Search Results (566)

The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the $(G^{\prime }/G)$ expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article

In response to the low efficiency of collaborative processing of sewing machine cases at the part level in network collaborative manufacturing, this paper proposes a sewing machine cases manufacturing service composition optimization method based on an improved multi-objective artificial hummingbird algorithm. The structure and production process of sewing machine cases are analyzed; a framework for service composition optimization in the sewing machine cases manufacturing service platform is established; the required manufacturing resource service composition is determined; and a dual-objective service composition optimization mathematical model that considers Quality of Service (QoS) indicators and flexibility indicators is constructed. Opposition-based learning strategies, roulette wheel selection strategies, and improved differential evolution strategies are embedded in the multi-objective artificial hummingbird algorithm, and the improved artificial hummingbird algorithm (ORAHA_DE) is used to solve the sewing machine cases manufacturing service composition optimization model. The experimental results show the effectiveness and superiority of this composition optimization method in solving the sewing machine cases manufacturing composition optimization problem while avoiding entrapment in a local optimum during the solution process, thereby achieving the composition optimization of sewing machine cases collaborative manufacturing services. Full article

The intelligent upgrade of heating systems faces the challenge of accurately identifying high-dimensional pipe-network resistance coefficients; difficulties in accomplishing this can lead to hydraulic imbalance and redundant energy consumption. To address the limitations of traditional Differential Evolution (DE) algorithms under high-dimensional operating conditions, this paper proposes an Improved Differential Evolution Algorithm (SDEIA) incorporating chaotic mapping, adaptive mutation and crossover strategies, and an immune mechanism. Furthermore, a multi-constrained identification model is constructed based on Kirchhoff’s laws. Validation with actual engineering data demonstrates that the proposed method achieves a lower average relative error in resistance coefficients and exhibits a more concentrated error distribution. SDEIA provides a high-precision tool for multi-heat-source networking and dynamic regulation in heating systems, facilitating low-carbon and intelligent upgrades. Full article

In modern vehicles, Autonomous Driving Systems (ADSs) are designed to operate partially or fully without human intervention. The ADS pipeline comprises multiple layers, including sensors, perception, localization, mapping, path planning, and control. The Robot Operating System (ROS) is a widely adopted framework that supports the modular development and integration of these layers. Among them, the path-planning and control layers remain particularly challenging due to several limitations. Classical path planners often struggle with non-smooth trajectories and high computational demands. Meta-heuristic optimization algorithms have demonstrated strong theoretical potential in path planning; however, they are rarely implemented in real-time ROS-based systems due to integration challenges. Similarly, traditional PID controllers require manual tuning and are unable to adapt to system disturbances. This paper proposes a ROS-based ADS architecture composed of eight integrated nodes, designed to address these limitations. The path-planning node leverages a meta-heuristic optimization framework with a cost function that evaluates path feasibility using occupancy grids from the Hector SLAM and obstacle clusters detected through the DBSCAN algorithm. A dynamic goal-allocation strategy is introduced based on the LiDAR range and spatial boundaries to enhance planning flexibility. In the control layer, a modified Pure Pursuit algorithm is employed to translate target positions into velocity commands based on the drift angle. Additionally, an adaptive PID controller is tuned in real time using the Differential Evolution (DE) algorithm, ensuring robust speed regulation in the presence of external disturbances. The proposed system is practically validated on a four-wheel differential drive robot across six scenarios. Experimental results demonstrate that the proposed planner significantly outperforms state-of-the-art methods, ranking first in the Friedman test with a significance level less than 0.05, confirming the effectiveness of the proposed architecture. Full article

To address the growing demand for industrial software in the digital transformation of small and medium-sized enterprises (SMEs) in the manufacturing sector, and to ensure the stable integration and operation of multi-source heterogeneous industrial software under complex conditions—such as heterogeneous compatibility, component dependencies, and uncertainty disturbances—this study established a comprehensive evaluation index system for service composition and optimal selection (SCOS). The system incorporated key criteria including service time, service cost, service reputation, service delivery quality, and availability. Based on this, a bi-objective SCOS model was established with the goal of maximizing both quality of service (QoS) and availability. To efficiently solve the proposed model, a hybrid enhanced multi-objective Gray Wolf Optimizer (HEMOGWO) was developed. This algorithm integrated Tent chaotic mapping and a Levy flight-enhanced differential evolution (DE) strategy. Extensive experiments were conducted, including performance evaluation on 17 benchmark functions and case studies involving nine industrial software integration scenarios of varying scales. Comparative results against state-of-the-art, multi-objective, optimization algorithms—such as MOGWO, MOEA/D_DE, MOPSO, and NSGA-III—demonstrate the effectiveness and feasibility of the proposed approach. Full article

The performance of meta-heuristic algorithms on optimisation problems depend on the values of control parameters. These parameters greatly influence the behaviour of algorithms and affect the quality of the solutions. In order to optimise an algorithm for a specific problem set, a structured approach is followed to carefully select the appropriate control parameters. This approach is called control parameter tuning. Most existing tuning approaches focus on tuning an algorithm based on only one performance objective, such as accuracy or convergence speed. However, these objectives often work against each other, and improving the algorithm based on one objective can worsen the performance based on another objective. For example, obtaining a more accurate solution generally requires the algorithm to run for a longer time. The goal of this research is to develop a tuning approach that takes multiple performance objectives into account when tuning the control parameters of a meta-heuristic. The result of the tuning algorithm presents the experimenter with multiple values for control parameters, each representing different trade-offs between the various objectives. Experimental results demonstrate that M-race successfully discovered between 9 and 15 non-dominated parameter configurations across benchmark functions for both particle swarm optimisation (PSO) and differential evolution (DE) algorithms. These non-dominated parameter configurations represent balances among the tuning objectives used. Full article

This study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under consideration has a track-to-wheelbase ratio of 0.5 and an inner wheel steering angle of 70 degrees. The mechanisms synthesized include the Ackermann steering mechanism and two variants (Type I and Type II) of the Watt-I six-bar steering mechanisms, also known as central-lever steering mechanisms. To ensure accurate steering and minimize tire wear during cornering, adherence to the Ackermann steering condition is enforced. The objective function combines the mean squared structural error at selected steering positions with a penalty term for violations of the Grashoff inequality constraint. Each optimization run involved 100 or 200 iterations, with numerical experiments repeated 100 times to ensure robustness. Kinematic simulations were conducted in ADAMS v2015 to visualize and validate the synthesized mechanisms. Performance was evaluated based on maximum structural error (steering accuracy) and mechanical advantage (transmission efficiency). The results indicate that the optimized Watt-I six-bar steering mechanisms outperform the Ackermann mechanism in terms of steering accuracy. Among the Watt-I variants, the Type II designs demonstrated superior performance and convergence precision compared to the Type I designs, as well as improved results compared to prior studies. Additionally, the optimal Type I-2 and Type II-2 mechanisms consist of two symmetric Grashof mechanisms, can be classified as non-Ackermann-like steering mechanisms. Both optimization methods proved easy to implement and showed reliable, efficient convergence. The DE-gr algorithm exhibited slightly superior overall performance, achieving optimal solutions in seven cases compared to four for the IPSO method. Full article

Multimodal optimization problems represent a category of complex optimization challenges characterized by the presence of multiple global optimal solutions. Addressing these problems requires an algorithm that can not only efficiently locate and identify as many peaks as possible but also pinpoint the precise coordinates of these peaks with a high degree of accuracy. Evolutionary algorithms are frequently employed to tackle multimodal optimization problems, and their heuristic approach often leads to the high-probability discarding of suboptimal individuals generated during the evolutionary process. If all individuals are utilized to depict the contours of the problem space, the contours will be depicted increasingly accurately as the algorithm iterates. By optimizing in this way, the results will become increasingly accurate. Therefore, in this paper, a topographical-contour-based differential evolution (TCDE) method is introduced to address multimodal optimization problems. The method initially applies DE for terrain exploration, followed by the construction of terrain contours to obtain more accurate landform representation, and it finally employs a niching search to investigate the landforms for optimal peaks. Experiments were conducted on a set of eight widely recognized benchmark functions with 15 excellent optimization algorithms, including both DE and non-DE multimodal optimization approaches. The outcomes of these experiments conclusively demonstrate the superior performance of the TCDE algorithm over its counterparts. Full article

The Sustainable Supply Chain Network Design Problem (SSCNDP) is to determine the optimal network configuration and resource allocation that achieve the trade-off among economic, environmental, social, and resilience objectives. The Sustainable Supply Chain Network Design Problem (SSCNDP) involves determining the optimal network configuration and resource allocation that allows trade-off among economic, environmental, social, and resilience objectives. This paper addresses the SSCNDP under hybrid uncertainty, which combines objective randomness got from historical data, and subjective beliefs induced by expert judgment. Building on chance theory, we formulate a dependent-chance goal programming model that specifies target probability levels for achieving sustainability objectives and minimizes deviations from these targets using a lexicographic approach. To solve this complex optimization problem, we develop a hybrid intelligent algorithm that combines uncertain random simulation with Reinforcement Learning-enhanced Salp Swarm Optimization (RL-SSO). The proposed RL-SSO algorithm is benchmarked against standard metaheuristics—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and standard SSO, across diverse problem instances. Results show that our method consistently outperforms these techniques in both solution quality and computational efficiency. The paper concludes with managerial insights and discusses limitations and future research directions. Full article

Differential evolution (DE) has emerged as a numerical optimization technique due to its conceptual simplicity and demonstrated effectiveness across diverse problem domains. However, the algorithm’s performance remains critically dependent on appropriate control parameter settings. This paper introduces a novel diversity-based parameter adaptation (div) mechanism, generates two sets of symmetrical parameters, F and CR, adaptively first, and then dynamically selects the final parameters based on individual diversity rankings. It employs a straightforward approach to identify the more effective option from two sets of symmetrical parameters. Comprehensive experimental evaluation demonstrated that the div mechanism significantly enhanced the performance of the DE algorithm. Furthermore, by incorporating div, our enhanced algorithm exhibited superior optimization capability compared to five state-of-the-art DE variants. The results show that, among the 145 cases studied, DTDE-div outperformed others in 92 cases and underperformed in 32 cases, with the lowest performance ranking of 2.59. Consequently, DTDE-div demonstrated superior performance compared to other advanced DE variants. The results highlight the effectiveness of div in enhancing solution precision while preventing premature convergence. Full article

Straw row grouping is vital in conservation tillage for precision seeding, and accurate centerline extraction of the seedling bands enhances agricultural spraying efficiency. However, the traditional single-threshold Otsu segmentation struggles with adaptability and accuracy under complex field conditions. To overcome these issues, this study proposes an adaptive multi-threshold Otsu algorithm optimized by a Simulated Annealing-Enhanced Differential Evolution–Whale Optimization Algorithm (SADE-WOA). The method avoids premature convergence and improves population diversity by embedding the crossover mechanism of Differential Evolution (DE) into the Whale Optimization Algorithm (WOA) and introducing a vector disturbance strategy. It adaptively selects thresholds based on straw-covered image features. Combined with least-squares fitting, it suppresses noise and improves centerline continuity. The experimental results show that SADE-WOA accurately separates soil regions while preserving straw texture, achieving higher between-class variance and significantly faster convergence than the other tested algorithms. It runs at just one-tenth of the time of the Grey Wolf Optimizer and one-ninth of that of DE and requires only one-sixth to one-seventh of the time needed by DE-GWO. During centerline fitting, the mean yaw angle error (MEA) ranged from 0.34° to 0.67°, remaining well within the 5° tolerance required for agricultural navigation. The root-mean-square error (RMSE) fell between 0.37° and 0.73°, while the mean relative error (MRE) stayed below 0.2%, effectively reducing the influence of noise and improving both accuracy and robustness. Full article

In wireless sensor networks, evolutionary algorithms have emerged as pivotal tools for addressing complex localization challenges inherent in non-convex and nonlinear maximum likelihood estimation problems associated with received signal strength (RSS) measurements. While differential evolution (DE) has demonstrated notable efficacy in optimizing multimodal cost functions, conventional implementations often grapple with suboptimal convergence rates and susceptibility to local optima. To overcome these limitations, this paper proposes a novel enhancement of DE by integrating opposition-based learning (OBL) principles. The proposed method introduces an adaptive scaling factor that dynamically balances global exploration and local exploitation during the evolutionary process, coupled with a penalty-augmented cost function to effectively utilize boundary information while eliminating explicit constraint handling. Comparative evaluations against state-of-the-art techniques—including semidefinite programming, linear least squares, and simulated annealing—reveal significant improvements in both convergence speed and positioning precision. Experimental results under diverse noise conditions and network configurations further validate the robustness and superiority of the proposed approach, particularly in scenarios characterized by high environmental uncertainty or sparse anchor node deployments. Full article

With rapid advancements in the Internet of Things (IoT), Low-Power Wide-Area Networks (LPWANs) play a crucial role in expanding IoT’s capabilities while using minimal energy. Among the various LPWAN technologies, LoRaWAN (Long-Range Wide-Area Network) is particularly notable for its capacity to enable long-range, low-rate communications with low power needs. This study investigates how to optimize the placement of LoRaWAN gateways by using a combination of Particle Swarm Optimization (PSO) and Differential Evolution (DE). The approach is validated through simulations driven by HTZ to evaluate network performance in urban settings. Centered around the area of the Politehnica University of Bucharest, this research examines how different gateway placements on various floors of a building affect network coverage and packet loss. The experiment employs Adeunis Field Test Devices (FTDs) and Dragino LG308-EC25 gateways, systematically testing two spreading factors, SF7 and SF12, to assess their effectiveness in terms of signal quality and reliability. An innovative optimization algorithm, GateOpt PSODE, is introduced, which combines PSO and DE to optimize gateway placements based on real-time network performance metrics, like the Received Signal Strength Indicator (RSSI), the Signal-to-Noise Ratio (SNR), and packet loss. The findings reveal that strategically positioning gateways, especially on higher floors, significantly improves communication reliability and network efficiency, providing a solid framework for deploying LoRaWAN networks in intricate urban environments. Full article

Robotic tack welding poses challenges in path optimization due to local optimum entrapment, limited adaptability, and high-dimensional complexity. To overcome these challenges, a Lévy flight-enhanced improved whale optimization algorithm (LF-IWOA) was developed. The algorithm combines elite opposition-based learning (EOBL), differential evolution (DE), and Lévy flight (LF) to improve global exploration capability, increase population diversity, and improve convergence. Additionally, a dynamic trajectory optimization model is designed to consider joint-level constraints, including velocity, acceleration, and jerk. The performance of LF-IWOA was evaluated using two industrial workpieces with varying welding point distributions. Comparative experiments with metaheuristic algorithms, such as the genetic algorithm (GA), WOA and other recent nature-inspired methods, show that LF-IWOA consistently achieves shorter paths and faster convergence. For Workpiece 1, the algorithm reduces the welding path by up to 25.53% compared to the genetic algorithm, with an average reduction of 14.82% across benchmarks. For Workpiece 2, the optimized path is 18.41% shorter than the baseline. Moreover, the dynamic trajectory optimization strategy decreases execution time by 26.83% and reduces mechanical energy consumption by 15.40% while maintaining smooth and stable joint motion. Experimental results demonstrated the effectiveness and practical applicability of the LF-IWOA in robotic welding tasks. Full article

Wind data are often cyclostationary due to cyclic variations, non-constant variance resulting from fluctuating weather conditions, and structural breaks due to transient behaviour (due to wind gusts and turbulence), resulting in unreliable wind power supply. In wavelet hybrid forecasting, wind prediction accuracy depends heavily on the decomposition level ($L$) and the wavelet filter technique selected. Hence, we examined the efficacy of wind predictions as a function of $L$and wavelet filters. In the proposed hybrid approach, differential evolution (DE) optimises the decomposition level of various wavelet filters (i.e., least asymmetric (LA), Daubechies (DB), and Morris minimum-bandwidth (MB)) using the maximal overlap discrete wavelet transform (MODWT), allowing for the decomposition of wind data into more statistically sound sub-signals. These sub-signals are used as inputs into the gated recurrent unit (GRU) to accurately capture wind speed. The final predicted values are obtained by reconciling the sub-signal predictions using multiresolution analysis (MRA) to form wavelet-MODWT-GRUs. Using wind data from three Wind Atlas South Africa (WASA) locations, Alexander Bay, Humansdorp, and Jozini, the root mean square error, mean absolute error, coefficient of determination, probability integral transform, pinball loss, and Dawid-Sebastiani showed that the MB-MODWT-GRU at $L=3$ was best across the three locations. Full article