Update Formula Research Articles

Dynamic step opposition-based learning sparrow search algorithm for UAV path planning

In this paper, aiming at the problems of large randomness, low convergence accuracy, and easy falling into local optimum in the application of sparrow search algorithm to UAV three-dimensional path planning, a dynamic step opposition-based learning sparrow search algorithm is proposed. The algorithm first uses a good point set in the population initialization phase to improve the quality of the initial solution; secondly, the piecewise dynamic step size is used to optimize the update formula of the discoverer, and the extensive search is carried out in the early stage of the iteration. In the later stage, the known area is mined as much as possible to improve the search accuracy and convergence speed of the algorithm. Then, the crazy operator is integrated to optimize the predator update formula and improve the local search ability. Finally, t-distribution opposition-based learning is used to prevent the algorithm from falling into the local optimum. In this paper, the effectiveness of the improved algorithm is verified by six test functions and applied to the three-dimensional path planning of UAVs. The experimental results show that the proposed algorithm has a faster convergence speed than the traditional algorithm, and the planned path is shorter.

Integrity management system of hydrogen pipeline based on big data mining model optimized by improved whale algorithm

ABSTRACT In order to improve the integrity management level of the hydrogen pipeline, the intelligent information management system of the hydrogen pipeline based on big data intelligent mining model is proposed. The improved whale optimization algorithm is proposed by applying the adaptive weight update formula and quantum revolving door operation. Finally, a hydrogen pipeline is selected to carry out abnormal data detection, and the running time with different nodes and different clustering algorithms optimized by different intelligent algorithms is obtained, and the results show that the proposed Gaussian clustering optimized by an improved whale optimization algorithm can effectively find out abnormal data of integrity management of hydrogen pipeline. Monitoring precision of the proposed model is improved effectively, and the running time of the proposed model is also shortened; therefore, the proposed model can be an effective means for integrity management of the hydrogen pipeline.

Optimization of Synchronous Control Parameters Based on Improved Sinusoidal Gray Wolf Algorithm

High precision control is often accompanied by many control parameters, which are interrelated and difficult to adjust directly. It is difficult to convert the system control effect directly into mathematical expression, so it is difficult to optimize it by intelligent algorithm. To solve this problem, we propose an improved sinusoidal gray wolf optimization algorithm (ISGWO). In this algorithm, a particle crossing processing mechanism based on the symmetry idea is introduced to maximize the retention of the position information of the optimal individual and improve the search accuracy of the algorithm. In addition, a differential cross-perturbation strategy is adopted to help the algorithm jump out of the local optimal solution in time, which enhances the development capability of ISGWO. Meanwhile, the position update formula with improved sinusoidal can better balance the development and exploration of ISGWO. The ISGWO algorithm is compared with three improved Gray Wolf algorithms on the CEC2017 test set as well as the synchronization controller. The experimental results show that the ISGWO algorithm has better selectivity, speed and robustness.

Adjoint-based shape optimization for compressible flow based on volume penalization method

AbstractReducing the resistance of compressible flow around a blunt body is of great interest in engineering applications, while an efficient shape optimization method for compressible flows remains far from well established, especially for high Mach numbers. To this end, a volume penalization method for simulating compressible flows past a no-slip and isothermal solid is established by introducing an artificial body force and a heat sink into the governing equations. The level-set functions are introduced as design variables, and the cost functional is defined as the total drag acting on the solid. Then, a continuous adjoint-based shape optimization algorithm for drag reduction is developed by deriving the adjoint equations, the adjoint boundary conditions, and the shape update formula. Both the forward and adjoint simulations are verified by existing studies. The results show that the relative deviations of the drag coefficients obtained in the present study from those reported in the reference studies are around 5% at most, and also a comparable drag reduction rate and also optimal shapes can be reproduced by the present optimization scheme for benchmark problems at relatively low Mach numbers considered in previous studies. Finally, the present method is applied to shape optimization of an initially two-dimensional cylinder and also a three-dimensional sphere in the transonic regime of Ma∞ = 1.2. The drag reduction of over 20% is achieved for both two-dimensional and three-dimensional cases.

LinFa-Q: Accurate Q-learning with linear function approximation

Although Q-learning has achieved remarkable success in some practical cases, it often suffers from the overestimation problem in stochastic environments, which is commonly viewed as a shortcoming of Q-learning. Overestimated values are introduced by estimations on the next state Q value, which is well-known as the maximization bias. In this paper, we propose a more accurate method for estimating the Q value by the Q value decomposition and re-evaluation with similar samples based on linear function approximation. Specifically, we reform the parameterized incremental update formula of Q-learning and also demonstrate that the new formula is equivalent to the original one. Moreover, we propose a new parameterized incremental update formula of Q-learning to address the overestimation problem and present the more accurate computing method, which can be used in problems with continuous state spaces and stochastic environments. Experimentally, when compared with Doubly Bounded Q-learning and other Q-learning based methods, the new algorithm has more than 31% improvement of performance in Mountain Car and Cart Pole. Furthermore, the algorithm is robust to the learning rate and its memory capacity. Finally, the practical applicability of our algorithm is discussed through an analysis of time consumption.

Design of a PID Controller for Microbial Fuel Cells Using Improved Particle Swarm Optimization

The microbial fuel cell (MFC) is a renewable energy technology that utilizes the oxidative decomposition processes of anaerobic microorganisms to convert the chemical energy in organic matter, such as wastewater, sediments, or other biomass, into electrical power. This technology is not only applicable to wastewater treatment but can also be used for resource recovery from various organic wastes. The MFC usually requires an external controller that allows it to operate under controlled conditions to obtain a stable output voltage. Therefore, the application of a PID controller to the MFC is proposed in this paper. The design phase for this controller involves the identification of three parameters. Although the particle swarm optimization (PSO) algorithm is an advanced optimization algorithm based on swarm intelligence, it suffers from issues such as unreasonable population initialization and slow convergence speed. Therefore, this paper proposes an improved particle swarm algorithm based on the Golden Sine Strategy (GSCPSO). Using Circle chaotic mapping to make the distribution of the initial population more uniform, and then using the Golden Sine Strategy to improve the position update formula, not only improves the convergence speed of the population but also enhances convergence precision. The GSCPSO algorithm is applied to execute the described design process. The results of the simulation show that the designed control method exhibits smaller steady-state error, overshoot, and chattering compared with sliding-mode control (SMC), backstepping control, fuzzy SMC (FSMC), PSO-PID, and CPSO-PID.

An optimal midcourse guidance method for dual pulse air-to-air missiles using linear Gauss pseudospectral model predictive control method

This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles, which is based on the framework of the linear Gauss pseudospectral model predictive control method. Firstly, a multistage optimal control problem with unspecified terminal time is formulated. Secondly, the control and terminal time update formulas are derived analytically. In contrast to previous work, the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time, which is coupled with control, state, and costate. On the assumption of small perturbation, a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time. Also, using Gauss pseudospectral collocation, error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations. Furthermore, analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control. Even with their mathematical complexity, these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters. Finally, several numerical simulations, comparisons with typical methods, and Monte Carlo simulations have been done to verify its optimality, high convergence rate, great stability and robustness.

A FDA-based multi-robot cooperation algorithm for multi-target searching in unknown environments

Target search using a swarm of robots is a classic research topic that poses challenges, particularly in conducting multi-target searching in unknown environments. Key challenges include high communication cost among robots, unknown positions of obstacles, and the presence of multiple targets. To address these challenges, we propose a novel Robotic Flow Direction Algorithm (RFDA), building upon the modified Flow Direction Algorithm (FDA) to suit the characteristics of the robot’s motion. RFDA efficiently reduces the communication cost and navigates around unknown obstacles. The algorithm also accounts for scenarios involving isolated robots. The pipeline of the proposed RFDA method is outlined as follows: (1). Learning strategy: a neighborhood information based learning strategy is adopted to enhance the FDA’s position update formula. This allows swarm robots to systematically locate the target (the lowest height) in a stepwise manner. (2). Adaptive inertia weighting: An adaptive inertia weighting mechanism is employed to maintain diversity among robots during the search and avoid premature convergence. (3). Sink-filling process: The algorithm simulates the sink-filling process and moving to the aspect slope to escape from local optima. (4). Isolated robot scenario: The case of an isolated robot (a robot without neighbors) is considered. Global optimal information is only required when the robot is isolated or undergoing the sink-filling process, thereby reducing communication costs. We not only demonstrate the probabilistic completeness of RFDA but also validate its effectiveness by comparing it with six other competing algorithms in a simulated environment. Experiments cover various aspects such as target number, population size, and environment size. Our findings indicate that RFDA outperforms other methods in terms of the number of required iterations and the full success rate. The Friedman and Wilcoxon tests further demonstrate the superiority of RFDA.

Optimal splitk-plot designs

Completely randomized designs are often infeasible due to the hard-to-change nature of one or more experimental factors. In those cases, restrictions are imposed on the order of the experimental tests. The resulting experimental designs are often split-plot or split-split-plot designs in which the levels of certain hard-to-change factors are varied only a limited number of times. In agricultural machinery optimization, the number of hard-to-change factors is so large and the available time for experimentation is so short that split-plot or split-split-plot designs are infeasible as well. The only feasible kinds of designs are generalizations of split-split-plot designs, which are referred to as splitk-designs, where k is larger than 2. The coordinate-exchange algorithm is extended to construct optimal splitk-plot designs and the added value of the algorithm is demonstrated by applying it to an experiment involving a self propelled forage harvester. The optimal design generated using the extended algorithm is substantially more efficient than the design that was actually used. Update formulas for the determinant and the inverse of the information matrix speed up the coordinate-exchange algorithm, making it feasible for large designs.

LSTA-Net framework: Pioneering intelligent diagnostics for insulating bearings under real-world complex operational conditions and its interpretability

Deep Learning has been attracting considerable attention as it can autonomously learn important signal features and has shown great potential for fault diagnosis. However, given the variability of high-power variable-frequency industrial systems, especially under unfavorable service conditions such as voltage and load fluctuations, the identification of insulated bearing faults in variable-frequency motors has become a key challenge to be addressed. Moreover, the time-varying nature of insulated bearing data poses common technical difficulties for existing models. To bridge these gaps, this research spearheaded the development of a lightweight spatial–temporal focusing framework equipped with a novel optimizer called LSTA-Net, which was designed to address the challenging problem of insulated bearing fault identification in real-world engineering scenarios. Specifically, this involves an innovative design of the Weight Reducing Recursive Unit (WDRU) strategy and an updated backpropagation formulation, which was skillfully applied to the feature extraction module of the LSTA-Net framework for the first time. Furthermore, a novel optimizer called Stochastic Newton Descent (SND) has been developed and skillfully integrated into the LSTA-Net framework with the newly derived weight update formula, providing unique insights to improve diagnostic performance. Finally, the diagnostic performance of the LSTA-Net framework was evaluated from multiple dimensions based on the same dataset, proving its superiority, generalizability, and robustness. t-SNE technique integration intuitively explains the framework’s fault characterization mining process, improving its credibility, reliability, and accuracy.

A trust-region scheme for constrained multi-objective optimization problems with superlinear convergence property

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable l ∞ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front.

A modified quasi-Newton method for uncertain multiobjective optimization problems under a finite uncertainty set

ABSTRACT In this article, a modified quasi-Newton method is developed for the robust counterpart (RC) of an uncertain multiobjective optimization problem (UMOP). Specifically, the RC of a UMOP is the minimum of an objective-wise worst-case (OWWC) type RC. To determine the descent direction for the RC, a subproblem using a common Hessian approximation is constructed. An inexact line search technique based on the Armijo technique is employed to find an appropriate step length. Furthermore, a modified version of the Davidon–Fletcher–Powell (DFP) update formula is developed for the RC. A modified quasi-Newton algorithm is built using descent direction step length, and DFP Hessian update formula. Furthermore, the convergence of the modified quasi-Newton algorithm is also discussed. Finally, the modified quasi-Newton algorithm is illustrated with a set of test problems and compared with the weighted sum method. Moreover, it is demonstrated that the algorithm is effective for both convex and non-convex problems.

A many objective based feature selection model for software defect prediction

SummaryGiven the escalating magnitude and intricacy of software systems, software measurement data often contains irrelevant and redundant features, resulting in significant resource and storage requirements for software defect prediction (SDP). Feature selection (FS) has a vital impact on the initial data preparation phase of SDP. Nonetheless, existing FS methods suffer from issues such as insignificant dimensionality reduction, low accuracy in classifying chosen optimal feature sets, and neglect of complex interactions and dependencies between defect data and features as well as between features and classes. To tackle the aforementioned problems, this paper proposes a many‐objective SDPFS (MOSDPFS) model and the binary many‐objective PSO algorithm with adaptive enhanced selection strategy (BMaOPSO‐AR2) is proposed within this paper. MOSDPFS selects F1 score, the number of features within subsets, and correlation and redundancy measures based on mutual information (MI) as optimization objectives. BMaOPSO‐AR2 constructs a binary version of MaOPSO using transfer functions specifically for binary classification. Adaptive update formulas and the introduction of the R2 indicator are employed to augment the variety and convergence of algorithm. Additionally, performance of MOSDPFS and BMaOPSO‐AR2 are tested on the NASA‐MDP and PROMISE datasets. Numerical results prove that a proposed model and algorithm effectively reduces feature count while enhancing predictive accuracy and minimizing model complexity.

Modified snake optimizer based multi-level thresholding for color image segmentation of agricultural diseases

Image segmentation is crucial for early identification and diagnosis of crop diseases in agriculture. It helps identify disease areas and characteristics, laying the groundwork for disease diagnosis and treatment. However, color image thresholding segmentation method faces challenges in finding the optimal threshold as the number of thresholds increases, which affects segmentation quality. In this paper, a modified snake optimizer (MSO) is proposed to address the color image thresholding segmentation problem using Kapur’s entropy as the objective function. MSO incorporates a dynamic adaptive parameter adjustment method. The improved global position update formula introduces guidance from the optimal individual and disturbance from random individuals, effectively achieving a balance between global and local search capabilities. A dynamic parameter adjustment method is added to accelerate convergence speed during snake movement to food. Lévy flight is introduced to the Flight mode to help the algorithm escape local extremums. A balancing strategy is implemented in the Mating mode, incorporating guidance from the optimal individual and information exchange between sub-populations, enabling balanced exploration and local exploitation capabilities. The hill-climbing jump operation for the optimal individual is added to help the algorithm overcome local stagnation. The proposed MSO is evaluated on CEC 2017 test functions and color test images, and the obtained results are compared with other segmentation methods and other intelligent optimization algorithms. The results demonstrate that MSO exhibits stable and excellent performance in both complex global optimization problems and color image thresholding segmentation problems. Finally, MSO is applied to segment rice disease images, and the results reveal significantly better segmentation performance compared to other algorithms. MSO shows great potential in solving the thresholding segmentation problem for agricultural disease images, thereby assisting in the accurate identification, diagnosis, and treatment of agricultural diseases and insect pests.

Slime mould algorithm with mechanism of leadership and self-phagocytosis for multilevel thresholding of color image

Threshold based segmentation method is widely used because of its simplicity, high efficiency and easy implementation. However, as the number of thresholds increases, the algorithm's search space also increases, increasing computational complexity, which reduces computational efficiency and segmentation accuracy. Additionally, the existing multi-threshold (MT) segmentation methods still struggle with slow convergence speed and low solution accuracy. The optimum threshold for the image is determined in this study using the Slime Mould Algorithm with the Mechanism of Leadership and Self-phagocytosis (SMA-MLS). Firstly, the initial population production method based on Logistic-Tent mapping is introduced to enhance the diversity of algorithm solutions. Secondly, the position update formula with leadership mechanism is proposed to improve the convergence speed and accuracy. In addition, the adaptive combined mutation mechanism balances the exploration and exploitation ability. Finally, the self-phagocytosis mechanism maintains population diversity and heritability. A series of benchmark test suites are employed to evaluate the performance of the algorithm. Experimental results demonstrate that SMA-MLS does show good performance. It is superior in terms of convergence accuracy, convergence speed and stability. In the MT segmentation experiments, by using Kapur as the objective function and working with color images, SMA-MLS proved to be effective in the MT segmentation problem of images. Moreover, SMA-MLS will be applied to mechanical parameter optimization, neural network and other fields in future research.

Application of Improved Sparrow Search Algorithm to Path Planning of Mobile Robots.

Path planning is an important research direction in the field of robotics; however, with the advancement of modern science and technology, the study of efficient, stable, and safe path-planning technology has become a realistic need in the field of robotics research. This paper introduces an improved sparrow search algorithm (ISSA) with a fusion strategy to further improve the ability to solve challenging tasks. First, the sparrow population is initialized using circle chaotic mapping to enhance diversity. Second, the location update formula of the northern goshawk is used in the exploration phase to replace the sparrow search algorithm's location update formula in the security situation. This improves the discoverer model's search breadth in the solution space and optimizes the problem-solving efficiency. Third, the algorithm adopts the Lévy flight strategy to improve the global optimization ability, so that the sparrow jumps out of the local optimum in the later stage of iteration. Finally, the adaptive T-distribution mutation strategy enhances the local exploration ability in late iterations, thus improving the sparrow search algorithm's convergence speed. This was applied to the CEC2021 function set and compared with other standard intelligent optimization algorithms to test its performance. In addition, the ISSA was implemented in the path-planning problem of mobile robots. The comparative study shows that the proposed algorithm is superior to the SSA in terms of path length, running time, path optimality, and stability. The results show that the proposed method is more effective, robust, and feasible in mobile robot path planning.

A Full-Coverage Path Planning Method for an Orchard Mower Based on the Dung Beetle Optimization Algorithm

In order to optimize the operating path of orchard mowers and improve their efficiency, we propose an MI-DBO (multi-strategy improved dung beetle optimization algorithm) to solve the problem of full-coverage path planning for mowers in standardized quadrilateral orchard environments. First, we analyzed the operation scenario of lawn mowers in standardized orchards, transformed the full-coverage path planning problem into a TSP (traveling salesman problem), and mathematically modeled the U-turn and T-turn strategies based on the characteristics of lawn mowers in orchards. Furthermore, in order to overcome the issue of uneven distribution of individual positions in the DBO (dung beetle optimization) algorithm and the tendency to fall into local optimal solutions, we incorporated Bernoulli mapping and the convex lens reverse-learning strategy in the initialization stage of DBO to ensure a uniform distribution of the initial population. During the algorithm iteration stage, we incorporated the Levy flight strategy into the position update formulas of breeding beetles, foraging beetles, and stealing beetles in the DBO algorithm, allowing them to escape from local optimal solutions. Simulation experiments show that for 18 types of orchards with different parameters, MI-DBO can find the mowing machine’s operation paths. Compared with other common swarm intelligence algorithms, MI-DBO has the shortest average path length of 456.36 m and can ensure faster optimization efficiency. Field experiments indicate that the algorithm-optimized paths do not effectively reduce the mowing machine’s missed mowing rate, but the overall missed mowing rate is controlled below 0.8%, allowing for the completion of mowing operations effectively. Compared with other algorithms, MI-DBO has the least time and fuel consumption for operations. Compared to the row-by-row operation method, using paths generated by MI-DBO reduces the operation time by an average of 1193.67 s and the fuel consumption rate by an average of 9.99%. Compared to paths generated by DBO, the operation time is reduced by an average of 314.33 s and the fuel consumption rate by an average of 2.79%.

Improved Dual-Center Particle Swarm Optimization Algorithm

This paper proposes an improved dual-center particle swarm optimization (IDCPSO) algorithm which can effectively improve some inherent defects of particle swarm optimization algorithms such as being prone to premature convergence and low optimization accuracy. Based on the in-depth analysis of the velocity updating formula, the most innovative feature is the vectorial decomposition of the velocity update formula of each particle to obtain three different flight directions. After combining these three directions, six different flight paths and eight intermediate positions can be obtained. This method allows the particles to search for the optimal solution in a wider space, and the individual extreme values are greatly improved. In addition, in order to improve the global extreme value, it is designed to construct the population virtual center and the optimal individual virtual center by using the optimal position and the current position searched by the particle. Combining the above strategies, an adaptive mutation factor that accumulates the coefficient of mutation according to the number of iterations is added to make the particle escape from the local optimum. By running the 12 typical test functions independently 50 times, the results show an average improvement of 97.9% for the minimum value and 97.7% for the average value. The IDCPSO algorithm in this paper is better than other improved particle swarm optimization algorithms in finding the optimum.

An improved slime mould algorithm using multiple strategies

Aiming at the defects of standard slime mould algorithm (SMA), such as local optima stagnation, slow convergence and improper balance between exploitation and exploration, we propose an improved SMA that contains the adaptive t-distributed variation strategy, improved location update formula and chaotic opposition-based learning strategy, that is, the MISMA. Utilizing comparative experiments and ablation studies on classical benchmark and CEC2020 benchmark suite, we proved that MISMA outperforms other state-of-the-art rival algorithms on convergence speed, solution accuracy, and robustness, each component of MISMA achieves an improvement on the defects of SMA at each stage and exhibits synergistic effects.

Comparison of a quasi Newton method using Broyden’s update formula and an adjoint method for determining local magnetic material properties of electrical steel sheets

PurposePerforming accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.Design/methodology/approachThe general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.FindingsThe QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.Originality/valueThe presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.