Search Results (113)

To address the difficulty of accurately capturing the dynamic patterns of carbon emission time series—characterized by nonlinearity, non-stationarity, and complex fluctuations—this paper proposes a carbon emission prediction model based on an elite-guided collaborative social spider learning optimization algorithm (EGC-SSLO) integrated with a Long short-term memory (LSTM) network. First, considering the limitations of the standard stochastic social learning optimization (SSLO) algorithm in complex high-dimensional optimization problems, such as insufficient elite information guidance, weak local exploitation in the later stages, and a tendency to become trapped in local optima, three complementary improvement strategies are introduced. The adaptive elite mean-guided search strategy enhances the search directionality by incorporating the cooperative information of the best individual and the elite mean. The worst-individual hybrid Cauchy–Lévy search mechanism achieves a dynamic balance between early-stage global exploration and late-stage local exploitation through long-range Lévy flights and fine-grained Cauchy perturbations. The quadratic directional exploitation strategy further refines the search trajectory of candidate solutions, thereby improving convergence accuracy. These three strategies significantly enhance the optimization performance without increasing the time complexity order of the algorithm. Experimental results on the CEC2017 (30-dimensional), CEC2020 (20-dimensional), and CEC2022 (20-dimensional) benchmark suites demonstrate that EGC-SSLO consistently outperforms classical algorithms such as PSO, GWO, and HHO, as well as their improved variants, in terms of convergence accuracy, convergence speed, and robustness. Furthermore, the Wilcoxon rank-sum test and Friedman test confirm that the observed improvements are statistically significant. Finally, an EGC-SSLO-LSTM carbon emission prediction model is constructed and applied to daily carbon emission data in China from 2019 to 2025 for empirical analysis. The experimental findings show that the EGC-SSLO-LSTM model markedly outperforms both the standard LSTM and SSLO-LSTM approaches across key evaluation metrics, including mean absolute error (MAE), root mean square error (RMSE), and the coefficient of determination (R²). In particular, the MAE is decreased by 39.9% and 4.64% compared with the two benchmark models, respectively, which highlights the strong effectiveness and practical potential of the proposed method in real-world carbon emission forecasting applications. Full article

When addressing high-dimensional complex optimization problems, the vanilla Dung Beetle Optimizer (DBO) suffers from slow convergence, frequent stagnation in local optima, and progressive degradation of population diversity. To overcome the above inherent defects, this paper proposes a multi-strategy hybrid improved DBO variant named the SWDBO, which incorporates three targeted enhancement modules. First, an adaptive population proportion strategy is developed to dynamically adjust the population sizes of rolling beetles, brood beetles, small beetles and thief beetles throughout iterations. More individuals are allocated for extensive global exploration at the early evolutionary stage, while more search agents are reserved for delicate local exploitation in later iterations, which maintains stable population diversity over the entire optimization process. Second, the bubble-net encircling and spiral predation mechanisms of the Whale Optimization Algorithm (WOA) are embedded into the position update formula of rolling beetles. This integration strengthens fine local search performance and accelerates the overall convergence rate. Third, a modified seagull optimization operator combined with Lévy random perturbation is introduced into the position updating rule of thief beetles. This improved jump mechanism optimizes individual movement trajectories and enables the algorithm to effectively escape local optimal traps. Numerical experiments are implemented on the 100-dimensional benchmark functions of CEC2017 and CEC2020. Moreover, the proposed SWDBO is validated on three classical constrained engineering optimization tasks, including three-bar truss design, ten-bar truss design and cantilever beam sizing optimization. Wilcoxon rank-sum tests statistically verify significant performance disparities between the SWDBO and competing optimizers. For the three structural engineering cases, the design solutions obtained by the SWDBO produce lighter structural mass while satisfying all constraint requirements. Overall experimental evidence proves that the proposed multi-strategy improvement framework can efficiently tackle high-dimensional numerical optimization and constrained engineering design problems, and the SWDBO exhibits prominent performance in balancing global exploration and local exploitation. Full article

The rapid development of intelligent systems has introduced increasingly sophisticated optimization problems across diverse domains. While contemporary metaheuristic algorithms, including the recent Artificial Lemming Algorithm (ALA), have shown considerable promise, they frequently encounter difficulties such as premature convergence, inadequate local refinement, and diminished performance in high-dimensional multimodal environments. To overcome these issues, this study presents HALA, a new hybrid dual-subpopulation optimizer that effectively integrates an enhanced ALA with the SHADE algorithm. HALA employs two interacting subpopulations: one leverages an improved ALA with hybrid t-distribution and Levy flight perturbations to promote persistent long-range exploration and diversity preservation; the other applies SHADE’s success-history adaptation and external archive for accurate local exploitation. Periodic bidirectional elite migration facilitates knowledge transfer between the subpopulations, reducing early stagnation in the enhanced ALA and strengthening SHADE’s global search capability. HALA is thoroughly benchmarked against 17 advanced metaheuristics, including ALA, LSHADE, LSHADE-SPACMA, AOOA, BAEO, BPBO, CCO, CEO, CQALA, DFL, DMOA, DHOA, FGO, KLA, PGA, SO, and SOO, using the IEEE CEC2017 suite in 10, 30, 50, and 100 dimensions and the IEEE CEC2022 suite in 10 dimensions. Comprehensive analyses involving qualitative visualization, convergence curves, boxplots, and statistical tests indicate that HALA achieves competitive or superior solution quality, comparable or faster convergence, and robust stability on a substantial proportion of the test instances. In particular, HALA obtains the most favorable Friedman average ranking values among the compared algorithms, which are 2.55, 2.38, 2.34, and 2.55 for the 10-, 30-, 50-, and 100-dimensional CEC2017 functions, respectively, and 2.58 for the 12 10-dimensional CEC2022 functions. Moreover, HALA is successfully applied to five well-known constrained engineering design problems—pressure vessel, rolling element bearing, tension/compression spring, cantilever beam, and gear train—where it reliably achieves optimal or near-optimal results that match or surpass the compared methods. These findings underscore HALA’s competitive strength and broad potential for practical engineering optimization. Full article

In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes a model-constraint-aware optimal PID tuning method based on a Hybrid Differential Evolution–Chaotic Grey Wolf Optimizer (HDE-CGWO). First, a nonlinear LFC model incorporating data sampling, communication delay, governor deadband (GDB), and generation rate constraint (GRC) is established, and a PID-based LFC model is formulated. Next, an objective function based on the integral of time-weighted absolute area control error (ACE), namely ACE-based integral of time-weighted absolute error (ITAE), is constructed. Accordingly, quasi-opposition-based learning (QOBL), chaotic warm-up, Lévy flight, and differential evolution (DE) are incorporated into the standard Grey Wolf Optimizer (GWO) to develop an HDE-CGWO-based PID design scheme for LFC under sampled-data delay and nonlinear unit constraints. Finally, simulation studies are carried out on a multi-area LFC system. The resulting time-domain responses and statistical results show that, compared with standard GWO in the single-area test, HDE-CGWO reduces the ACE-based ITAE by about 43.3%. In the three-area system, the ACE-based ITAE is reduced by about 3.0% under step disturbances and about 1.4% under random disturbances compared with the warm-up Grey Wolf Optimizer (WGWO), indicating that the proposed method can reduce frequency deviations, attenuate post-disturbance oscillations, and accelerate the dynamic recovery process under the considered disturbance conditions. Full article

Efficient task scheduling in heterogeneous IoT–Fog environments is challenging due to limited fog resources, diverse task demands, and conflicting QoS objectives. This paper proposes ASQS, a Quality-Source-driven Multi-Anchor Synchronized Search algorithm for IoT–Fog task scheduling. ASQS is biomimetically motivated by collective search behaviors in natural systems, where distributed exploration, collective memory, and probabilistic cooperation support an exploration–exploitation balance. Specifically, ASQS constructs quality layers from candidate schedules, extracts representative quality-source anchors, and reuses them through an ACO-inspired probabilistic synchronization mechanism, thereby improving the utilization of high-quality historical search information. FNO-based search and Lévy-flight perturbation are further incorporated to enhance directional guidance and long-range exploration. Experiments on 33 benchmark functions, ablation studies, sensitivity analysis, standard fog scheduling scenarios, and large-scale task-intensive scenarios were conducted to evaluate ASQS. The results show that ASQS achieves competitive optimization accuracy, stable convergence, and superior comprehensive scheduling performance in terms of fitness, makespan, latency, load balance, and constraint handling. In particular, the large-scale experiment with 100 fog nodes and up to 8000 IoT tasks verifies the scalability of ASQS under heavy workload pressure. Statistical tests further confirm the reliability of the observed improvements. These results demonstrate that ASQS is an effective, scalable, and biomimetically motivated optimizer for IoT–Fog task scheduling. Full article

This paper presents a comprehensive spatiotemporal decomposition of equity returns for nine top-weighted constituents of the Dow Jones Industrial Average (DJIA) over a twenty-year period spanning January 2004 through December 2023, encompassing 5033 trading days and multiple market regimes, including the Global Financial Crisis (2008–2009), the COVID-19 crash and recovery (2020), and the Federal Reserve tightening cycle (2022–2023). Daily price movements are systematically partitioned into two orthogonal sessions: the open-to-close (OTC, or daytime) session, capturing within-session price discovery, and the close-to-open (CTO, or overnight) session, capturing the accumulated information arrival and liquidity dynamics between market closes and subsequent opens. Within this bipartite return framework, we construct and rigorously evaluate 24 distinct trading strategies, spanning directional (long/short), neutral (cash), momentum (inertia), and contrarian (reversal) approaches, applied independently to each session or in combinatorial cross-session configurations. Each strategy is evaluated under three transaction cost regimes (0, 1, and 2 basis points per trade) using an initial investment of $100, and assessed using annualized return, annualised volatility, Sharpe ratio, Sortino ratio, and maximum drawdown. The study universe—comprising UnitedHealth Group (UNH), Goldman Sachs (GS), Microsoft (MSFT), Home Depot (HD), Caterpillar (CAT), Amgen (AMGN), McDonald’s (MCD), Salesforce (CRM), and Honeywell (HON)—captures cross-sector heterogeneity across Healthcare, Financials, Technology, Consumer Discretionary, Industrials, Biotech, and Consumer Staples. The universe is selected from the top-weighted DJIA constituents as of early 2026; the paper is, therefore, best read as a focused, in-depth case study of index-representative large-cap names rather than a general cross-sectional statement about all U.S. equities. The principal findings are threefold. First, the overnight session consistently delivers superior risk-adjusted performance: seven of nine stocks record higher Sharpe ratios during the overnight period versus the daytime period, with the mean overnight Sharpe ratio (0.662) substantially exceeding the mean daytime Sharpe ratio (0.357), a statistically and economically significant overnight premium. Second, the hybrid Strategy #18—Long Overnight coupled with Daytime Reversal—emerges as the dominant cross-asset configuration, generating portfolio values as high as $8464 from a $100 initial investment (AMGN; Sharpe: 0.991) over the 20-year horizon. Third, Trajectory Change Analysis reveals (i) Lévy-stable tails with a mean stability index $\overline{\alpha }=1.667$ across all constituents, substantially below the Gaussian benchmark of $\alpha =2.0$; (ii) Hurst exponents clustering below 0.5 ($\overline{H}=0.417$), confirming dominant mean-reverting dynamics; and (iii) positive rolling CAPM alpha in 51–79% of rolling windows, indicating persistent risk-adjusted outperformance above the S&P 500 benchmark. These findings provide a rigorous empirical foundation for session-aware algorithmic trading system design and challenge the prevailing assumption of temporal homogeneity in equity return processes. Full article

Three-dimensional (3D) path planning for Unmanned Underwater Vehicles (UUVs) in typical marine operating conditions presents high-dimensional, non-convex optimization challenges due to undulating seabed topography, underwater threat sources, and coupled multi-physical constraints. Existing studies lack multi-strategy collaborative optimization mechanisms specifically designed for UUV 3D marine navigation constraints, thereby hindering the simultaneous achievement of real-time performance, safety, and energy efficiency in path planning. This paper first develops a comprehensive multi-dimensional cost function based on the dynamic characteristics of UUV underwater 3D navigation, operational rules for typical marine operating conditions, and safe navigation requirements through mathematical modeling, thereby formally transforming the UUV 3D path planning problem in typical marine operating conditions into a multi-constrained nonlinear global optimization problem. To address this challenge, an Adaptive Cooperative WMA (ACWMA) is proposed. The key improvements include: (i) an adaptive parameter switching and Lévy flight disturbance mechanism to balance exploration and exploitation capabilities; (ii) an optimal value leadership strategy to accelerate convergence; and (iii) a team collaborative learning mechanism to enhance population optimization efficiency. Algorithm benchmark performance is validated using the CEC 2017 standard test suite, while comparative and ablation experiments are conducted in multi-gradient complex marine 3D scenarios. The statistical significance of the algorithm performance improvement is verified using the Wilcoxon rank-sum test. The proposed ACWMA achieves a significant performance improvement of 8.71% over the suboptimal WMA in terms of core performance metrics and generates low-energy-consumption 3D paths that satisfy multiple constraints. These findings provide valuable engineering insights for 3D path planning in UUV autonomous operations within typical marine operating conditions. Full article

Multi-UAV coverage planning in complex mountainous environments is often constrained by idealized energy modeling, the “wood barrel effect” of traditional global energy minimization paradigms, and a lack of dynamic fault tolerance. To address these limitations, this study proposes a survivability-oriented Min–Max optimization architecture driven by the novel Lévy–Flight Terrain-Following Constrained Planning Optimization (LF-TF-CPO) algorithm. Coupling a high-fidelity 3D topographical matrix with a nonlinear aerodynamic energy model, the framework prioritizes individual UAV safety. Monte Carlo simulations demonstrate that LF-TF-CPO compresses the average maximum individual energy consumption to 665.64 kJ, preserving an adequate operational margin below the 950 kJ physical redline to absorb unmodeled aerodynamic perturbations while ensuring a 31.30 min mission duration. Ablation studies verify the Min–Max objective mitigates localized overloads with a marginal 0.4% energy trade-off. Furthermore, an emergency recovery protocol validates dynamic resilience across simultaneous and cascading failures by consistently stabilizing post-failure peak loads within safe margins. Notably, statistical evaluations establish a robust empirical sweet spot (λ = 0.05), demonstrating the framework’s low sensitivity to parameter variations. By minimizing the need for manual retuning, this architecture serves as a promising simulation-validated planning framework for future rapid deployment in time-critical disaster responses. Full article

Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration of three biologically realistic features that have not previously been combined: (i) fractional-order memory effects via a Caputo derivative of order $\alpha \in (0,1]$, (ii) two distinct biological delays—an infection transmission delay ${\tau }_1$ and a predator handling delay ${\tau }_2$—and (iii) nonlocal spatial dispersal modeled through fractional Laplacian operators ${(-\Delta )}^{\gamma /2}$. This triple integration enables the model to capture long-range temporal memory, delayed biological responses, and nonlocal spatial interactions simultaneously, offering insights into dynamics that are challenging to capture with classical integer-order or single-delay formulations. The fractional Laplacian generalizes classical diffusion by allowing long-range dispersal events (Lévy flights), where individuals can occasionally move over large distances with heavy-tailed step-size distributions—a phenomenon observed in many animal movement patterns but absent from standard diffusion models. We provide rigorous proofs of solution existence, uniqueness, non-negativity, and boundedness in both temporal and spatiotemporal settings. Local asymptotic stability conditions are derived for all feasible equilibrium states via characteristic equation analysis. The coexistence equilibrium undergoes a Hopf bifurcation when either delay crosses a critical threshold, with fractional order $\alpha$ modulating the bifurcation point and post-bifurcation oscillation frequency. A Lyapunov functional demonstrates global asymptotic stability of the infection-free equilibrium under biologically interpretable conditions. Turing instability analysis reveals conditions for spontaneous pattern formation, with the fractional exponent $\gamma$ controlling pattern wavelength and correlation length. Numerical simulations validate theoretical predictions, including spatial patterns, traveling waves, and chaos. To bridge theory with potential applications, we outline a statistical framework for parameter estimation and uncertainty quantification, suggesting that $\beta$, $\alpha$, and ${\tau }_1$ may be priority targets for parameter estimation. Full article

In response to the decline in population diversity, the imbalance between exploration and exploitation, and the low convergence efficiency in the middle and later stages of the Red-billed Blue Magpie Optimizer (RBMO) when addressing complex optimization problems, this study proposes a multi-strategy enhanced variant termed CLD-RBMO. The proposed algorithm improves the original search mechanism from three perspectives: strengthened global exploration, enhanced local refinement, and directed exploitation in the middle and later stages. During the exploration phase, a hierarchical perturbation mechanism based on Logistic chaotic mapping and Lévy flight is introduced to enhance randomness and spatial coverage in the early search process. In the local exploitation phase, a Cauchy–Gauss hybrid mutation operator is employed to improve the algorithm’s capability to escape from local optima. In the middle and later search stages, a stochastic differential mutation strategy is incorporated to provide population-structure-based directional guidance for individuals, thereby accelerating convergence and improving optimization accuracy. Simulation results on the CEC2017 benchmark test functions indicate that CLD-RBMO demonstrates clear superiority over the original algorithm and several representative swarm intelligence optimization algorithms in terms of optimization accuracy, stability, and overall performance ranking. Convergence curve analysis confirms its dynamic performance improvements across different search stages, and the Wilcoxon rank-sum test further statistically validates the significance of the performance enhancement achieved by the proposed improvements compared with the original algorithm. Moreover, evaluations on two representative mechanical engineering optimization case studies further demonstrate the algorithm’s strong stability and engineering generalization capability. Full article

Metaheuristic optimization algorithms have attracted considerable research interest for solving complex optimization problems, yet many existing algorithms suffer from premature convergence and an inadequate balance between exploration and exploitation. The Coati Optimization Algorithm (COA) is a recently proposed nature-inspired metaheuristic that models the hunting and escape behaviors of coatis; however, it exhibits limited search diversity and tends to stagnate in local optima on high-dimensional, multimodal landscapes. This paper proposes an Improved Coati Optimization Algorithm (ICOA) that integrates four complementary enhancement strategies: (1) a Dynamic Adaptive Step-Size strategy that combines Lévy flights with Student’s t-distribution perturbations for heavy-tailed exploration; (2) a Population-Adaptive Dynamic Perturbation strategy that incorporates differential evolution operators with fitness-proportional scaling; (3) an Iterative-Cyclic Differential Perturbation strategy that employs sinusoidal scheduling and population-differential guidance; and (4) a Cosine-Adaptive Gaussian Perturbation strategy for refined exploitation with time-decaying intensity. ICOA is evaluated on 29 CEC2017, 10 CEC2020, and 12 CEC2022 benchmark functions across dimensions ranging from 10 to 100, compared against seven state-of-the-art algorithms in each benchmark suite. A statistical analysis using the Friedman test and the Wilcoxon rank-sum test confirms that ICOA achieves overall rank 1 on all three benchmark suites, with Friedman mean ranks of 1.207 (CEC2017, $D=100$), 1.000 (CEC2020, $D=10$), and 2.208 (CEC2022, $D=10$); the CEC2020 result should be interpreted in the context of its low dimensionality. A scalability analysis across four dimensionalities (10D, 30D, 50D, 100D) demonstrates consistent first-place rankings with mean ranks between 1.000 and 1.207. An ablation study and a sensitivity analysis of the strategy activation probability validate the contribution of each individual strategy and the optimality of the 50% activation setting. Furthermore, ICOA achieves the best results on all six constrained engineering design problems tested, with all improvements confirmed as statistically significant ($p<0.05$). Full article

Autonomous ground vehicles operating in structured and semi-structured environments—such as urban roads, parking lots, and logistics warehouses—require fast, reliable, and collision-free path planning on occupancy grid maps. Existing metaheuristic planners often suffer from premature convergence, insufficient population diversity, and poor feasibility maintenance, limiting their deployment in safety-critical vehicular navigation. This paper proposes a multi-strategy enhanced Crested Porcupine Optimizer (MSCPO) that systematically addresses these limitations through four coordinated enhancements: chaos-opposition initialization with feasibility repair to ensure high-quality and diverse initial routes; a diversity-coupled adaptive mechanism for dynamic strategy scheduling throughout the search; elite-guided differential Lévy perturbation to escape local optima and accelerate convergence; and a two-stage safety-aware objective with elite local refinement to sharpen final solution precision. Experiments on four representative grid maps with varying obstacle densities, conducted over 30 independent runs per algorithm, demonstrate that MSCPO consistently outperforms state-of-the-art metaheuristic planners and deterministic baselines in path length, smoothness, and convergence speed. Statistical analysis via Wilcoxon rank-sum and Friedman tests confirms the significance of the improvements. An ablation study quantifies the individual contribution of each enhancement module, confirming the practical effectiveness of MSCPO for autonomous vehicle navigation tasks. Full article

This review paper comprehensively examines the influence of spatial torsion on quantum fluctuations from the perspectives of metric-affine gravity (MAG) and the stochastic variational method (SVM). We first outline the fundamental framework of MAG, a generalized theory that includes both torsion and non-metricity, and discuss the geometrical significance of torsion within this context. Subsequently, we summarize SVM, a powerful technique that facilitates quantization while effectively incorporating geometrical effects. By integrating these frameworks, we evaluate how the geometrical structures originating from torsion affect quantum fluctuations, demonstrating that they induce non-linearity in quantum mechanics. Notably, torsion, traditionally believed to influence only spin degrees of freedom, can also affect spinless degrees of freedom via quantum fluctuations. Furthermore, extending beyond the results of previous work [Koide and van de Venn, Phys. Rev. A112, 052217 (2025)], we investigate the competitive interplay between the Levi-Civita curvature and torsion within the non-linearity of the Schrödinger equation. Finally, we discuss the structural parallelism between SVM and information geometry, highlighting that the splitting of time derivatives in stochastic processes corresponds to the dual connections in statistical manifolds. These insights pave the way for future extensions to gravity theories involving non-metricity and are expected to deepen our understanding of unresolved cosmological problems. Full article

We study one-dimensional diffusions reflected at a boundary and analyze their pathwise “episodes” away from the boundary through Itô’s excursion theory. Under a fixed height cap of $a>0$, each excursion is equipped with three natural marks: its lifetime $\zeta$, its maximum $M$, and an additive (area-type) functional $A_f={\int }_0^{\zeta }f\left(e_t\right)dt$. Our main object is the height-truncated Itô-excursion Laplace exponent ${\mathsf{\Psi }}_{\alpha ,\lambda ;af}:=n\left(1-e^{-\alpha \zeta -\lambda A_f}; M<a\right)$ which jointly characterizes episode duration and cumulative load while excluding barrier-crossing spikes. We establish a general boundary–flux representation: ${\mathsf{\Psi }}_{\alpha ,\lambda ;af}$ is obtained as a boundary flux (in scale) of the unique solution to a one-dimensional killed Feynman–Kac boundary-value problem on $(0, a)$. This transfer principle yields a unified and tractable route to explicit computation. We implement it in three solvable families—the reflected arithmetic Brownian motion, reflected Ornstein–Uhlenbeck diffusions, and squared Bessel/Bessel-type diffusions—obtaining closed forms in terms of Airy, parabolic-cylinder, and confluent hypergeometric/Whittaker functions. Using the Poisson point process structure of excursions indexed by local time, we derive explicit extreme-burst laws (maxima and order statistics) for the additive marks up to a local-time horizon, and connect tail intensities to Laplace exponents via numerical Laplace inversion. Finally, we identify the strictly truncated cumulative load in local time as a (typically infinite-activity) subordinator whose Lévy measure coincides with the excursion-mark intensity, linking cumulative-load and extreme-burst statistics through the same exponent. Full article

Clustering is a fundamental unsupervised learning technique used to uncover hidden patterns in unlabeled data. Although metaheuristic algorithms have demonstrated effectiveness in clustering, many suffer from premature convergence and limited population diversity. This study employs the Black-Winged Kite Algorithm (BKA) and its enhanced variants, Chaotic BKA (CBKA), Lévy Flight-based BKA (LBKA), and Chaotic Levy BKA (CLBKA), to address these limitations in centroid-based clustering formulated as a Sum of Squared Errors (SSE) minimization problem. Chaotic logistic mapping improves search diversity and adaptability, while Levy flight introduces long-range exploration. In addition, Cauchy based perturbations are incorporated to enhance convergence stability. The algorithms are evaluated on sixteen UCI benchmark datasets, with 30 independent runs conducted under different population and iteration settings. Experimental results show that CLBKA consistently achieves superior clustering performance in terms of accuracy and stability. Statistical validation using the Friedman and Wilcoxon tests confirms significant performance differences, with CLBKA obtaining the lowest mean rank across configurations. The findings indicate that integrating chaotic dynamics and Levy flight mechanisms enhances clustering robustness and optimization efficiency. Full article