust Region-based Optimization Algorithm), a novel sampling framework that integrates prior knowledge of experimental uncertainty to construct more accurate surrogate models while employing trust regions to focus sampling on promising areas of the design space. By strategically leveraging prior information and refining search regions, NOSTRA accelerates convergence to the Pareto frontier, enhances data efficiency, and improves solution quality. Through two test functions with varying levels of experimental uncertainty, we demonstrate that NOSTRA outperforms existing methods in handling noisy, sparse, and scarce data. Specifically, we illustrate that, NOSTRA effectively prioritizes regions where samples enhance the accuracy of the identified Pareto frontier, offering a resource-efficient algorithm that is practical in scenarios with limited experimental budgets while ensuring efficient performance.