Premature Convergence Problem Research Articles

Particle swarm optimization with Chebychev functional-link network model for engineering design problems

In recent years, many improved particle swarm optimization (PSO) algorithms have been developed to improve the performance of PSO. These improved algorithms have greatly improved PSO performance, but PSO still has some shortcomings. So, an particle swarm optimization with Chebychev functional-link network model is proposed (APSOCFLN) in this paper. Firstly, in order to make up for the shortcomings of the canonical PSO update search, a novel Chebychev functional-link network (CFLN) elite guidance strategy is proposed. Two different update mechanisms are executed alternately, increasing the diversity of the algorithm population and making the algorithm more capable of jumping out of local optimization. Secondly, in order to better balance the exploration and exploitation of the algorithm, an adaptive probability strategy is proposed. Thirdly, an adaptive weighting strategy is proposed. It will be used for CFLN elite guidance strategy and give different weights to the two alternating update strategies, which can effectively solve the problem of premature convergence of PSO. Fourthly, the APSOCFLN and comparison algorithms are used to solve the practical engineering problems, and the results show that APSOCFLN has high precision, fast convergence , and excellent performance. Finally, the performance of the algorithm is tested with CEC2017 and CEC2022 benchmark functions. The comparative algorithm includes the classical PSO improvement algorithms and the classical other algorithms, and the experimental results show the effectiveness of the proposed strategy and the good performance of the improved algorithm.

Fuzzy-based hunger games search algorithm for global optimization and feature selection using medical data

Feature selection (FS) is one of the basic data preprocessing steps in data mining and machine learning. It is used to reduce feature size and increase model generalization. In addition to minimizing feature dimensionality, it also enhances classification accuracy and reduces model complexity, which are essential in several applications. Traditional methods for feature selection often fail in the optimal global solution due to the large search space. Many hybrid techniques have been proposed depending on merging several search strategies which have been used individually as a solution to the FS problem. This study proposes a modified hunger games search algorithm (mHGS), for solving optimization and FS problems. The main advantages of the proposed mHGS are to resolve the following drawbacks that have been raised in the original HGS; (1) avoiding the local search, (2) solving the problem of premature convergence, and (3) balancing between the exploitation and exploration phases. The mHGS has been evaluated by using the IEEE Congress on Evolutionary Computation 2020 (CEC’20) for optimization test and ten medical and chemical datasets. The data have dimensions up to 20000 features or more. The results of the proposed algorithm have been compared to a variety of well-known optimization methods, including improved multi-operator differential evolution algorithm (IMODE), gravitational search algorithm, grey wolf optimization, Harris Hawks optimization, whale optimization algorithm, slime mould algorithm and hunger search games search. The experimental results suggest that the proposed mHGS can generate effective search results without increasing the computational cost and improving the convergence speed. It has also improved the SVM classification performance.

A Self‐adaptive Bald Eagle Search optimization algorithm with dynamic opposition‐based learning for global optimization problems

AbstractBald Eagle Search optimization (BES) is introduced recently, which mimics the bald eagles' hunting and food searching behaviour. The capability of a BES algorithm is enhanced in this paper by avoiding local optima stagnation and premature convergence problems. The BES algorithm is modified to enhance the performance of the algorithm and the modified algorithm is called the Self Adaptive Bald Eagle Search (SABES) algorithm. Dynamic‐opposite Learning (DOL) method is invoked in the initialization phase to increase the population diversity and convergence speed. To find better global solutions, the exploitation capability of the SBES algorithm is enhanced by considering the dynamic‐opposite solutions. In addition, the algorithmic parameter values of the BES algorithm have been determined using the linear and non‐linear time‐varying adaption strategy to create a balance between the search abilities which promotes the overall performance of the algorithm. The performance of the SABES algorithm is validated by comparing the results of 50 benchmark functions and CEC2017 functions with different erstwhile algorithms. The proposed algorithm achieves the best results in 80% of the benchmark functions, whereas the BES only gets the best results in 56% of functions. For the CEC2017, the SABES algorithm achieves optimal results for 20 functions which are highest in comparison to state‐of‐the‐art algorithms. The feasibility and effectiveness of the proposed algorithm are checked using the 15 CEC2020 competition real‐world single‐objective constrained optimization problems. The SABES achieves a 100% success rate and 100% feasibility rate in comparison to other well‐regarded algorithms. The statistical significance of the algorithm has been proved using Friedman's mean rank and Wilcoxon sign rank test.

Risk Assessment of Deep Coal and Gas Outbursts Based on IQPSO-SVM.

Coal and gas outbursts seriously threaten the mining safety of deep coal mines. The evaluation of the risk grade of these events can effectively prevent the occurrence of safety accidents in deep coal mines. Characterized as a high-dimensional, nonlinear, and small-sample problem, a risk evaluation method for deep coal and gas outbursts based on an improved quantum particle swarm optimization support vector machine (IQPSO-SVM) was constructed by leveraging the unique advantages of a support vector machine (SVM) in solving small-sample, high-dimension, and nonlinear problems. Improved quantum particle swarm optimization (IQPSO) is used to optimize the penalty and kernel function parameters of SVM, which can solve the optimal local risk and premature convergence problems of particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO) in the training process. The proposed algorithm can also balance the relationship between the global search and local search in the algorithm design to improve the parallelism, stability, robustness, global optimum, and model generalization ability of data fitting. The experimental results prove that, compared with the test results of the standard SVM, particle swarm optimization support vector machine (PSO-SVM), and quantum particle swarm optimization support vector machine (QPSO-SVM) models, IQPSO-SVM significantly improves the risk assessment accuracy of coal and gas outbursts in deep coal mines. Therefore, this study provides a new idea for the prevention of deep coal and gas outburst accidents based on risk prediction and also provides an essential reference for the scientific evaluation of other high-dimensional and nonlinear problems in other fields. This study can also provide a theoretical basis for preventing coal and gas outburst accidents in deep coal mines and help coal mining enterprises improve their safety management ability.

Tourism Route Selection Model for Tourism Sustainable Development Based on Improved Genetic Algorithm

The improvement of people’s quality of life also promotes the development of tourism. The traditional travel mode is no longer suitable for the needs of modern people. How to quickly determine the optimal tourist route according to the needs of different families is the current sustainable development direction of tourism. Scientific planning of tourist routes to minimize the cost and time of tourists is very important for the improvement of tourism experience. This study employs an improved genetic algorithm (IGA) to find the best tourist route based on this requirement. With the increase of tourist attractions, routes, and demands, the traditional genetic algorithm (GA) has problems such as premature convergence and poor local search ability when planning the tourist route. The existence of these problems will affect the effect of route planning. IGA proposes three improvements to traditional GA. One is to introduce the ant colony algorithm (ACA) to initialize the parameters in the GA. This algorithm is introduced to alleviate the over-reliance of GA on initializing the population and the poor adaptability of individual populations. Second, because the crossover probability parameter in GA has such a large influence on the final solution, this study proposes an adaptive strategy for adjusting the crossover probability to improve population fitness. Third, considering the weak local search ability of GA and the problem of premature convergence, this study introduces the 2-opt optimization algorithm to improve the quality of the solution. The results of the experimental analysis confirm the effectiveness of the proposed method.

Symmetric uncertainty-incorporated probabilistic sequence-based ant colony optimization for feature selection in classification

Feature selection (FS), which aims to select informative feature subsets and improve classification performance, is a crucial data-mining technique. Recently, swarm intelligence has attracted considerable attention and has been successfully applied to FS. Ant colony optimization (ACO), a swarm intelligence algorithm, has shown great potential in FS owing to its graphical representation and search ability. However, designing an effective ACO-based approach for FS is challenging because of issues originating from feature interactions and premature convergence problems. In this study, a novel ACO is proposed that incorporates symmetric uncertainty (SU). By constructing a probabilistic sequence-based graphical representation, the proposed algorithm significantly outperformed six other algorithms on 16 problems in terms of the classification error rate. This study also considers an extensive investigation of the contribution of the two components, namely, probabilistic sequence and SU. The experimental results indicated that these components significantly improved the performance of the ACO-based approach.

An Effective Fault Diagnosis Technique for Wind Energy Conversion Systems Based on an Improved Particle Swarm Optimization

The current paper proposes intelligent Fault Detection and Diagnosis (FDD) approaches, aimed to ensure the high-performance operation of Wind energy conversion (WEC) systems. First, an efficient feature selection algorithm based on particle swarm optimization (PSO) is proposed. The main idea behind the use of the PSO algorithm is to remove irrelevant features and extract only the most significant ones from raw data in order to improve the classification task using a neural networks classifier. Then, to overcome the problem of premature convergence and local sub-optimal areas when using the classical PSO optimization algorithm, an improved extension of the PSO algorithm is proposed. The basic idea behind this proposal is to use the Euclidean distance as a dissimilarity metric between observations in which a single observation is kept in case of redundancies. In addition, the proposed reduced PSO-NN (RPSO-NN) technique not only enhances the results in terms of accuracy but also provides a significant reduction in computation time and storage cost by reducing the size of the training dataset and removing irrelevant and redundant samples. The experimental results showed the robustness and high performance of the proposed diagnosis paradigms.

On Solving 0/1 Multidimensional Knapsack Problem with a Genetic Algorithm Using a Selection Operator Based on K-Means Clustering Principle

Abstract The growing need for profit maximization and cost minimization has made the optimization field very attractive to both researchers and practitioners. In fact, many authors were interested in this field and they have developed a large number of optimization algorithms to solve either academic or real-life problems. Among such algorithms, we cite a well-known metaheuristic called the genetic algorithm. This optimizer tool, as any algorithm, suffers from some drawbacks; like the problem of premature convergence. In this paper, we propose a new selection strategy hoping to avoid such a problem. The proposed selection operator is based on the principle of the k-means clustering method for the purpose of guiding the genetic algorithm to explore different regions of the search space. We have elaborated a genetic algorithm based on this new selection mechanism. We have then tested our algorithm on various data instances of the 0/1 multidimensional knapsack problem. The obtained results are encouraging when compared with those reached by other versions of genetic algorithms and those reached by an adapted version of the particle swarm optimization algorithm.

A novel algorithm for optimal equipment scheduling and dispatch of chilled water systems with ice thermal storage

Using thermal energy storage in chilled water systems can reduce electricity bill charges and required chiller cooling capacity through load shifting and peak demand shavings. As opposed to simple heuristic strategies, optimal storage dispatch maximizes savings by considering the time of use tariffs and system efficiency. In this paper, we propose a solution to the optimal equipment scheduling and storage dispatch problem of multi-chiller chilled water systems with ice thermal storage. We model the system in a bi-level optimization formulation that is solved using the genetic algorithm. The upper level minimizes daily operation costs and decides the storage dispatch amount over the next 24 h. The decided upon dispatch amount is fed to the lower-level optimizer to solve the equipment scheduling problem sequentially and return the corresponding system power consumption over the next 24 h. Flowrate and energy balancing constraints are handled using the penalty function method. Tuning of the penalty factors and genetic algorithm parameters significantly diminished and eliminated the problem of premature convergence. While the genetic algorithm is computationally taxing, we reduced the run time to 1–2 min by pre-solving the lower-level problem under various input conditions and tri-linearly interpolating between them. We compared the developed optimal control strategy to two commonly used heuristic storage dispatch strategies: chiller priority control and storage priority control in three scenarios of cooling demand under a time of use electricity pricing. Our model suggests optimal control reduces cost and energy by 11–14% and 10–12%, respectively, relative to storage priority control, and 16–33% and 1–9%, respectively, relative to chiller priority control. In a scenario with a demand charge, optimized control reduces demand charges by 17% relative to storage priority and 26% relative to chiller priority control. The gains from the proposed approach are augmented when a more sophisticated tariff structure is present.

Improved DV-Hop Algorithm Based on Swarm Intelligence for AI and IoT-Federated Applications in Industry 4.0

In the Internet of Things (IoT) ecosystem, localization is critical for tracking and monitoring targets via nodes. The distance vector-hop (DV-Hop) technique is a good choice for localizing neighborhood in IoT networks. The conventional DV-Hop algorithm is a distributed localization approach that does not consider the distribution of the nodes into full deliberation when calculating the hop count from the source to destined nodes. The transfer distance and node positions thus do not attain higher efficiency while ascertaining the distance between sources and destined nodes. The study aims to resolve the pitfalls in the traditional algorithm by making enhancements in controlling the original DV-Hop algorithm’s hop count and transfer distance method by utilizing the particle swarm to estimate the node positions. Error rate in the distance between beacon nodes and unseen nodes is effectively reduced with the proposed technique that calculate error factors with corrections in a reversed fashion to revise hop counts. An escape factor is introduced to take control of updating particles’ velocity in the system, and the inertia weight is defined by a piecewise function to enlarge search space. This mechanism increases the diversity of the particle populations and mitigates the tendency of estimations on node positions to be trapped into local optima under stationary state. Also, the improved DV-Hop algorithm described in the paper has a better convergence speed due to the presence of random inertia weight logarithmic method. Finally, the problem of premature convergence is also tackled as a variation factor is adopted in collaboration with a fitness function that affects the particles’ movement range and assists in global convergence. The overall performance of improved DV-Hop is evaluated by statistical metrics and also compared with the traditional DV-Hop algorithm under simulated environment with the data collected from real-world scenarios. Industry 4.0 is fully dependent upon IoT and the count of hops is very important for deciding the routing from the source to destination for speedy transmission of data. The improved DV-hop algorithm can achieve better results and has reduced error rate by more than 30%. The DV-Hop algorithm plays an important role in IoT-enabled environment especially in Industry 4.0.

Golden-Sine dynamic marine predator algorithm for addressing engineering design optimization

In engineering design optimization problems, the optimal solution can improve the design quality of complex engineering system and reduce a lot of cost consumption, so it is of great practical significance to study the optimization algorithm of engineering design problems. Evolutionary computation is widely used to solve engineering design optimization problems, which are mostly mixed-integer nonlinear programming (MINLP) problems. As a newly developed evolutionary computing method, Marine Predator Algorithm (MPA) currently suffers from weak convergence and easily falls into local optimum. In order to overcome the disadvantage, this study proposed a Golden-Sine Dynamic Marine Predator Algorithm (GDMPA). Firstly, Logistic-Logistic (L-L) cascade chaos was used to adjust the initial position of the population to generate a high-quality initial prey population while ensuring ergodicity and randomness. Secondly, the dynamic adjustment transition probability strategy was added to improve the discriminant conditions when predators entered different stages, which effectively maintained the balance between global exploration and local exploitation. The adaptive inertial weight based on Sigmoid function was used in updating the step information of predators to avoid the problem of falling into local extrema. Finally, the Golden-Sine factor is employed to achieve a better balance between exploration and exploitation, further improve the premature convergence problem, enhance the population diversity, and improve the convergence rate. A series of validation studies were conducted over twelve standard test functions and the CEC2017 test set to verify the effectiveness and robustness of the improved GDMPA strategy. Mechanical optimization and size optimization study for truss structures was carried out using the proposed GDMPA, which yielded excellent results. The results of the 27-bar truss structure show that the proposed GDMPA reduces 3.24%, 27.18%, 39.38%, 27.65% and 9.67% compared to the total mass of MPA, BOA, SSA, SOA and HHO, respectively. In the other cases, the optimization results of GDMPA have been improved substantially compared with other algorithms. Therefore, GDMPA has a broad application prospect in structural design and optimization.

Good point set and double attractors based-QPSO and application in portfolio with transaction fee and financing cost

In order to overcome the premature convergence problem of quantum-behaved particle swarm optimization algorithm (QPSO) in the face of high-dimensional complexity, an improved QPSO based on good point set and double attractor point mechanism (GDQPSO) is presented. In the initialization phase of GDQPSO, the idea of good point set is used to allow particles to explore more uniformly and comprehensively at the beginning of the iteration. To better balance the exploration ability of individuals and the global search capability of the algorithm, the local attraction point is redefined by combining dynamic and fixed methods. Then the global perturbation mechanism is considered to maintain the diversity of the population. And the comparison results with nine intelligent algorithms on 18 benchmark functions indicate that GDQPSO has obvious advantages in convergence accuracy and stability. Finally, the simulation experiments demonstrate very competitive performance of GDQPSO while solving the portfolio model with transaction fee and financing cost when compared with other evolutionary algorithms.

Enhancing the take-off performance of hypersonic vehicles using the improved chimp optimisation algorithm

AbstractThe performance of hypersonic vehicles in the take-off stage considerably influences their capability of accomplishing the flight tasks. This study is aimed at enhancing the take-off performance of a cruise aircraft using the improved chimp optimisation algorithm. The proposed algorithm, which uses the Sobol sequence for initial population generation and a function of the weight factors, can effectively overcome the problems of premature convergence and low accuracy of the original algorithm. In particular, the Sobol sequence aims to obtain a better fitness value in the first iteration, and the weight factor aims to accelerate the convergence speed and avoid the local optimal solution. The take-off mass model of the hypersonic vehicle is constructed considering the flight data obtained using the pseudo-spectral method in the climb phase. Simulations are performed to evaluate the algorithm performance, and the results show that the algorithm can rapidly and stably optimise the benchmark function. Compared to the original algorithm, the proposed algorithm requires 28.89% less optimisation time and yields an optimised take-off mass that is 1.72kg smaller.

GPGPU based Dual Population Genetic Algorithm for solving Constrained Optimization Problem

Dual Population Genetic Algorithm is a variant of Genetic Algorithm that provides additional diversity to the main population. It covers the premature convergence problem as well as the diversity problem associated with Genetic Algorithm. But also its additional population introduces large search space that increases time required to find an optimal solution. This large scale search space problem can be easily solved using consumer-level graphics cards. The solution obtained using accelerated DPGA for solving a constrained optimization problem from CEC 2006 is compared with the obtained solution using sequential algorithm. The results show speed up maintaining solution quality.

An improved Harris Hawks Optimization algorithm for continuous and discrete optimization problems

Harris Hawks Optimization (HHO) is a population-based meta-heuristic optimization algorithm that has been used for the solution of test functions and real-world problems by many researchers. However, HHO has a premature convergence problem. The main motive of the novel approach in this paper is that the performance of an MHA could be improved by simplification and by modifying the way random parameters are determined. The proposed algorithm aims to solve both continuous and discrete optimization problems. HHO is improved in three stages. First, the method to determine the random parameters is modified. Second, the strategy of HHO to produce a new solution is updated. Third, the six-step decision mechanism of HHO is shortened to four. The proposed algorithm is compared to five recently published competitor algorithms by applying to the CEC2019 test functions and a three-dimensional bin packing problem (3D-BPP) dataset with 320 samples. All the algorithms are run on the same computer and the results of 30 independent studies are saved. Minimum, average, and standard deviation values and solution times of CEC2019 functions are used as comparison parameters. For the 3D-BPP, the number of bins and the solution time are used as comparison parameters for in the Wilcoxon test. The proposed algorithm performs better than the selected competitors in terms of its %5 significance level. Moreover, the algorithm proposed in the 3D-BPP data set is the most successful algorithm with its 9745 bins. Besides, the proposed algorithm is also compared to the four most popular algorithms in the literature. The results obtained confirm the validity of the proposed algorithm.

Knowledge Application to Crossover Operators in Genetic Algorithm for Solving the Traveling Salesman Problem

Genetic Algorithm often bears with Premature Convergence for solving combinatorial optimization problems but can be improved by modification at different prospectives. In this research, an effective knowledge is applied in the procedure of Genetic Algorithm used for solving TSP. The key concept for the proposed GA is a modification in the crossover operators by applying knowledge of smallest distant cities (shortest edge) assuming that it would improve the process to find the shortest path, by optimizing the new generations. As TSP is represented as a graph, considering cities as nodes and paths as edges, in the proposed approach, crossover point selection for crossover operators is selected upon the basis of minimum edge in the given graph. To test the effect of the proposed method of knowledge application, Linear Order Crossover, Cycle Crossover Operator, and Sequential Constructive Crossover are modified and results are proved on the randomly generated data sets for TSP. This optimization not only improved the shortest path but also reduced the problem of Premature Convergence.

An adaptive clonal selection algorithm with multiple differential evolution strategies

Clonal selection algorithms have provided significant insights into numerical optimization problems. However, most mutation operators in conventional clonal selection algorithms have semi-blindness and lack an effective guidance mechanism, which has thus become one of the important factors restricting the performance of algorithms. To address these problems, this study develops an improved clonal selection algorithm called an adaptive clonal selection algorithm with multiple differential evolution strategies (ADECSA) with three features: (1) an adaptive mutation strategy pool based on its historical records of success is introduced to guide the immune response process effectively; (2) an adaptive population resizing method is adopted to speed up convergence; and (3) a premature convergence detection method and a stagnation detection method are proposed to alleviate premature convergence and stagnation problems in the evolution by enhancing the diversity of the population. Experimental results on a wide variety of benchmark functions demonstrate that our proposed method achieves better performance than both state-of-the-art clonal selection algorithms and differential evolution algorithms. Especially in the comparisons with other clonal selection algorithms, our proposed method outperforms at least 23 out of 30 benchmark functions from the CEC2014 test suite.

Alternated superior chaotic variants of gravitational search algorithm for optimization problems

Nature inspired algorithms like Gravitational Search Algorithm (GSA) has been able to solve complex optimization problems with a reasonable performance. But still there is problem of premature convergence to the local optimal solutions due to lack of appropriate balancing between exploration and exploitation procedures. In the literature, chaotic maps have been successful in diversifying the population to a greater level to avoid the entrapment of the solutions in local region(s), and provide better convergence speed with high precision. Recent developments in nonlinear dynamical systems, especially discrete alternated systems, have proved their worth in enhancing the functionality of the metaheuristic algorithms to a great extent (Kumar and Rani, 2019). We have integrated alternated discrete dynamical systems in superior orbit with GSA for more diversification of the population with the aim of increasing the chances for the candidate solutions to arrive at global solutions which otherwise remain stagnant in local optimal points. From the obtained results, we have verified that the proposed methods have outperformed the competing algorithms significantly as they have been able to arrive at global optimal points with much improved optimization rates. In some cases, the improvement in optimization values (mean and standard deviation) have reduced to less than twice the optimization values of the chaotic GSA.

Fuzzy Adaptive Teaching Learning-Based Optimization for Solving Unconstrained Numerical Optimization Problems

Teaching learning-based optimization is one of the widely accepted metaheuristic algorithms inspired by teaching and learning within classrooms. It has successfully addressed several real-world optimization problems, but it may still be trapped in local optima and may suffer from the problem of premature convergence in the case of solving some challenging optimization problems. To overcome these drawbacks and to achieve an appropriate percentage of exploitation and exploration, this study presents a new modified teaching learning-based optimization algorithm called the fuzzy adaptive teaching learning-based optimization algorithm. The proposed fuzzy adaptive teaching learning-based optimization algorithm uses three measures from the search space, namely, quality measure, diversification measure, and intensification measure. As the 50-50 probabilities for exploitation and exploration in the basic teaching learning-based optimization algorithm may be counterproductive, the Mamdani-type fuzzy inference system of the new algorithm takes these measures as a crisp inputs and generates selection as crisp output to choose either exploitation or exploration based on the current search requirement. This fuzzy-based adaptive selection helps to adequately balance global search or exploration and local search or exploitation operations during the search process as these operations are intrinsically dynamic. The performance of the fuzzy adaptive teaching learning-based optimization is evaluated against other metaheuristic algorithms including basic teaching learning-based optimization on 23 unconstrained global test functions. Moreover, adaptive teaching learning-based optimization is used to search for near-optimal values for the four parameters of the COCOMO II model, which are then tested for validity on a software project of NASA. Analysis and comparison of the obtained results indicate the efficiency and competitiveness of the proposed algorithm in addressing unconstrained continuous optimization tasks.

A Path Optimization Algorithm for Multiple Unmanned Tractors in Peach Orchard Management

In order to improve the management efficiency of peach orchards, this paper considers the cooperative operation scheme of multiple unmanned tractors. According to the actual situation, this paper constructs the path planning model of multiple unmanned tractors in a standard peach orchard, designs the objective function to optimize the total turning time and total operating time according to the tractor driving parameters, and solves it by improving the differential evolution algorithm. Aiming at the premature convergence problem, the permutation matrix is introduced to represent the driving paths of multiple unmanned tractors. Then, the dynamic parameters are adopted to make the parameters change with the number of iterations, and the elite selection strategy is used to eliminate the redundant feasible solutions. An Adaptive Elite Differential Evolution (AEDE) algorithm suitable for multi-tractor path optimization is proposed. The results show that, compared with the traditional Differential Evolution algorithm (Differential Evolution, DE), the total turning time and total operating time in the rectangular peach orchard optimized by AEDE are reduced by 3.34% and 0.87%, respectively. Compared with the block operation, the total turning time and total operating time of the AEDE-optimized rectangular peach orchard operation path were reduced by 37.37% and 9.47%, respectively. Experiments show that AEDE, which optimizes the operating path of multi-tractors in standard peach orchards, is able to improve the efficiency and reduce the operating time.