Grey wolf optimizer (GWO) is a nature-inspired stochastic meta-heuristic of the swarm intelligence field that mimics the hunting behavior of grey wolves. Differential evolution (DE) is a popular stochastic algorithm of the evolutionary computation field that is well suited for global optimization. In this part, we introduce a new algorithm based on the hybridization of GWO and two DE variants, namely the GWO-DE algorithm. We evaluate the new algorithm by applying various numerical benchmark functions. The numerical results of the comparative study are quite satisfactory in terms of performance and solution quality.
Detection-free methods typically follow a coarse-to-fine pipeline, extracting image and point cloud features for patch-level matching and refining dense pixel-to-point correspondences. However, differences in feature channel attention between images and point clouds may lead to degraded matching results, ultimately impairing registration accuracy. Furthermore, similar structures in the scene could lead to redundant correspondences in cross-modal matching. To address these issues, we propose Channel Adaptive Adjustment Module (CAA) and Global Optimal Selection Module (GOS). CAA enhances intra-modal features and suppresses cross-modal sensitivity, while GOS replaces local selection with global optimization. Experiments on RGB-D Scenes V2 and 7-Scenes demonstrate the superiority of our method, achieving state-of-the-art performance in image-to-point cloud registration.
The complex regulatory dynamics of a biological network can be succinctly captured using discrete logic models. Given even sparse time-course data from the system of interest, previous work has shown that global optimization schemes are suitable for proposing logic models that explain the data and make predictions about how the system will behave under varying conditions. Considering the large scale of the parameter search spaces associated with these regulatory systems, performance optimizations on the level of both hardware and software are necessary for making this a practical tool for in silico pharmaceutical research. We show here how the implementation of these global optimization algorithms in a GPU-computing environment can accelerate the solution of these parameter search problems considerably. We carry out parameter searches on two model biological regulatory systems that represent almost an order of magnitude scale-up in complexity, and we find the gains in efficiency from GPU to be a 33%-43% improvement compared to multi-thread CPU implementations and a 33%-1866% increase compared to CPU in serial. These improvements make global optimization of logic model identification a far more attractive and feasible method for in silico hypothesis generation and design of experiments.
Cone Beam Computed Tomography (CBCT) is widely used in medical imaging. However, the limited number and intensity of X-ray projections make reconstruction an ill-posed problem with severe artifacts. NeRF-based methods have achieved great success in this task. However, they suffer from a local-global training mismatch between their two key components: the hash encoder and the neural network. Specifically, in each training step, only a subset of the hash encoder's parameters is used (local sparse), whereas all parameters in the neural network participate (global dense). Consequently, hash features generated in each step are highly misaligned, as they come from different subsets of the hash encoder. These misalignments from different training steps are then fed into the neural network, causing repeated inconsistent global updates in training, which leads to unstable training, slower convergence, and degraded reconstruction quality. Aiming to alleviate the impact of this local-global optimization mismatch, we introduce a Normalized Hash Encoder, which enhances feature consistency and mitigates the mismatch. Additionally, we propose a Mapping Consistency Initialization(MCI) strategy that initializes the neural network before training by leveraging the global mapping property from a well-trained model. The initialized neural network exhibits improved stability during early training, enabling faster convergence and enhanced reconstruction performance. Our method is simple yet effective, requiring only a few lines of code while substantially improving training efficiency on 128 CT cases collected from 4 different datasets, covering 7 distinct anatomical regions.
GA LLM is a hybrid framework that combines Genetic Algorithms with Large Language Models to handle structured generation tasks under strict constraints. Each output, such as a plan or report, is treated as a gene, and evolutionary operations like selection, crossover, and mutation are guided by the language model to iteratively improve solutions. The language model provides domain knowledge and creative variation, while the genetic algorithm ensures structural integrity and global optimization. GA LLM has proven effective in tasks such as itinerary planning, academic outlining, and business reporting, consistently producing well structured and requirement satisfying results. Its modular design also makes it easy to adapt to new tasks. Compared to using a language model alone, GA LLM achieves better constraint satisfaction and higher quality solutions by combining the strengths of both components.
A random-key genetic algorithm is an evolutionary metaheuristic for discrete and global optimization. Each solution is encoded as a vector of N random keys, where a random key is a real number randomly generated in the continuous interval [0, 1). A decoder maps each vector of random keys to a solution of the optimization problem being solved and computes its cost. The benefit of this approach is that all genetic operators and transformations can be maintained within the unitary hypercube, regardless of the problem being addressed. This enhances the productivity and maintainability of the core framework. The algorithm starts with a population of P vectors of random keys. At each iteration, the vectors are partitioned into two sets: a smaller set of high-valued elite solutions and the remaining non-elite solutions. All elite elements are copied, without change, to the next population. A small number of random-key vectors (the mutants) is added to the population of the next iteration. The remaining elements of the population of the next iteration are generated by combining, with the parametrized uniform crossover of Spears and DeJong (1991), pairs of solutions. This chapter reviews random-key genetic algorithms and describes an effective variant called biased random-key genetic algorithms.
This paper addresses the global optimization of the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere. While various methods have been proposed for this problem, they do not guarantee convergence to the global maximizer. To overcome this limitation, we introduce a probability-one homotopy optimization method that, under certain conditions, guarantees convergence to the global maximizer. The proposed method is analyzed alongside state-of-the-art approaches through numerical experiments, evaluating their performance in terms of convergence speed and ability to reach the global maximizer. Furthermore, we demonstrate how this ties in with the multi-source Bayesian Generalized Total Least-Squares (B-GTLS) problem, illustrating its applicability.
This paper proposes Load-aware Tram-FL, an extension of Tram-FL that introduces a training scheduling mechanism to minimize total training time in decentralized federated learning by accounting for both computational and communication loads. The scheduling problem is formulated as a global optimization task, which-though intractable in its original form-is made solvable by decomposing it into node-wise subproblems. To promote balanced data utilization under non-IID distributions, a variance constraint is introduced, while the overall training latency, including both computation and communication costs, is minimized through the objective function. Simulation results on MNIST and CIFAR-10 demonstrate that Load-aware Tram-FL significantly reduces training time and accelerates convergence compared to baseline methods.
Large Language Models (LLMs) have recently emerged as effective surrogate models and candidate generators within global optimization frameworks for expensive blackbox functions. Despite promising results, LLM-based methods often struggle in high-dimensional search spaces or when lacking domain-specific priors, leading to sparse or uninformative suggestions. To overcome these limitations, we propose HOLLM, a novel global optimization algorithm that enhances LLM-driven sampling by partitioning the search space into promising subregions. Each subregion acts as a ``meta-arm'' selected via a bandit-inspired scoring mechanism that effectively balances exploration and exploitation. Within each selected subregion, an LLM then proposes high-quality candidate points, without any explicit domain knowledge. Empirical evaluation on standard optimization benchmarks shows that HOLLM consistently matches or surpasses leading Bayesian optimization and trust-region methods, while substantially outperforming global LLM-based sampling strategies.
Orienting point clouds is a fundamental problem in computer graphics and 3D vision, with applications in reconstruction, segmentation, and analysis. While significant progress has been made, existing approaches mainly focus on watertight, object-level 3D models. The orientation of large-scale, non-watertight 3D scenes remains an underexplored challenge. To address this gap, we propose DACPO (Divide-And-Conquer Point Orientation), a novel framework that leverages a divide-and-conquer strategy for scalable and robust point cloud orientation. Rather than attempting to orient an unbounded scene at once, DACPO segments the input point cloud into smaller, manageable blocks, processes each block independently, and integrates the results through a global optimization stage. For each block, we introduce a two-step process: estimating initial normal orientations by a randomized greedy method and refining them by an adapted iterative Poisson surface reconstruction. To achieve consistency across blocks, we model inter-block relationships using an an undirected graph, where nodes represent blocks and edges connect spatially adjacent blocks. To reliably evaluate orientation consistency between adjacent blocks, we introduce the concept of the visible connected region, which defines the region over which visibility-based assessments are performed. The global integration is then formulated as a 0-1 integer-constrained optimization problem, with block flip states as binary variables. Despite the combinatorial nature of the problem, DACPO remains scalable by limiting the number of blocks (typically a few hundred for 3D scenes) involved in the optimization. Experiments on benchmark datasets demonstrate DACPO's strong performance, particularly in challenging large-scale, non-watertight scenarios where existing methods often fail. The source code is available at https://github.com/zd-lee/DACPO.
Graph Bayesian optimization (BO) has shown potential as a powerful and data-efficient tool for neural architecture search (NAS). Most existing graph BO works focus on developing graph surrogates models, i.e., metrics of networks and/or different kernels to quantify the similarity between networks. However, the acquisition optimization, as a discrete optimization task over graph structures, is not well studied due to the complexity of formulating the graph search space and acquisition functions. This paper presents explicit optimization formulations for graph input space including properties such as reachability and shortest paths, which are used later to formulate graph kernels and the acquisition function. We theoretically prove that the proposed encoding is an equivalent representation of the graph space and provide restrictions for the NAS domain with either node or edge labels. Numerical results over several NAS benchmarks show that our method efficiently finds the optimal architecture for most cases, highlighting its efficacy.
Phase retrieval (PR) reconstructs phase information from magnitude measurements, known as coded diffraction patterns (CDPs), whose quality depends on the number of snapshots captured using coded phase masks. High-quality phase estimation requires multiple snapshots, which is not desired for efficient PR systems. End-to-end frameworks enable joint optimization of the optical system and the recovery neural network. However, their application is constrained by physical implementation limitations. Additionally, the framework is prone to gradient vanishing issues related to its global optimization process. This paper introduces a Knowledge Distillation (KD) optimization approach to address these limitations. KD transfers knowledge from a larger, lower-constrained network (teacher) to a smaller, more efficient, and implementable network (student). In this method, the teacher, a PR system trained with multiple snapshots, distills its knowledge into a single-snapshot PR system, the student. The loss functions compare the CPMs and the feature space of the recovery network. Simulations demonstrate that this approach improves reconstruction performance compared to a PR system trained without the teacher's guidance.
Cometary activity is a compelling subject of study, with thermophysical models playing a pivotal role in its understanding. However, traditional numerical solutions for small body thermophysical models are computationally intensive, posing challenges for investigations requiring high-resolution or repetitive modeling. To address this limitation, we employed a machine learning approach to develop ThermoONet - a neural network designed to predict the temperature and water ice sublimation flux of comets. Performance evaluations indicate that ThermoONet achieves a low average error in subsurface temperature of approximately 2% relative to the numerical simulation, while reducing computational time by nearly six orders of magnitude. We applied ThermoONet to model the water activity of comets 67P/Churyumov-Gerasimenko and 21P/Giacobini-Zinner. By successfully fitting the water production rate curves of these comets, as obtained by the Rosetta mission and the SOHO telescope, respectively, we demonstrate the network's effectiveness and efficiency. Furthermore, when combined with a global optimization algorithm, ThermoONet proves capable of retrieving the physical properties of target bodies.
The recently developed Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) have shown encouraging and impressive results for visual SLAM. However, most representative methods require RGBD sensors and are only available for indoor environments. The robustness of reconstruction in large-scale outdoor scenarios remains unexplored. This paper introduces a large-scale 3DGS-based visual SLAM with stereo cameras, termed LSG-SLAM. The proposed LSG-SLAM employs a multi-modality strategy to estimate prior poses under large view changes. In tracking, we introduce feature-alignment warping constraints to alleviate the adverse effects of appearance similarity in rendering losses. For the scalability of large-scale scenarios, we introduce continuous Gaussian Splatting submaps to tackle unbounded scenes with limited memory. Loops are detected between GS submaps by place recognition and the relative pose between looped keyframes is optimized utilizing rendering and feature warping losses. After the global optimization of camera poses and Gaussian points, a structure refinement module enhances the reconstruction quality. With extensive evaluations on the EuRoc and KITTI datasets, LSG-SLAM achieves superior performance over existing Neural, 3DGS-based, and even traditional approaches. Project page: https://lsg-slam.github.io.
We propose a generative, end-to-end solver for black-box combinatorial optimization that emphasizes both sample efficiency and solution quality on NP problems. Drawing inspiration from annealing-based algorithms, we treat the black-box objective as an energy function and train a neural network to model the associated Boltzmann distribution. By conditioning on temperature, the network captures a continuum of distributions--from near-uniform at high temperatures to sharply peaked around global optima at low temperatures--thereby learning the structure of the energy landscape and facilitating global optimization. When queries are expensive, the temperature-dependent distributions naturally enable data augmentation and improve sample efficiency. When queries are cheap but the problem remains hard, the model learns implicit variable interactions, effectively "opening" the black box. We validate our approach on challenging combinatorial tasks under both limited and unlimited query budgets, showing competitive performance against state-of-the-art black-box optimizers.
An innovative solution, based on the exploitation of the harmonic beams generated by time-modulated electromagnetic skins (TM-EMSs), is proposed for the implementation of integrated sensing and communication (ISAC) functionalities in a Smart Electromagnetic Environment (SEME) scenario. More in detail, the field radiated by a user terminal, located at an unknown position, is assumed to illuminate a passive TM-EMS that, thanks to a suitable modulation of the local reflection coefficients at the meta-atom level of the EMS surface, simultaneously reflects towards a receiving base station (BS) a "sum" beam and a "difference" one at slightly different frequencies. By processing the received signals and exploiting monopulse radar tracking concepts, the BS both localizes the user terminal and, as a by-product, establishes a communication link with it by leveraging on the "sum" reflected beam. Towards this purpose, the arising harmonic beam control problem is reformulated as a global optimization one, which is successively solved by means of an evolutionary iterative approach to determine the desired TM-EMS modulation sequence. The results from selected numerical and experimental tests are reported to assess the effectiveness and the reliability of the proposed approach.
Current Structure-from-Motion (SfM) methods typically follow a two-stage pipeline, combining learned or geometric pairwise reasoning with a subsequent global optimization step. In contrast, we propose a data-driven multi-view reasoning approach that directly infers 3D scene geometry and camera poses from multi-view images. Our framework, DiffusionSfM, parameterizes scene geometry and cameras as pixel-wise ray origins and endpoints in a global frame and employs a transformer-based denoising diffusion model to predict them from multi-view inputs. To address practical challenges in training diffusion models with missing data and unbounded scene coordinates, we introduce specialized mechanisms that ensure robust learning. We empirically validate DiffusionSfM on both synthetic and real datasets, demonstrating that it outperforms classical and learning-based approaches while naturally modeling uncertainty.
Convergence analysis is a fundamental research topic in evolutionary computation (EC). The commonly used analysis method models the EC algorithm as a homogeneous Markov chain for analysis, which is not always suitable for different EC variants, and also sometimes causes misuse and confusion due to their complex process. In this article, we categorize the existing researches on convergence analysis in EC algorithms into stable convergence and global convergence, and then prove that the conditions for these two convergence properties are somehow mutually exclusive. Inspired by this proof, we propose a new scope and domain measure comparison (SDMC) method for analyzing the global convergence of EC algorithms and provide a rigorous proof of its necessity and sufficiency as an alternative condition. Unlike traditional methods, the SDMC method is straightforward, bypasses Markov chain modeling, and minimizes errors from misapplication as it only focuses on the measure of the algorithm's search scope. We apply SDMC to two algorithm types that are unsuitable for traditional methods, confirming its effectiveness in global convergence analysis. Furthermore, we apply the SDMC method to explore the gene targeting mechanism's impact on the global convergence in large-scale global optimization, deriving insights into how to design EC algorithms that guarantee global convergence and exploring how theoretical analysis can guide EC algorithm design.
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint via Lagrangian relaxation, transforming it into a regularization term in the objective function. A particularly challenging class includes the zero-norm function, which promotes sparsity in statistical parameter estimation. Most existing exact methods for solving these problems introduce binary variables and artificial bounds to reformulate them as higher-dimensional mixed-integer programs, solvable by standard solvers. Other exact approaches exploit specific structural properties of the objective, making them difficult to generalize across different problem types. Alternative methods employ nonconvex penalties with favorable statistical characteristics, but these are typically addressed using heuristic or local optimization techniques due to their structural complexity. In this paper, we propose a novel graph-based method to globally solve optimization problems involving generalized norm-bounding constraints. Our approach encompasses standard $\ell_p$-norms for $p \in [0, \infty)$ and nonconvex penalties such as SCAD and MCP. We leverage decision diagrams to construct strong convex relaxations directly in the original variable space, eliminating the need for auxiliary variables or artificial bounds. Integrated into a spatial branch-and-cut framework, our method guarantees convergence to the global optimum. We demonstrate its effectiveness through preliminary computational experiments on benchmark sparse linear regression problems involving complex nonconvex penalties, which are not tractable using existing global optimization techniques.
Designing free-form photonic devices is fundamentally challenging due to the vast number of possible geometries and the complex requirements of fabrication constraints. Traditional inverse-design approaches--whether driven by human intuition, global optimization, or adjoint-based gradient methods--often involve intricate binarization and filtering steps, while recent deep learning strategies demand prohibitively large numbers of simulations (10^5 to 10^6). To overcome these limitations, we present AdjointDiffusion, a physics-guided framework that integrates adjoint sensitivity gradients into the sampling process of diffusion models. AdjointDiffusion begins by training a diffusion network on a synthetic, fabrication-aware dataset of binary masks. During inference, we compute the adjoint gradient of a candidate structure and inject this physics-based guidance at each denoising step, steering the generative process toward high figure-of-merit (FoM) solutions without additional post-processing. We demonstrate our method on two canonical photonic design problems--a bent waveguide and a CMOS image sensor color router--and show that our method consistently outperforms state-of-the-art nonlinear optimizers (such as MMA and SLSQP) in both efficiency and manufacturability, while using orders of magnitude fewer simulations (approximately 2 x 10^2) than pure deep learning approaches (approximately 10^5 to 10^6). By eliminating complex binarization schedules and minimizing simulation overhead, AdjointDiffusion offers a streamlined, simulation-efficient, and fabrication-aware pipeline for next-generation photonic device design. Our open-source implementation is available at https://github.com/dongjin-seo2020/AdjointDiffusion.