Search Results (39)

With the increasing complexity of engineering optimization and intelligent decision-making problems, traditional metaheuristic algorithms often suffer from premature convergence, loss of population diversity, and insufficient adaptability to complex fitness landscapes. To address these issues, this paper proposes a Multi-strategy Symmetry-Aware Improved Golden Sine Algorithm (MIGoldSA). The proposed algorithm introduces a symmetry-guided multi-strategy framework in which multiple complementary search operators are organized in a structurally balanced manner. Specifically, a strategy pool consisting of the original golden sine update rule, three differential evolution mutation strategies, and an elite-based quadratic interpolation local search operator is constructed. An adaptive strategy selection mechanism is further developed to dynamically regulate the selection probabilities of different strategies according to their historical success rates, forming a dynamic probabilistic symmetry that balances global exploration and local exploitation throughout the optimization process. The numerical performance of the resulting method is assessed using the CEC2014, 30-dimensional CEC2017, and 20-dimensional CEC2022 test collections. Comparative and statistical findings confirm that MIGoldSA generally delivers more accurate final solutions, more consistent outcomes across independent trials, and stronger convergence behavior than established algorithms and recently developed competitors. Its applicability is further examined in corporate insolvency forecasting by employing MIGoldSA to determine the hyperparameter configuration of a K-nearest neighbors classifier. Tests conducted on the Wieslaw financial database show that the resulting MIGoldSA-KNN system outperforms the selected reference models in classification accuracy, Matthews correlation coefficient, F1-score, and recall. These findings suggest that the proposed symmetry-inspired architecture offers an effective means of coordinating diversified search and intensive refinement, thereby providing a valuable computational approach for challenging global optimization and financial classification tasks. Full article

Multi-UAV cooperative path planning is an important technical basis for improving offshore emergency response efficiency in complex maritime environments. However, in complex offshore environments, cooperative trajectory planning is affected not only by geometric obstacles but also by wind disturbances, island terrain, restricted flight zones, and inter-UAV safety and communication constraints. These coupled factors make it difficult for conventional swarm intelligence optimizers to maintain risk awareness, local correction capability, and stable late-stage refinement. To address this problem, this paper proposes a risk-aware Modified Traffic Jam Optimizer for cooperative multi-UAV path planning in complex offshore missions. Unlike the original Traffic Jam Optimizer, the proposed method explicitly incorporates risk information into the population update process. A risk-opposition collaborative guidance strategy is designed to adjust the global search direction away from high-risk regions; a risk-based geometric multiscale adaptive mutation strategy is developed to identify and correct high-risk local control blocks; and a generalized quadratic interpolation decision-vector reconfiguration mechanism is introduced to refine the current best solution during stagnation or late-stage search. Two-UAV and three-UAV simulations are conducted using the constructed offshore environment and cooperative constraint models. The results show that the proposed method can generate feasible cooperative trajectories and achieve better performance than the comparison algorithms in path cost, path length, synchronized flight time, and convergence behavior. These results verify the feasibility and effectiveness of the proposed method for risk-aware multi-UAV cooperative path planning in complex offshore environments. Full article

We develop a quantitative Hardy scale for mixed quadratic energies combining the classical Dirichlet form and a fractional Dirichlet form, ${\mathcal{E}}_{\lambda ,s}\left(u\right)={\int }_{{\mathbb{R}}^n}{|\mathrm{\nabla }u\left(x\right)|}^2\mathrm{d}x+\lambda {\int }_{{\mathbb{R}}^n}{\left|{(-\mathrm{\Delta })}^{s/2}u\left(x\right)\right|}^2\mathrm{d}x,0<s<1,\lambda >0.$ Here, the word scale denotes a parameterized family with a fixed interpolation variable, explicit constants, and the scaling exponent forced by the coexistence of the orders 2 and $2s$. For $n\ge 3$, we prove weighted $L^2$ inequalities indexed by $\gamma \in [s,1]$, which control ${\left|x\right|}^{-2\gamma }$ by ${\mathcal{E}}_{\lambda ,s}$ with the factor ${\lambda }^{-\theta }$, where $\theta =(1-\gamma )/(1-s)$. In dimension $n=2$, the local endpoint is replaced by the logarithmic Hardy weight and gives a mixed log–power family governed by the same parameter. The novelty lies in organizing the endpoint Hardy estimates into a $\lambda$-adapted form suitable for mixed-order operators, with explicit constants, scaling-level optimality of the $\lambda$ exponent, a planar endpoint formulation, and directly usable singular-potential thresholds. The operator consequences are stated at the level of form boundedness, coercivity, spectral lower bounds on bounded domains, semigroup generation, and variational well-posedness; they are presented as consequences of the Hardy scale rather than as a separate spectral theory. Full article

This study addresses the challenge of modeling the complex non-linear relationship between process parameters and relative density in selective laser melting (SLM) of IN718 nickel-based superalloy under small-sample conditions. A data-driven prediction framework integrating data augmentation, physics-informed feature engineering, machine learning, and model interpretability analysis was developed and systematically validated. Fourteen sets of experimental data covering both vertical and horizontal building directions were collected by varying laser power (P), scan speed (v), and hatch spacing (h). To overcome the small-sample limitation, three augmentation strategies—radial basis function (RBF) interpolation, generative adversarial network (GAN), and K-nearest neighbors (KNN)—were systematically compared under unified physical constraints combining local perturbation and volumetric energy density (E_vol) filtering, with Pearson correlation coefficient consistency used to select the optimal strategy. Eight physically meaningful input features were constructed, including E_vol and line energy density (E_line), explicitly embedding SLM process physics into the learning framework. Support vector regression (SVR), random forest (RF), and artificial neural network (ANN) models were trained and their hyperparameters were systematically optimized via exhaustive grid search combined with leave-one-out cross-validation (LOO-CV), ensuring robust model selection under small-sample constraints. A physics-based baseline model (E_vol quadratic fitting, LOO-CV average R² = 0.2534) was established to quantify the gain of machine learning over empirical formulas. LOO-CV results show that ANN achieves the highest average R² of 0.9269, followed by SVR (0.9148) and RF (0.8393), all of which substantially outperform the physical baseline. Feature importance analysis reveals that E_vol accounts for 51.58% of the predictive power, and ablation experiments confirm that introducing physics-derived features improves the average R² by 0.0246 compared with raw process parameters alone. To further elucidate the predictive mechanism of the optimal ANN model, Partial Dependence Plot (PDP) analysis was conducted for all eight input features, visualizing their marginal effects on predicted density and confirming physical consistency with SLM mechanisms. This framework provides a reliable, interpretable, data-driven solution for intelligent SLM process optimization with limited experimental data. Full article

To address the limitations of the traditional Teaching–Learning-Based Optimization (TLBO) algorithm when solving high-dimensional, multimodal, strongly nonlinear, and constrained global optimization problems—such as single search direction, inefficient population information exchange, insufficient local exploitation capability, susceptibility to premature convergence, and low solution accuracy—this paper proposes a multi-strategy collaborative enhanced Teaching–Learning-Based Optimization algorithm (CSTLBO). While retaining the fundamental two-phase framework of the original TLBO, namely the teacher phase and learner phase, three novel strategies are sequentially incorporated: a Collaborative Differential Guidance (CDG) strategy to enrich global search directions, an Elite-Guided Collaborative Interaction (EGCI) strategy to enhance efficient transmission of high-quality population information, and a Quadratic Interpolation Local Refinement (QILR) strategy to improve fine-grained exploitation in promising regions. Together, these strategies enable an adaptive trade-off between broad search capability and refined local optimization. The effectiveness of CSTLBO is systematically assessed using the CEC2017 and CEC2022 benchmark suites, with comparative analyses conducted against multiple advanced algorithms and the baseline TLBO method. Experimental results demonstrate that CSTLBO exhibits significant superiority in terms of convergence speed, solution accuracy, robustness, and statistical performance, particularly in the 100-dimensional CEC2017 benchmark problems and the WSN deployment problem, while maintaining competitive performance on the 10- and 20-dimensional CEC2022 benchmarks. The superiority of CSTLBO is further validated through the Wilcoxon rank-sum test and Friedman mean rank test. Furthermore, the proposed algorithm is applied to the coverage deployment optimization problem in Wireless Sensor Networks (WSNs), a typical high-dimensional engineering problem involving multiple conflicting deployment indicators, which is formulated as a weighted single-objective optimization problem in this study. The results show that CSTLBO achieves a coverage rate of up to 95.71% with a fitness value as low as 0.1344, outperforming the compared algorithms in overall performance. Owing to its simple structure, low computational complexity, and strong generalization capability, CSTLBO provides an efficient and reliable solution for complex global optimization problems and practical engineering applications. Full article

In Time Division Duplex (TDD) Direct-Sequence Code Division Multiple Access (DS/CDMA) architectures, Pre-Rake filtering serves as a powerful transmitter-side strategy to alleviate receiver hardware constraints by leveraging channel reciprocity. Nevertheless, rapid channel fluctuations induced by high Doppler spreads critically undermine this reciprocity assumption. This failure is primarily driven by the unavoidable latency between uplink reception and downlink transmission, leading to severe performance deterioration. To address these challenges and enhance system robustness in modern high-speed scenarios, we propose an improved hybrid transceiver architecture. This scheme integrates multiplexed Pre-Rake processing with a Matched Filter-based Rake receiver and employs a Minimum Mean Square Error (MMSE) equalizer to suppress the severe Inter-Symbol Interference (ISI) and Multi-User Interference (MUI). Furthermore, we conduct a comparative analysis of channel estimation methods tailored for a 10 Mbps high-speed transmission environment.Our investigation reveals that while complex quadratic interpolation is often prioritized in low-data-rate studies, simple averaging is sufficient and even superior in high-speed communications. This is because the shortened slot duration allows simple averaging to effectively track channel variations while avoiding the noise overfitting associated with higher-order interpolation. The simulation results demonstrate that the proposed MMSE-optimized architecture achieves superior Bit Error Rate (BER) performance, providing a practical and computationally efficient solution for next-generation mobile networks. Full article

Newton–Raphson-Based Optimizer (NRBO) is a recently proposed metaheuristic that combines mathematical search rules with population-based optimization; however, it still suffers from an insufficient balance between global exploration and local exploitation, limited local refinement accuracy, and weak adaptability in complex optimization scenarios. To address these limitations, this paper proposes an Improved Newton–Raphson-Based Optimizer (INRBO), which enhances the original framework through a multi-strategy augmentation mechanism. Specifically, INRBO integrates three complementary strategies: (1) an adaptive differential operator with a linearly decaying scaling factor to dynamically regulate exploration and exploitation throughout the search process; (2) a quadratic interpolation strategy that exploits high-quality individuals to improve local search directionality and precision; and (3) an elitist population genetic strategy that preserves superior solution characteristics while maintaining population diversity and preventing premature convergence. The performance of INRBO is systematically evaluated on the CEC2017 benchmark suite under multiple dimensions and compared with several state-of-the-art metaheuristic algorithms. Experimental results demonstrate that INRBO achieves superior optimization accuracy, convergence efficiency, and robustness across unimodal, multimodal, hybrid, and composite functions, which is further confirmed by statistical significance tests. In addition, INRBO is applied to mobile robot path planning in grid-based environments of different scales, where it consistently generates shorter, smoother, and safer paths than competing algorithms. Overall, the proposed INRBO provides an effective and robust optimization framework for global continuous optimization problems and real-world engineering applications, demonstrating both strong theoretical value and practical applicability. Full article

This paper introduces a fractional generalization of the classical Legendre differential equation based on the Atangana–Baleanu–Caputo (ABC) derivative. A novel fractional Legendre-type operator is rigorously defined within a functional framework of continuously differentiable functions with absolutely continuous derivatives. The associated initial value problem is reformulated as an equivalent Volterra integral equation, and existence and uniqueness of classical solutions are established via the Banach fixed-point theorem, supported by a proved Lipschitz estimate for the ABC derivative. A constructive solution representation is obtained through a Volterra–Neumann series, explicitly revealing the role of Mittag–Leffler functions. We prove that the fractional solutions converge uniformly to the classical Legendre polynomials as the fractional order approaches unity, with a quantitative convergence rate of order $O(1-\alpha )$ under mild regularity assumptions on the Volterra kernel. A fully reproducible quadrature-based numerical scheme is developed, with explicit kernel formulas and implementation algorithms provided in appendices. Numerical experiments for the quadratic Legendre mode confirm the theoretical convergence and illustrate the smooth interpolation between fractional and classical regimes. An application to time-fractional diffusion in spherical coordinates demonstrates that the operator arises naturally in physical models, providing a mathematically consistent tool for extending classical angular analysis to fractional settings with memory. Full article

To address the limitations of the traditional Balancing Composite Motion Optimization (BCMO) algorithm—namely weak directional global exploration, insufficient local exploitation accuracy, and a tendency to fall into local optima with reduced population diversity in feature selection tasks—this paper proposes a Multi-Strategy Enhanced Balancing Composite Motion Optimization algorithm (MEBCMO). From a symmetry perspective, MEBCMO exploits the symmetric and asymmetric relationships among candidate solutions in the search space to achieve a better balance between exploration and exploitation. The performance of MEBCMO is enhanced through three complementary strategies. First, an adaptive heat-conduction search mechanism is introduced to simulate thermal transmission behavior, where a Sigmoid function adjusts the heat-conduction coefficient α_T from 0.9 to 0.2 during iterations. By utilizing the symmetric fitness–distance relationship between the current solution and the global best, this mechanism improves the directionality and efficiency of global exploration. Second, a quadratic interpolation search strategy is designed. By constructing a quadratic model based on the current individual, a randomly selected individual, and the global best, the algorithm exploits local symmetric characteristics of the fitness landscape to strengthen local exploitation and alleviate performance degradation in high-dimensional spaces. Third, an elite population genetic strategy is incorporated, in which the top three individuals generate new candidates through symmetric linear combinations with non-elite individuals and Gaussian perturbations, preserving population diversity and preventing premature convergence. To evaluate MEBCMO, extensive global optimization experiments are conducted on the CEC2017 benchmark suite with dimensions of 30, 50, and 100, and comparisons are made with eight mainstream algorithms, including PSO, DE, and GWO. Experimental results demonstrate that MEBCMO achieves superior performance across unimodal, multimodal, hybrid, and composite functions. Furthermore, MEBCMO is combined with LightGBM to form the MEBCMO-LightGBM model for feature selection on 14 public datasets, yielding lower fitness values, higher classification accuracy, and fewer selected features. Statistical tests and convergence analyses confirm the effectiveness, stability, and rapid convergence of MEBCMO in symmetric and complex optimization landscapes. Full article

Background/Objectives: Ulcerative Colitis (UC) lacks longitudinal visual data, which limits both disease progression modeling and the effectiveness of computer-aided diagnosis systems. These systems are further constrained by sparse intermediate disease stages and the discrete nature of the Mayo Endoscopic Score (MES). Meanwhile, synthetic image generation has made significant advances. In this paper, we propose novel ordinal embedding architectures for conditional diffusion models to generate realistic UC progression sequences from cross-sectional endoscopic images. Methods: By adapting Stable Diffusion v1.4 with two specialized ordinal embeddings (Basic Ordinal Embedder using linear interpolation and Additive Ordinal Embedder modeling cumulative pathological features), our framework converts discrete MES categories into continuous progression representations. Results: The Additive Ordinal Embedder outperforms alternatives, achieving superior distributional alignment (CMMD 0.4137, recall 0.6331) and disease consistency comparable to real data (Quadratic Weighted Kappa 0.8425, UMAP Silhouette Score 0.0571). The generated sequences exhibit smooth transitions between severity levels while maintaining anatomical fidelity. Conclusions: This work establishes a foundation for transforming static medical datasets into dynamic progression models and demonstrates that ordinal-aware embeddings can effectively capture disease severity relationships, enabling synthesis of underrepresented intermediate stages. These advances support applications in medical education, diagnosis, and synthetic data generation. Full article

In the modern era of informatics, where data are very important, efficient management of data is necessary and critical. Two of the most important data management techniques are searching and data ordering (technically sorting). Traditional sorting algorithms work in quadratic time $\left(\mathcal{O}\left(x^2\right)\right)$, and in the optimized cases, they take linearithmic time $\left(\mathcal{O}\left(x·\log x\right)\right)$, with no existing method surpass this lower bound, given arbitrary data, i.e., ordering a list of cardinality x in $\left(\mathcal{O}\left(x·\log x\right)-ϵ\left(x\right)\right)\forall ϵ\left(x\right)>0$. This research proposes Search-o-Sort, which reinterprets sorting in terms of searching, thereby offering a new framework for ordering arbitrary data. The framework is applied to classical search algorithms,–Linear Search, Binary Search (in general, k-ary Search), and extended to more optimized methods such as Interpolation and Jump Search. The analysis suggests theoretical pathways to reduce the computational complexity of sorting algorithms, thus enabling algorithmic development based on the proposed viewpoint. Full article

In this work, we introduce a novel class of $C^1$ rational quadratic interpolation splines defined by two symmetric parameters. This generalization encompasses the rational quadratic interpolation schemes given by Schmidt in 1987 as a special case. For data sets with convexity, monotonicity, or positivity constraints, we derive the necessary and sufficient conditions, ensuring that the interpolant preserves these properties. Furthermore, we propose an algorithm for selecting visually appealing and shape-preserving spline curves by minimizing a particular approximated curvature functional. Full article

In this paper, we propose a robust deep learning (DL)-based method for Direction-of-Arrival (DOA) estimation. Specifically, we develop a novel CRDCNN-LSTM network architecture, which integrates a Cross-Residual Depthwise Convolutional Neural Network (CRDCNN) with a Long Short-Term Memory (LSTM) module for effective capture of both spatial and temporal features. The CRDCNN employs multi-level cross-residual connections and depthwise separable convolutions to enhance feature diversity while mitigating issues such as gradient vanishing and overfitting. Furthermore, a customized FD loss function, combining Focal Loss and Dice Loss, is introduced to emphasize low-confidence samples and promote sparsity in the spatial spectrum, thereby improving the precision and overall effectiveness of DOA estimation. A post-processing strategy based on peak detection and quadratic interpolation is also employed to refine DOA estimations and reduce quantization errors. Simulation results demonstrate that the proposed approach achieves significantly higher estimation accuracy and resolution than conventional methods and current DL models under varying SNR and snapshot conditions. In addition, it offers distinct advantages in terms of generalization and computational efficiency. Full article

This article presents an alternative variant of motion planning techniques for autonomous vehicles (AVs) centered on an inverse approach that concurrently optimizes both trajectory and speed. This method emphasizes searching for a trajectory and distributing its speed within a single road segment, regarded as a final element. The references for the road lanes are represented by splines that interpolate the path length, derivative, and curvature using Cartesian coordinates. This approach enables the determination of parameters at the final node of the road segment while varying the reference length. Instead of directly modeling the trajectory and velocity, the second derivatives of curvature and speed are modeled to ensure the continuity of all kinematic parameters, including jerk, at the nodes. A specialized inverse numerical integration procedure based on Gaussian quadrature has been adapted to reproduce the trajectory, speed, and other key parameters, which can be referenced during the motion tracking phase. The method emphasizes incorporating kinematic, dynamic, and physical restrictions into a set of nonlinear constraints that are part of the optimization procedure based on sequential quadratic optimization. The objective function allows for variation in multiple parameters, such as speed, longitudinal and lateral jerks, final time, final angular position, final lateral offset, and distances to obstacles. Additionally, several motion planning variants are calculated simultaneously based on the current vehicle position and the number of lanes available. Graphs depicting trajectories, speeds, accelerations, jerks, and other relevant parameters are presented based on the simulation results. Finally, this article evaluates the efficiency, speed, and quality of the predictions generated by the proposed method. The main quantitative assessment of the results may be associated with computing performance, which corresponds to time costs of 0.5–2.4 s for an average power notebook, depending on optimization settings, desired accuracy, and initial conditions. Full article

Accurate forecasting of offshore wind speed is crucial for the efficient operation and planning of wind energy systems. However, the inherently non-stationary and highly volatile nature of wind speed, coupled with the sensitivity of neural network-based models to parameter settings, poses significant challenges. To address these issues, this paper proposes an Adaptive Neuro-Fuzzy Inference System (ANFIS) optimized by CRGWAA. The proposed CRGWAA integrates Chebyshev mapping initialization, an elite-guided reflection refinement operator, and a generalized quadratic interpolation strategy to enhance population diversity, adaptive exploration, and local exploitation capabilities. The performance of CRGWAA is comprehensively evaluated on the CEC2022 benchmark function suite, where it demonstrates superior optimization accuracy, convergence speed, and robustness compared to six state-of-the-art algorithms. Furthermore, the ANFIS-CRGWAA model is applied to short-term offshore wind speed forecasting using real-world data from the offshore region of Fujian, China, at 10 m and 100 m above sea level. Experimental results show that the proposed model consistently outperforms conventional and hybrid baselines, achieving lower MAE, RMSE, and MAPE, as well as higher R², across both altitudes. Specifically, compared to the original ANFIS-WAA model, the RMSE is reduced by approximately 45% at 10 m and 24% at 100 m. These findings confirm the effectiveness, stability, and generalization ability of the ANFIS-CRGWAA model for complex, non-stationary offshore wind speed prediction tasks. Full article