Search Results (188)

In the service-oriented modern society, logistics enterprises focusing solely on cost minimization can no longer meet market demands, as customers place greater emphasis on timely delivery and service satisfaction. Therefore, this paper constructs a multi-objective optimization model that simultaneously minimizes distribution costs and hierarchical customer delivery duration. From the perspective of symmetry, the two objectives form a symmetric complementary system, which reflects the mutually restrictive and trade-off relationship between the two objectives, thereby facilitating the achievement of a balance between enterprise benefits and customer satisfaction. An improved multi-objective grey wolf optimizer (IMOGWO) is proposed to solve the model, incorporating a chaotic mapping initialization mechanism, a cosine nonlinear convergence factor, and a learning factor-based hunting mechanism to enhance global optimization capability. The algorithm’s effectiveness is validated through comparisons on benchmark cases. Applied to a Zhengzhou food company, the solution improved distribution efficiency while prioritizing key clients, thereby enhancing service levels and stabilizing important customer relationships, providing a practical reference for logistics enterprises to increase revenue and undergo digital transformation. Full article

Facial information carries key personal privacy, and it is crucial to ensure its security through encryption. Traditional encryption for portrait images typically processes the entire image, despite the fact that most regions lack sensitive facial information. This approach is notably inefficient and imposes unnecessary computational burdens. To address this inefficiency while maintaining security, we propose a novel dual-region encryption model for portrait images. Firstly, a Multi-task Cascaded Convolutional Network (MTCNN) was adopted to efficiently segment facial images into two regions: facial and non-facial. Subsequently, given the high sensitivity of facial regions, a robust encryption scheme was designed by integrating a CNN-based key generator, the proposed three-dimensional Multi-module Nonlinear Feedback-coupled Chaotic System (3D-MNFC), DNA encoding, and bit reversal. The 3D-MNFC incorporating time-varying parameters, nonlinear terms and state feedback terms and coupling mechanisms has been proven to exhibit excellent chaotic performance. As for non-facial regions, the Logistic map combined with XOR operations is used to balance efficiency and basic security. Finally, the encrypted image is obtained by restoring the two ciphertext images to their original positions. Comprehensive security analyses confirm the exceptional performance of the regional model: large key space ($2^{536}$) and near-ideal information entropy (7.9995), NPCR and UACI values of 99.6055% and 33.4599%. It is worth noting that the model has been verified to improve efficiency by at least 37.82%. Full article

To address the challenges of high computational costs, susceptibility to local optima, and heavy reliance on manual intervention in multi-physics parameter optimization for symmetric acoustic metamaterials, an enhanced Chimp Optimization Algorithm (DADCOA) is proposed in this paper. This algorithm integrates the double chaotic initialization strategy (DCS), adaptive multimodal convergence mechanism (AMC), and dual-weight pinhole imaging update operator (DWPI). It employs a Logistic–Tent composite chaotic mapping strategy for population initialization, significantly enhancing distribution uniformity within high-dimensional parameter spaces. An AMC factor is then introduced to dynamically balance global exploration and local exploitation based on the real-time evolutionary state of the population. A dual-weight population update mechanism, incorporating distance and historical contributions, is integrated with a pinhole imaging opposition-based learning strategy to improve population diversity. Additionally, a composite single objective error feedback local differential mutation operation is introduced to improve optimization accuracy for coupled multi-physics objectives. Experimental validation based on the CEC 2022 test function suite and an acoustic metamaterial parameter optimization model demonstrates that compared to the standard COA algorithm and existing improved algorithms, the DADCOA algorithm reduces simulation time by 28.46% to 60.76% while maintaining high accuracy. This approach effectively addresses the challenges of high computational cost, stringent accuracy requirements, and composite single objective coupling in COMSOL physical parameter optimization, providing an effective solution for the design of acoustic metamaterials based on symmetric structures. Full article

Classical integer-order chaotic maps usually exhibit chaotic degradation under prolonged iterations or finite-precision computation, which may compromise the reliability of chaos-based algorithms. Fractional difference chaotic systems with memory effects offer a promising alternative; however, existing studies rarely provide a systematic and quantitative understanding of how the nonlinear gain parameter, memory strength, and initial condition collectively influence the emergence and robustness of complex dynamics under finite-time iterations. It should be noted that memory effects do not inherently guarantee robust chaotic behavior under finite-precision computation, and appropriate parameter and initial-condition selection remains essential. In this paper, we conduct a systematic numerical dynamical analysis of a logistic-type fractional difference system with power-law memory by leveraging bifurcation diagrams and Lyapunov exponent mappings. Rather than aiming to select optimal parameter points, we propose a quantitative composite chaos evaluation (CCE) framework to identify admissible parameter intervals within which robust finite-time chaotic dynamics can be consistently sustained. Numerical results demonstrate the effectiveness and reliability of the proposed framework, which may facilitate future applications in chaos-enhanced optimization, nonlinear control, and secure communication. Full article

Image watermarking is an essential technique for protecting the copyright of digital images. This paper proposes a novel color image watermarking algorithm based on the Walsh–Hadamard Transform (WHT). By analyzing the differences among WHT coefficients, an asymmetric embedding position selection strategy is designed to enhance the robustness of the algorithm. Specifically, the color image is first separated into red (R), green (G), and blue (B) channels, each of which is divided into non-overlapping 4 × 4 blocks. Then, suitable embedding regions are selected based on the entropy of each block. Finally, the optimal embedding positions are determined by comparing the differences between WHT coefficient pairs. To ensure watermark security, the watermark is encrypted using Logistic chaotic map prior to embedding. During the extraction phase, the watermark is recovered using the chaotic key and the pre-stored embedding position information. Extensive simulation experiments are conducted to evaluate the effectiveness of the proposed algorithm. The comparative results demonstrate that the proposed method maintains high imperceptibility while exhibiting superior robustness against various attacks, outperforming existing state-of-the-art approaches in overall performance. Full article

To solve the limitations of single optimization algorithms, such as premature convergence, insufficient global exploration, and high susceptibility to local optima, a Hybrid Optimization Algorithm (HOA) based on multi-subpopulation collaboration and multi-strategy fusion is proposed. The HOA uses Logistic chaotic mapping for population initialization to enhance uniformity and diversity. The population is then divided into four subpopulations; each is optimized independently using different strategies, including the genetic algorithm (GA), Gray Wolf Optimizer (GWO), self-attention mechanism, and k-nearest neighbor graph (kNN). This design leverages the strengths of individual algorithms while mitigating their respective limitations. An elite information exchange mechanism facilitates knowledge transfer by randomly reassigning elite individuals across subpopulations at fixed iteration intervals. Additionally, global optimization strategies including differential evolution (DE), Simulated Annealing (SA), Local Search (LS), and time of arrival (TOA) position adjustment are integrated to balance exploration and exploitation, thereby enhancing convergence accuracy and the ability to escape local optima. Evaluated on the CEC2017 benchmark suite and real-world engineering problems, the HOA demonstrates superior performance in convergence speed, accuracy, and robustness compared to single-algorithm approaches—notably, HOA ranks 1st in 30-dimensional CEC2017 functions. By effectively integrating multiple optimization strategies, the HOA provides an effective and reliable solution to complex optimization challenges. Full article

Driven by the surging global demand for crude oil and its byproducts, liquid tanker vessels have undergone a marked shift toward ultra-large dimensions. This growth, while enhancing transport capacity, has also intensified congestion across many liquid terminals. As the Dead Weight Tonnage (DWT) of vessels rises, so does their draft, often requiring tide-dependent navigation for safe entry into ports. To address the resulting operational complexities, this study investigates the coordinated scheduling of three critical resources—channels, tugboats, and berths—at liquid terminals. A novel optimization framework, termed the Channel-Tugboat-Berth-Tide (CUBT) model, is proposed. The primary objective is to minimize the total operational cost over a planning horizon, accounting for anchorage waiting time, channel occupancy, tugboat utilization, and penalties from delayed departures. To solve this model efficiently, we adopt an enhanced variant of the Logistic-Hybrid-Adaptive Black Widow Optimization Algorithm (LHA-BWOA), incorporating Logistic-Sine-Cosine Chaotic Map (LSC-CM) initialization, hybrid reproduction mechanisms, and dynamic parameter adaptation. A series of case studies involving varying planning cycles are conducted to validate the model’s practical viability. Furthermore, sensitivity analyses are performed to evaluate the impact of channel choice, tugboat allocation, and vessel waiting time. Results indicate that tugboat operations account for the largest portion of the total costs. Notably, while two-way channels result in lower direct channel costs, they do not always yield the lowest overall expenditure. Among the service strategies evaluated, the First-In–First-Out (FIFO) rule is found to be the most cost-efficient. The results offer practical guidance for port improving the operational efficiency of liquid terminals under complex tidal and resource constraints. Full article

Aiming to solve the bottlenecks of the traditional Grey Wolf Optimizer (GWO) in UAV three-dimensional path planning—including uneven initial population distribution, slow convergence speed, and proneness to local optima—this paper proposes an improved algorithm (CPS-GWO) that integrates the Kent chaotic map with Particle Swarm Optimization (PSO) to mitigate these limitations. To enhance the diversity of the initial population, the Kent chaotic map is employed, as ergodicity ensures the symmetric distribution of the initial population, expanding search coverage; meanwhile, a nonlinear adaptive strategy is adopted to dynamically adjust the control parameter a, enabling flexible search behaviour. Furthermore, the grey wolf position update rule is optimized by incorporating the inertia weight and social learning mechanism of PSO, which strengthens the algorithm’s ability to balance exploration and exploitation. Additionally, a multi-objective comprehensive cost function is constructed, encompassing path length, collision penalty, height constraints, and path smoothness, to fully align with the practical demands of UAV path planning. To validate the performance of CPS-GWO, a three-dimensional urban simulation environment is established on the MATLAB platform. Comparative experiments with different population sizes are conducted, with the traditional GWO as the benchmark. The results demonstrate that, compared with the original GWO, (1) the average fitness of CPS-GWO is significantly reduced by 31.30–38.53%; (2) the path length is shortened by 15.62–22.12%; (3) path smoothness is improved by 43.44–51.52%; and (4) the fitness variance is only 9.58–12.16% of that of the traditional GWO, indicating notably enhanced robustness. Consequently, the proposed CPS-GWO effectively balances global exploration and local exploitation capabilities, thereby providing a novel technical solution for efficient path planning in UAV logistics and distribution under complex urban environments, which holds important engineering application value. Full article

Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision that is inherent in all computational machines. Beyond the horizon of predictability, numerical computations accumulate errors, often undetectable. We investigate the possibility of reliable (error-free) time series of chaos. We prove that this is feasible for two well-studied isomorphic chaotic maps, namely the Tent map and the Logistic map. The generated chaotic time series have an unlimited horizon of predictability. A new linear formula for the horizon of predictability of the Analytic Computation of the Logistic map, for any given precision and acceptable error, is obtained. Reliable (error-free) time series of chaos serve as the “gold standard” for chaos applications. The practical significance of our findings include: (i) the ability to compare the performance of neural networks that predict chaotic time series; (ii) the reliability and numerical accuracy of chaotic orbit computations in encryption, maintaining high cryptographic strength; and (iii) the reliable forecasting of future prices in chaotic economic and financial models. Full article

The Red-Billed Blue Magpie Optimization (RBMO) algorithm is a metaheuristic method inspired by the foraging behavior of red-billed blue magpies. However, the conventional RBMO often suffers from premature convergence and performance degradation when solving high-dimensional constrained optimization problems due to its over-reliance on population mean vectors. To address these limitations, this study proposes an Improved Red-Billed Blue Magpie Optimization (IRBMO) algorithm through a multi-strategy fusion framework. IRBMO enhances population diversity through Logistic-Tent chaotic mapping, coordinates global and local search capabilities via a dynamic balance factor, and integrates a dual-mode perturbation mechanism that synergizes Jacobi curve strategies with Lévy flight strategies to balance exploration and exploitation. To validate IRBMO’s efficacy, comprehensive comparisons with 16 algorithms were conducted on the CEC-2017 (30D, 50D, 100D) and CEC-2022 (10D, 20D) benchmark suites. Subsequently, IRBMO was rigorously evaluated against ten additional competing algorithms across four constrained engineering design problems to validate its practical effectiveness and robustness in real-world optimization scenarios. Finally, IRBMO was applied to 3D UAV path planning, successfully avoiding hazardous zones while outperforming 15 alternative algorithms. Experimental results confirm that IRBMO exhibits statistically significant improvements in robustness, convergence accuracy, and speed compared to classical RBMO and other peers, offering an efficient solution for complex optimization challenges. Full article

The large-scale integration of Distributed Generation (DG) poses significant challenges to the stable operation of distribution networks. It is particularly crucial to explore the power supply restoration capability of Soft Open Points with Energy Storage (E-SOP) and enhance power supply dependability. To address this issue, this paper proposes a power supply restoration method for flexible interconnected distribution networks (FIDN) considering wind–solar uncertainty. First, the control strategy and mathematical model of E-SOP are analyzed. Second, a wind–solar uncertainty model is established, with the weighted sum of maximizing restored node active load and minimizing power loss as the objective function, followed by a detailed analysis of constraints. Then, chance constraints are introduced to transform the proposed problem into a Mixed-Integer Second-Order Cone Programming (MISOCP) model. The Dung Beetle Optimization (DBO) algorithm is improved through logistic chaotic mapping, golden sine strategy, and position update coefficient to construct a distribution network power supply restoration model. Finally, simulations are conducted on the IEEE 33-node system using a hybrid optimization algorithm that combines Improved Dung Beetle Optimization (IDBO) with MISOCP. The simulation results demonstrate that the proposed method can effectively maximize power supply restoration in outage areas, further enhance the self-healing capability of distribution networks, and verify the feasibility of the method. Full article

Image clustering analysis faces the curse of dimensionality, distance concentration, multimodal landscapes, and rapid diversity loss that challenge meta-heuristics. Meanwhile, the standard Crayfish Optimization Algorithm (COA) has shown notable potential but often suffers from poor convergence speed and premature convergence. To address these issues, this paper introduces a Chaos-initiated and Adaptive Multi-guide Control-based COA (CMCOA). First, a chaotic initialization strategy is employed by explicitly exploiting the reflection symmetry of logistic-map chaotic sequences together with opposition-based learning, which enhances population diversity and facilitates early exploration of promising regions. Second, a fitness-feedback adaptive parameter control mechanism, motivated by the general idea of the MIT rule, is integrated to dynamically balance exploration and exploitation, thereby accelerating convergence while mitigating premature stagnation. Furthermore, a multi-guide stage-switching strategy is designed to avoid being trapped in local optima by promoting adaptive transitions between exploration phases and exploitation phases. CMCOA is benchmarked against competing algorithms on ten challenging test functions drawn from CEC2017, CEC2019, CEC2020, and CEC2022 suites. We also conducted multispectral clustering, where class differences often lie in reflectance magnitude; we adopt Euclidean distance for its efficiency and suitability in capturing such variations. Compared with other algorithms, CMCOA shows faster convergence, higher accuracy, and improved robustness, revealing its broader potential for image analysis tasks. Full article

This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used as a scalar reward to guide exploration toward regions with high sensitivity to initial conditions. Under matched evaluation budgets, the approach reduces redundant simulations relative to grid scans and accelerates discovery of parameter sets with large positive LLE. Experiments report learning curves, parameter heatmaps, and representative phase portraits that are consistent with Lyapunov-based assessments. Q-learning typically reaches high-reward regions earlier, whereas SARSA shows smoother improvements over iterations. Several evaluated systems possess equation-level symmetry—most notably sign-reversal invariance in the Lorenz system and Chua’s circuit models and a coordinate-wise sign pattern in the Lorenz–Haken equations—which manifests as mirror attractors and paired high-reward regions; one representative is reported for each symmetric pair. Overall, Lyapunov-guided reinforcement learning serves as a practical complement to grid and random search for chaos identification in both discrete maps and continuous flows, and transfers with minimal changes to higher-dimensional settings. The framework provides an efficient method for identifying high-complexity parameters for applications in chaos-based cryptography and for assessing stability boundaries in engineering design. Full article

The sine cosine algorithm (SCA) is a population-based stochastic optimization method that updates the position of each search agent using the oscillating properties of the sine and cosine functions to balance exploration and exploitation. While flexible and widely applied, the SCA often suffers from premature convergence and getting trapped in local optima due to weak exploration–exploitation balance. To overcome these issues, this study proposes a multi-faceted SCA (MFSCA) incorporating several improvements. The initial population is generated using dynamic opposition (DO) to increase diversity and global search capability. Chaotic logistic maps generate random coefficients to enhance exploration, while an elite-learning strategy allows agents to learn from multiple top-performing solutions. Adaptive parameters, including inertia weight, jumping rate, and local search strength, are applied to guide the search more effectively. In addition, Lévy flights and adaptive Gaussian local search with elitist selection strengthen exploration and exploitation, while reinitialization of stagnating agents maintains diversity. The developed MFSCA was tested against 23 benchmark optimization functions and assessed using the Wilcoxon rank-sum and Friedman rank tests. Results showed that MFSCA outperformed the original SCA and other variants. To further validate its applicability, this study developed a fuzzy c-means MFSCA-based adaptive neuro-fuzzy inference system to forecast energy consumption in student residences, using student apartments at a university in South Africa as a case study. The MFSCA-ANFIS achieved superior performance with respect to RMSE (1.9374), MAD (1.5483), MAE (1.5457), CVRMSE (42.8463), and SD (1.9373). These results highlight MFSCA’s effectiveness as a robust optimizer for both general optimization tasks and energy management applications. Full article

To capture bus passenger flow fluctuations and address the problems of slow convergence and high error in machine learning parameter optimization, this paper develops an improved Whale Optimization Algorithm (IWOA) integrated with a Bidirectional Gated Recurrent Unit (BiGRU). First, a Logistic–Tent chaotic mapping is introduced to generate a diverse and high-quality initial population. Second, a hybrid mechanism combining elite opposition-based learning and Cauchy mutation enhances population diversity and reduces premature convergence. Third, a cosine-based adaptive convergence factor and inertia weight strategy improve the balance between global exploration and local exploitation. Based on the correlation analysis between bus passenger flow and weather condition data in Harbin, and combined with the fluctuation characteristics of bus passenger flow, the data were divided into windows with a 7-day weekly cycle and processed by fuzzy information granulation to obtain three groups of fuzzy granulated window data, namely LOW, R, and UP, representing the fluctuation trend and spatial characteristics of bus passenger flow. The IWOA was employed to optimize and solve parameters such as the hidden layer weights and bias vectors of the BiGRU, thereby constructing a bus passenger flow fluctuation trend and spatial prediction model based on FIG-IWOA-BiGRU. Simulation experiments with 21 benchmark functions and real bus data verified its effectiveness. Results show that IWOA significantly improves optimization accuracy and convergence speed. For bus passenger flow forecasting, the average MAE, RMSE, and MAPE of LOW, R, and UP data are 2915, 3075, and 8.1%, representing improvements over existing classical models. The findings provide reliable decision support for bus scheduling and passenger travel planning. Full article