Search Results (149)

Aiming at the problems of uneven population initialization distribution, easy trapping in local optima, unbalanced exploration and exploitation capabilities, insufficient optimization accuracy and convergence speed of the original Greater Cane Rat Algorithm (GCRA), this paper proposes a Chaos-Integrated Difference-Enhanced Greater Cane Rat Algorithm (CEGCRA). Firstly, the algorithm adopts the piecewise chaotic map to generate the initial population, which effectively improves the uniformity and diversity of the population and reduces the risk of premature convergence. Secondly, an accumulated difference foraging strategy is designed to integrate the position and fitness difference information between individuals and the optimal individual, dynamically adjust the search direction and step size, and realize the adaptive balance between global exploration and local exploitation capabilities. Finally, the dynamic switching mechanism between the exploration and exploitation stages of the algorithm is improved, and the boundary constraint handling strategy is optimized to further enhance the algorithm stability. To verify the performance of the CEGCRA, comparative experiments were carried out on the CEC2014 and CEC2020 benchmark test suites. The results show that compared with the original GCRA, the optimal fitness value of the CEGCRA is reduced by an average of 35.3%, the standard deviation is reduced by an average of 22.7%, and the convergence speed is increased by an average of 28.9%. In two typical engineering constrained optimization problems, namely, welded beam design and cantilever beam design, the cost of the welded beam solved by the CEGCRA is 12.5% lower than that of the original GCRA and 8.7% lower than that of the PSO algorithm; the weight of the cantilever beam is 0.012% lower than that of the original GCRA and 0.008% lower than that of the GA, with a constraint satisfaction rate of 100%. The experimental results fully prove that the CEGCRA is superior to the original GCRA and seven comparison algorithms such as PSO, DE and SSA in terms of optimization accuracy, convergence speed, robustness and constraint handling ability and can effectively solve complex engineering optimization problems with high dimensionality, nonlinearity and multiple constraints. Full article

Particle swarm optimization (PSO) is an optimizing method that is based on the theory of swarm intelligence. PSO is an effective algorithm that is used to search in a parallel manner compared to other methods. However, PSO has a tendency towards local optima when tackling complex multimodal optimization problems. It also has the disadvantages of slow convergence process and poor stability in the latter evolutionary period. In view of these demerits, a hybrid PSO method based on chaotic opposition-based initialization and an adaptive learning strategy is presented in this work (abbreviated as ACMPSO). First, the chaos initialization and opposition-based learning (OBL) are employed to produce high-quality initial particles in the feasible region, which is able to improve the quality of the initial solutions. Second, the logistic mapping embedded inertia weight is formulated to better trade off the global and local search process. Third, the global optimal particle is regulated by an exclusive velocity and position updating strategy whereas the rest particles are adjusted by the standard updating mechanism so as to prevent particles from premature convergence. Furthermore, an adaptive position update paradigm is developed to finely regulate the global exploration and local exploitation. Finally, conducted experiments on CEC’13 and CEC’22 reveal that the proposed ACMPSO outperforms several other advanced PSO variants regarding their convergence rate and accuracy. Alternatively, to further illustrate the effect of ACMPSO, we have applied it to two real-world problems, and simulation results ascertain its effectiveness and robustness. Full article

Particle swarm optimization is a metaheuristic optimization algorithm that boasts advantages such as fast convergence speed, fewer tunable parameters, and a simple search mechanism. However, it suffers from premature convergence and insufficient later-stage exploitation, limiting its performance on multimodal and high-dimensional problems. In light of this, this paper proposes a Chaos-based Differential Mutation Particle Swarm Optimization (CDMPSO) algorithm to address these limitations. The algorithm employs four synergistic strategies: cubic chaotic mapping with inverse learning for population initialization; adaptive inertia weight to balance exploration and exploitation; convex lens imaging inverse learning to escape local optima; and random differential mutation to maintain population diversity. Ablation experiments validate the contribution of each strategy, with adaptive weight being the most significant. Comparative experiments demonstrate that CDMPSO achieves an average ranking of 1.00, outperforming standard PSO, CPSO (Constriction Particle Swarm Optimization), ACPSO (Adaptive Chaotic Particle Swarm Optimization), and HPSOALS (Hybrid Particle Swarm Optimization with Adaptive Learning Strategy). On the unimodal function f₁, it attains ultra-high precision of 7.07 × 10⁻²⁴⁸, and on the multimodal function f₉, it uniquely converges to the theoretical optimum of zero. The results demonstrate that CDMPSO possesses excellent convergence precision, global search capability, and robustness, providing an effective solution for complex engineering optimization problems. 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

Mobile robots play an important role in promoting industrial intelligence and modernization. However, the existing obstacle avoidance path planning algorithms for mobile robots have poor stability and applicability. To this end, this paper proposes a path planning scheme for mobile robots based on ISH5N1 algorithm. Firstly, aiming at the problem of low initial population quality of SH5N1 algorithm, Tent chaos initialization strategy was proposed, which increased the diversity of the population, improved the quality of initial solution, and laid a foundation for subsequent deeper search. Secondly, by fusing the multi-source direction vectors and applying them to the position update, the solution accuracy of the algorithm was improved and the convergence speed of the algorithm was accelerated. Then, the mutation step size control strategy enhanced by Logistic chaos was used to enhance the ability of the algorithm to jump out of local optimum. Finally, the attenuation coefficient of inertia weight is optimized by combining cosine annealing strategy, which strengthens the ability of the algorithm to balance global search and local development. The ISH5N1 algorithm was compared with several commonly used intelligent optimization algorithms on benchmark functions and grid maps with different complexities. The results show that ISH5N1 algorithm shows good stability, higher solution accuracy and faster convergence speed in solving most benchmark functions. In the path planning experiment, the ISH5N1 algorithm can plan a shorter and smoother path, which further proves that the algorithm has good optimization ability and robustness. Finally, ablation experiments were carried out on a 20 × 20 grid map to verify the effectiveness of each optimization strategy. Full article

Dynamical systems with chaotic attractors are an interesting topic not only for their complex behavior but also due to their potential applications. Along with the chaos, systems can also present interesting features such as multistability, global basin of attractions, entangled basins of attraction, etc. The existence of chaotic systems with multistable hidden attractors increases complexity but also the number of potential applications. Several systems with hidden attractors have already been found by numerical search; however, it is usually not possible to substantially modify their equations or attractor geometry. In this study, an approach to generate multistable systems with a class of hidden attractors is proposed. The approach allows for the control of the amplitude and frequency of the chaotic signals of the different attractors as well as their location in the space by preserving a simple matrix form in the vector field. Particular cases with mono-stability and multistability are shown. Also, chaotic signals obtained through the approach are used in a pseudorandom number generator to obtain binary sequences which are tested under the Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications provided by the National Institute of Standards and Technology (NIST). Full article

The “Great Bend” of the Yellow River, a region characterized by the tension between ecological fragility and economic growth, faces dual pressures from physical water scarcity and stringent policy redlines. Traditional allocation models often struggle to operationalize the rigid boundaries of the “Four Determinants” policy (water determines production, city, land, and population) and suffer from computational inefficiencies under high-dimensional non-linear constraints. To address these issues, this study proposes a policy-driven “Four-Determinant, Three-Multiple” (FDTM) rigid constraint optimization framework. First, a multi-level boundary system is constructed based on water-carrying capacity, thereby converting the policy into dynamic interaction constraints among industry, city, land, and population. Second, to overcome potential computational bottlenecks, an Improved Adaptive Cheetah Optimization Algorithm (IA-COA) is developed. By integrating chaos mapping initialization and an adaptive penalty function mechanism, the algorithm exhibits enhanced global search capability and convergence speed within confined search spaces. Using Baotou City as a representative case study, the model simulates scenarios for the 2030 planning horizon. The results indicate that (i) the integration of rigid constraints effectively identifies development bottlenecks, capping projected water demand at 1.075 × 10⁹ m³ and preventing ecological overdraft despite a 5.15% theoretical deficit; (ii) through IA-COA optimization, a balanced trade-off between economic benefits and ecological security is achieved. The comprehensive water supply guarantee rate increased to over 90%, and satisfaction levels for all sectors exceeded 0.8, demonstrating improved allocation efficiency. This study elucidates the marginal transformation mechanism of the water–economy–ecology nexus under rigid constraints and demonstrates the applicability of IA-COA in solving complex basin allocation problems constrained by strict boundaries. It provides a methodological reference for sustainable water management in similar resource-stressed arid regions. Full article

The rapid growth of Internet of Things (IoT) devices and the emergence of 5G/6G networks have created major challenges in secure and reliable data transmission. Traditional cryptographic algorithms, while robust, often suffer from high computational complexity and latency, making them less suitable for large-scale, real-time applications. This paper proposes a chaos-based encryption framework that uses the Sprott chaotic oscillator to generate secure and unpredictable signals for encryption. To achieve accurate synchronization between the transmitter and the receiver, two bio-inspired metaheuristic algorithms—the Pachycondyla Apicalis Algorithm (API) and the Penguin Search Optimization Algorithm (PeSOA)—are employed to identify the optimal control parameters of the Sprott system. This optimization improves synchronization accuracy and reduces computational overhead. Simulation results show that PeSOA-based synchronization outperforms API in convergence speed and Root Mean Square Error (RMSE). The proposed framework provides robust, scalable, and low-latency encryption for IoT and 5G/6G networks, where massive connectivity and real-time data protection are essential. Full article

In order to solve the problems of slow convergence speed, insufficient accuracy, and easily falling into the local optimum of the traditional whale optimization algorithm (WOA) in mobile robot path planning, an improved whale optimization algorithm (IWOA) combined with the bird navigation mechanism was proposed. Specific improvement measures include using logical chaos mapping to initialize the population to enhance the randomness and diversity of the initial solution, designing a nonlinear convergence factor to prevent the algorithm from prematurely entering the shrinking surround phase and extending the global search time, introducing an adaptive spiral shape constant to dynamically adjust the search range to balance exploration and development capabilities, optimizing the individual update strategy in combination with the bird navigation mechanism, and optimizing the algorithm through companion position information, thereby improving the stability and convergence speed of the algorithm. Path planning simulations were performed on 30 × 30 and 50 × 50 grid maps. The results show that compared with WOA, MSWOA, and GA, in the 30 × 30 map, the path length of IWOA is shortened by 3.23%, 7.16%, and 6.49%, respectively; in the 50 × 50 map, the path length is shortened by 4.88%, 4.53%, and 28.37%, respectively. This study shows that IWOA has significant advantages in the accuracy and efficiency of path planning, which verifies its feasibility and superiority. Full article

This study introduces a novel robotic control paradigm, “chaos redirection,” which utilizes a single chaotic Hopfield Neural Network (HNN). We introduce “false attractors” synthetic trajectories created by applying controlled temporal shifts to the HNN’s state variables. This method allows a single chaotic source to be sculpted into distinct, task-specific behaviors for autonomous robots. We apply this framework to three applications: area cleaning, systematic search, and security patrol. Quantitative, statistically validated analysis demonstrates the successful generation of functionally distinct behaviors, including high-frequency, confined re-visitation for security patrols; maximized exploratory efficiency for search tasks; and high-entropy, non-repetitive paths for thorough cleaning. Our findings establish this as a robust and computationally efficient framework for applications requiring unpredictable, yet structured, behavior. Full article

Maximum power point tracking (MPPT) control is a key technology for increasing the power generation of photovoltaic arrays under varying light and temperature conditions. Traditional perturb and observe methods and incremental conductance methods can achieve good tracking performance for single-peak characteristics. However, under complex conditions such as partial shading or dust accumulation, the power-voltage curve of a photovoltaic array exhibits multi-peak characteristics. In such cases, traditional methods may get trapped in local optima, preventing the photovoltaic array from operating at the maximum power point. Swarm intelligence algorithms perform well when solving multi-extremum functions and can be used for MPPT control of photovoltaic arrays in complex environments. Therefore, this paper focuses on the fireworks algorithm (FWA). To improve the computational speed and global optimization capability of the FWA, the characteristics of each stage of the algorithm are analyzed, a comprehensive improved fireworks algorithm (CIFWA) is proposed, and it is applied to the MPPT control of photovoltaic systems. The improved algorithm introduces an adaptive resource allocation and selection strategy with community inheritance features and applies tent chaos mapping to the algorithm’s explosion behavior. Multiple sets of test functions are used to compare the performance metrics of the optimization algorithm, demonstrating improvements in computational speed and global search capability of CIFWA. Finally, a control strategy for the MPPT of photovoltaic arrays based on CIFWA is presented, and a simulation experimental platform is built to analyze and verify the control performance. Full article

Against the backdrop of the rapid development of the manufacturing industry, online monitoring of tool wear status is of great significance for enhancing the reliability and intelligence of CNC machine tools. This paper presents an intelligent tool wear condition monitoring model (CPSO-CNN-BiLSTM-AM) that integrates the improved Chaotic Particle Swarm Optimization (CPSO) algorithm with the CNN-BiLSTM network incorporating an attention mechanism. The aim is to extract the global features of long-sequence monitoring data and the local features of multi-spatial data. Chaos theory and the mutation mechanism are introduced into the CPSO algorithm, which enhances the algorithm’s global search ability and its capacity to escape local optimal solutions, enabling more efficient optimization of the hyperparameters of the CNN-BiLSTM network. The CNN-BiLSTM network with the introduced attention mechanism can more accurately extract the spatial features of wear signals and the dependencies of time-series signals, and focus on the key features in wear signals. The study utilized the IEEE PHM2010 Challenge dataset, extracted wear features through time-domain, frequency-domain, and time-frequency domain methods, and divided the training set and validation set using cross-validation. The results show that in the public PHM2010 dataset, the average MAE of the model for tools C1, C4, and C6 is 0.83 μm, 1.01 μm, and 1.34 μm, respectively; the RMSE is 0.99 μm, 1.79 μm, and 0.88 μm, respectively; and the MAPE is 0.95%, 1.41%, and 1.01%, respectively. In the self-built dataset, the average MAE for tools A1, A2, and A3 is 1.35 μm, 1.19 μm, and 1.83 μm, respectively; the RMSE is 1.41 μm, 1.98 μm, and 1.90 μm, respectively; and the MAPE is 1.67%, 1.55%, and 1.81%, respectively. All indicators are superior to those of comparative models such as LSTM and PSO-CNN. The proposed model can effectively capture changes in different stages of tool wear, providing a more accurate solution for tool wear condition monitoring. Full article

WSN coverage optimization faces two key challenges: firstly, traditional algorithms are prone to getting stuck in local optima, leading to ‘coverage holes’ in node deployment; Secondly, in dynamic scenarios (such as imbalanced energy consumption of nodes), the convergence speed of the algorithm is slow, making it difficult to maintain high coverage in real time. This study focuses on the coverage optimization problem of wireless sensor networks (WSNs) and proposes improvements to the Flamingo Search Optimization Algorithm (FSA). Specifically, the algorithm is enhanced by integrating the elite opposition-based learning strategy and the stagewise step-size control strategy, which significantly improves its overall performance. Additionally, the introduction of a cosine variation factor combined with the stagewise step-size control strategy enables the algorithm to effectively break free from local optima constraints in the later stages of iteration. The improved Flamingo Algorithm is applied to optimize the deployment strategy of sensing nodes, thereby enhancing the coverage rate of the sensor network. First, an appropriate number of sensing nodes is selected according to the target area, and the population is initialized using a chaotic sequence. Subsequently, the improved Flamingo Algorithm is adopted to optimize and solve the coverage model, with the coverage rate as the fitness function and the coordinates of all randomly distributed sensing nodes as the initial foraging positions. Next, a search for candidate foraging sources is performed to obtain the coordinates of sensing nodes with higher fitness; the coordinate components of these candidate foraging sources are further optimized through chaos theory to derive the foraging source with the highest fitness. Finally, the coordinates of the optimal foraging source are output, which correspond to the coordinate values of all sensing nodes in the target area. Experimental results show that after 100 and 200 iterations, the coverage rate of the improved Flamingo Search Optimization Algorithm is 7.48% and 5.68% higher than that of the original FSA, respectively. Furthermore, the findings indicate that, by properly configuring the Flamingo population size and the number of iterations, the improved algorithm achieves a higher coverage rate compared to other benchmark algorithms. 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

In the pursuit of sustainable development, optimizing water resources management while maintaining ecological balance is crucial. This study introduces a Chaos-enhanced Harris Hawks Optimizer (CEHHO) aimed at optimizing natural flow patterns in cascade reservoirs. First, an ecological scheduling model considering ensuring guaranteed output is established based on the similarity of ecological flows. Subsequently, the CEHHO algorithm is proposed, which uses tilted skew chaos mapping for population initialization, improving the quality of the initial population. In the exploration phase, an adaptive strategy enhances the efficiency of group search algorithms, enabling effective navigation of the complex solution space. A random difference mutation strategy, combined with the Q-learning algorithm, mitigates premature convergence and maintains algorithmic diversity. Comparative analysis with the existing technology under different typical hydrological frequency shows that the search accuracy and convergence efficiency of the proposed method are significantly improved. Under the guaranteed output limit of 1000 MW, the proposed method enhances the optimal, median, mean, and worst values by 293.92, 493.23, 422.14, and 381.15, respectively, compared to the HHO. Furthermore, the results of the multi-purpose guaranteed output scenario highlight the superior detection and exploitation capabilities of this algorithm. These findings highlight the great potential of the proposed method for practical engineering applications, providing a reliable tool for optimizing water resources management while maintaining ecological balance. Full article