Traditional Differential Evolution Algorithm Research Articles

Adaptive Differential Evolutionary Algorithm for Innovative Teaching and Learning in High School Project-Based Courses

Abstract In this paper, for the innovative teaching of high school project-based courses, an adaptive differential evolutionary algorithm is used as one of the tools of the project to help students solve complex problems. The traditional adaptive differential evolution algorithm has the problems of local optimum and low convergence accuracy; to overcome these limitations, this paper proposes an enhanced reverse learning adaptive differential evolution algorithm. The OL-ADE algorithm is improved by introducing the reverse learning strategy in machine learning to extract the reverse elite individual population from the original individual population and select the better-adapted individuals for mutation operation. After the project-based teaching, the students’ works have high scores in layout color matching, technical operation, organization, information awareness, and information social responsibility, and their scores are 8.6, 9.75, 9, 9.35, and 8.75, respectively. Therefore, this paper proves the Adaptive Difference Evolution algorithm’s effectiveness in innovative teaching of high school project-based courses.

Differential evolution with stage stratification method and dual balanced mutation strategy for real-parameter numerical optimization

Traditional differential evolution (DE) algorithms have functional limitations in effectively addressing increasingly intricate numerical optimization problems. The key to responding to this challenge is to strike a suitable balance between exploration and exploitation. Exploration is used to find the global optimal solution, and exploitation is used to improve the accuracy of the global optimal solution. Therefore, this study introduces a novel differential evolution algorithm with a stage stratification method and a dual balanced mutation strategy framework, named SbmDE. To enhance the balance between convergence and diversity, the population is stratified into exploration and exploitation layers based on the size of the fitness value and evolutionary period. In the exploitation layer, a hybridization mutation is applied as the first mutation. A novel dual improved mutation operation is proposed and applied to the exploration layer. For the first mutation, the hybridization mutation is used in the same manner as for the exploitation layer. For the secondary mutation, two improved mutation strategies are proposed to alleviate premature convergence at the early stage of evolution and to enhance the local neighborhood search at a later stage, named DE/ranking-to-rand/1 and DE/best-current-dev/1. Experiments were conducted on the CEC2017 benchmark suite, which contains 29 single-objective real-parameter numerical optimization problems, to evaluate the performance of the proposed algorithm. Compared with 11 state-of-the-art algorithms, the results demonstrate the superiority of the proposed algorithm, which does not increase the time complexity. Additionally, based on the four engineering design problems, the proposed algorithm is fully competent in solving practical constrained optimization problems.

Distribution network planning with distributed photovoltaic and electric vehicle charging stations based on multi-population traction differential evolution algorithm

Currently, in the background of a large number of distributed photovoltaic and electric vehicle charging stations with access to the distribution network, this paper presents a distribution network planning method with distributed photovoltaic and electric vehicle charging stations based on multi-population traction differential evolution algorithm. Firstly, this paper considers the curve characteristics of photovoltaic and load, and uses cluster analysis to determine the planning scenery, so that the planning results are more accurate. Then, the distribution network planning model is constructed from the aspects of the minimum investment cost, operation cost and performance index. Then, to improve the speed and the accuracy of planning results, the multi-population traction differential evolution algorithm is used to solve the planning model. Finally, a 10kV line is used as an example to verify the reliability of the proposed method. Then, the traditional differential evolution algorithm and the other two algorithms are compared and analyzed to verify the effectiveness of the proposed planning method.

Approximate Logical Dendritic Neuron Model Based on Selection Operator Improved Differential Evolution Algorithm

In order to solve the problem that the classification effect of approximate logic dendritic neuron model is largely limited by the training effect of learning algorithm. The differential evolution algorithm of the population evolution algorithm is selected as the training algorithm of the model. Differential evolution algorithm is a branch of population evolution algorithm, which has the advantages of good robustness and easy implementation. But it also has the disadvantage that it is easy to fall into the stagnation of evolution. In order to solve this key problem, several differential evolution algorithms are investigated. Finally, we noticed that a differential evolution algorithm improved by selection operator can better solve the problem of algorithm evolution stagnation. This paper studies the training of logic dendritic neuron model using the differential evolution algorithm improved by this selection operator. In order to evaluate the performance of the algorithm training model, four representative data sets were used for experiments. When comparing the classification effect, particle swarm optimization algorithm, traditional differential evolution algorithm and genetic algorithm are selected as the comparison experiment.

An adaptive genetic algorithm-based background elimination model for English text

In this paper, an adaptive genetic algorithm is used to conduct an in-depth study and analysis of English text background elimination, and a corresponding model is designed. The curve results after the initial character editorialization are curved and transformed, and the adaptive genetic algorithm is used for the transformation to solve the influence of multiple inflection points of curve images on feature extraction. Then, using the minimum deviation method, the error values of the input characters and the sample set in the spatial coordinate system are calculated, and the deviation values of the angle and the straight line are used to match the characters with the smallest deviation value to match the highest degree. To enhance identification accuracy, a genetic algorithm is used to iterate the feature sets of angles and line segments, and the optimum features are ultimately generated via cross evolution of generations. The character library is then utilized as an input item for average grouping for trials, and the resulting feature sets are placed in a position matrix and compared one by one to the samples in the database. It is found that the improved stroke-structure feature extraction algorithm based on a genetic algorithm can improve the recognition accuracy and better accomplish the recognition task with better results compared to others. Finally, by analyzing the limitations and characteristics of traditional particle swarm optimization algorithm and differential evolution algorithm, and giving full play to the advantages and applicability of different algorithms, a new differential evolution particle swarm algorithm with better performance and more stable performance is proposed. The algorithm is based on the PSO algorithm, and when the population update of the PSO algorithm is stagnant and the search space is limited, the crossover and mutation operations of the DE algorithm are used to perturb the population, increase the diversity of the population, and improve the global optimization ability of the algorithm. The algorithm is tested on a common dataset for text mining to verify the effectiveness and feasibility of the algorithm.

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.

A differential evolution algorithm combined with linear programming for solving a closed loop facility layout problem

Closed loop layout problem (CLLP) is an important class of design problems encountered in flexible manufacturing system. It is to determine the locations of manufacturing cells along a closed material handling loop. Existing studies on CLLPs typically ignore clearances between adjacent cells and do not optimize the dimension of the closed loop. However, separating adjacent cells with suitable clearances may achieve a better solution with lower material flow cost, and optimizing cell sequence and the dimension of closed loop simultaneously can also improve the solution quality. In this paper, a mixed integer programming formulation (MIP) is established for the CLLP. Then, based on the formulation, a hybrid approach combining an improved differential evolution algorithm and an exact approach (iDE-EA) is proposed to solve the CLLP. The iDE with a hybrid coding is utilized to optimize the dimension of closed loop and the placement sequence of cells simultaneously. The EA is to determine the exact location of each cell (i.e., the clearance between each pair of adjacent cells). iDE-EA is verified on 10 problem instances, and experiments show that iDE-EA improves upon the best-known material handling cost by 0–9.97% compared against the traditional differential evolution algorithm and three state-of-the-art approaches. In addition, using EA to further optimize clearances among cells in the solution obtained by iDE can achieve a more competitive layout in most cases.

UAV Stocktaking Task-Planning for Industrial Warehouses Based on the Improved Hybrid Differential Evolution Algorithm

Tobacco industry companies need to conduct a regular inventory of finished products and raw and auxiliary materials, and drones with radio frequency identification (RFID) readers are becoming a major application trend of inventory. Under the condition of ensuring the accuracy of inventory, this article considers the physical performance constraints of the drone, the constraints of the RFID reader, etc., and introduces the force of the drone into the model establishment, and a task planning model for UAV inventory library equipped with RFID reader is proposed. Then, in view of the problem that the greedy strategy in the traditional differential evolution (DE) algorithm will cause the location information retained by other individuals to be lost, a hybrid DE algorithm based on the lion swarm optimization is proposed. Finally, the proposed algorithm was verified by environmental modeling based on the data of the tobacco enterprise warehouse.

Three-Dimensional Unmanned Aerial Vehicle Route Planning Using Hybrid Differential Evolution

Unmanned aerial vehicles (UAVs) have been investigated proactively owing to their promising applications. A route planner is key to UAV autonomous task execution. Herein, a hybrid differential evolution (HDE) algorithm is proposed to generate a high-quality and feasible route for fixed-wing UAVs in complex three-dimensional environments. A multiobjective function is designed, and both the route length and risk are optimized. Multiple constraints based on actual situations are considered, including UAV mobility, terrain, forbidden flying areas, and interference area constraints. Inspired by the wolf pack search algorithm, the proposed HDE algorithm combines differential evolution (DE) with an approaching strategy to improve the search capability. Moreover, considering the dynamic properties of fixed-wing UAVs, the quadratic B-spline curve is used for route smoothing. The HDE algorithm is compared with a state-of-the-art UAV route planning algorithm, i.e., the modified wolf pack search algorithm, and the traditional DE algorithm. Several numerical experiments are performed, and the performance comparison of algorithms shows that the HDE algorithm demonstrates better performances in terms of solution quality and constraint-handling ability in complex three-dimensional environments.

Synthesis of Sparse Rectangular Planar Arrays with Multiple Constraints Based on Dynamic Parameters Differential Evolution Algorithm

For solving the problem of the synthesis of sparse rectangular planar arrays with multiple constraints, this paper proposes a Dynamic Parameters Differential Evolution (DPDE) based algorithm. Firstly, to improve searching efficiency and accuracy of Differential Evolution (DE), the proposed method introduces dynamically changing strategies to the scaling factor and the crossover probability of the traditional Differential Evolution algorithm. Secondly, a modified matrix mapping method and the redefinition of mapping principles are presented to make up the defects of strong randomness and low accuracy in existing methods. Finally, simulation experiments of antenna arrays are performed to validate the effectiveness of the proposed method, and the results demonstrate that the proposed method performs out the existing methods in the respect of reducing peak sidelobe level of antenna arrays.

Synthesis of Sparse Concentric Ring Arrays Based on Fitness-Associated Differential Evolution Algorithm

In this paper, fitness-associated differential evolution (FITDE) algorithm is proposed and applied to the synthesis of sparse concentric ring arrays under constraint conditions, whose goal is to reduce peak sidelobe level. In unmodified differential evolution (DE) algorithm, crossover probability is constant and remains unchanged during the whole optimization process, resulting in the negative effect on the population diversity and convergence speed. Therefore, FITDE is proposed where crossover probability can change according to certain information. Firstly, the population fitness variance is introduced to the traditional differential evolution algorithm to adjust the constant crossover probability dynamically. The fitness variance in the earlier iterations is relatively large. Under this circumstance, the corresponding crossover probability shall be small to speed up the exploration process. As the iteration progresses, the fitness variance becomes small on the whole and the crossover probability should be set large to enrich population diversity. Thereby, we construct three variation strategies of crossover probability according to the above changing trend. Secondly, FITDE is tested on benchmark functions, and the best one of the three strategies is determined according to the test results. Finally, sparse concentric ring arrays are optimized using FITDE, of which the results are compared with reference algorithms. The optimization results manifest the advantageous effectiveness of FITDE.

Multiscale Cooperative Differential Evolution Algorithm.

A multiscale cooperative differential evolution algorithm is proposed to solve the problems of narrow search range at the early stage and slow convergence at the later stage in the performance of the traditional differential evolution algorithms. Firstly, the population structure of multipopulation mechanism is adopted so that each subpopulation is combined with a corresponding mutation strategy to ensure the individual diversity during evolution. Then, the covariance learning among populations is developed to establish a suitable rotating coordinate system for cross operation. Meanwhile, an adaptive parameter adjustment strategy is introduced to balance the population survey and convergence. Finally, the proposed algorithm is tested on the CEC 2005 benchmark function and compared with other state-of-the-art evolutionary algorithms. The experiment results showed that the proposed algorithm has better performance in solving global optimization problems than other compared algorithms.

Performance Analyses of Differential Evolution Algorithm Based on Dynamic Fitness Landscape

Dynamic fitness landscape analyses contain different metrics to attempt to analyze optimization problems. In this article, some of dynamic fitness landscape metrics are selected to discuss differential evolution (DE) algorithm properties and performance. Based on traditional differential evolution algorithm, benchmark functions and dynamic fitness landscape measures such as fitness distance correlation for calculating the distance to the nearest global optimum, ruggedness based on entropy, dynamic severity for estimating dynamic properties, a fitness cloud for getting a visual rendering of evolvability and a gradient for analyzing micro changes of benchmark functions in differential evolution algorithm, the authors obtain useful results and try to apply effective data, figures and graphs to analyze the performance differential evolution algorithm and make conclusions. Those metrics have great value and more details as DE performance.

A Differential Evolution Algorithm Based on Multi-Population for Economic Dispatch Problems With Valve-Point Effects

Economic dispatch (ED) problem with valve-point effects of generation units is a non-smooth and non-convex problem. This paper presents a differential evolution algorithm based on multi-population (MPDE) to solve ED problems with valve-point effects. The proposed MPDE algorithm employs the evolutional methodology of multiple populations to overcome the limitations of the traditional differential evolution algorithm. In multiple populations, each population has its mutation strategy and parameters to enhance the searching ability. Moreover, information exchange among multiple populations to increase the diversity of individuals in a single population. In addition, the algorithm also introduces the normal distribution function to dynamically adjust the scaling factor and crossover rate to accelerate convergence speed. The proposed algorithm is tested on the 13-, 40-, 80-, and 140-unit test systems. The simulation results show that the MPDE algorithm can achieve much smaller variances compared with other intelligent algorithms. The proposed algorithm has significant performance in accuracy for solving economic dispatch problems with valve-point effects.

Optimization of Wave Energy Converter Arrays by an Improved Differential Evolution Algorithm

Since different incident waves will cause the same array to perform differently with respect to the wave energy converter (WEC), the parameters of the incident wave, including the incident angle and the incident wave number, are taken into account for optimizing the wave energy converter array. Then, the differential evolution (DE) algorithm, which has the advantages of simple operation procedures and a strong global search ability, is used to optimize the wave energy converter array. However, the traditional differential evolution algorithm cannot satisfy the convergence precision and speed simultaneously. In order to make the optimization results more accurate, the concept of an adaptive mutation operator is presented to improve the performance of differential evolution algorithm. It gives the improved algorithm a faster convergence and a higher precision ability. The three-float, five-float, and eight-float arrays were optimized, respectively. It can be concluded that the larger the size of the array is, the greater the interaction between the floats is. Hence, a higher efficiency of wave energy extraction for wave energy converter arrays is achieved by the layout optimization of the array of wave energy converters. The results also show that the optimal layout of the array system is inhomogeneously distributed and that the improved DE algorithm used on array optimization is superior to the traditional DE algorithm.

Research of Dynamic Economic Emission Dispatch Based on Parallel Molecular Differential Evolution Algorithm

Power system dynamic economic emission dispatch plays an important role in energy saving and emission reduction. The model is set up with generation cost and pollution emission minimum as the optimization objectives. The energy cost caused by the valve point effect of the conventional thermal power unit is included in the generation cost. The network loss is considered in the equality constraint, and the solution equation is used to deal with the complex constraint relation. In view of the premature diversity caused by the low diversity of differential evolution algorithm, the molecular differential evolution algorithm is adopted to solve the model. Under the premise of ensuring the accuracy of the original calculation, using the ability of Matlab multi-core parallel computing to improve the molecular differential evolution algorithm, the computational efficiency of the algorithm is improved. The simulation results of the classical 10-unit test system show that, compared with the traditional differential evolution algorithm, the parallel molecular differential evolution algorithm is improved, not only has better global search ability, but also can provide a faster and better choice for decision maker.

Optimal Scheduling of Integrated Energy Systems with Combined Heat and Power Generation, Photovoltaic and Energy Storage Considering Battery Lifetime Loss

Integrated energy systems (IESs) are considered a trending solution for the energy crisis and environmental problems. However, the diversity of energy sources and the complexity of the IES have brought challenges to the economic operation of IESs. Aiming at achieving optimal scheduling of components, an IES operation optimization model including photovoltaic, combined heat and power generation system (CHP) and battery energy storage is developed in this paper. The goal of the optimization model is to minimize the operation cost under the system constraints. For the optimization process, an optimization principle is conducted, which achieves maximized utilization of photovoltaic by adjusting the controllable units such as energy storage and gas turbine, as well as taking into account the battery lifetime loss. In addition, an integrated energy system project is taken as a research case to validate the effectiveness of the model via the improved differential evolution algorithm (IDEA). The comparison between IDEA and a traditional differential evolution algorithm shows that IDEA could find the optimal solution faster, owing to the double variation differential strategy. The simulation results in three different battery states which show that the battery lifetime loss is an inevitable factor in the optimization model, and the optimized operation cost in 2016 drastically decreased compared with actual operation data.

Dynamic Economic Dispatch in Thermal-Wind-Small Hydropower Generation System

With the large-scale wind power integration, the uncertainty of wind power poses a great threat to the safe and stable operation of the system. This paper proposes dynamic economic dispatch problem formulation in thermal power system incorporating stochastic wind and small-hydro (run-in-river) power, called thermal-wind-small hydropower system (TWSHS). Weibull and Gumbel probability density functions are used to calculate available wind and small-hydro power respectively. An improved differential evolution algorithm based on gradient descent information (DE-GD) is proposed to solve the dynamic economic dispatch (DED) problem considering uncertainty of wind power and small-hydro power, as well as complicated constraints in TWSHS. Based on the traditional differential evolution algorithm, the gradient information of the objective function is introduced after the mutation process to enrich the diversity of the population, thus increasing the possibility of convergence to the global optimization. Generation scheduling is simulated on a TWSHS with the proposed approach. Simulation results verify feasibility and effectiveness of the proposed method while considering various complex constraints in the thermal-windsmall hydropower system.

Optimal feature selection using a modified differential evolution algorithm and its effectiveness for prediction of heart disease

Enormous data growth in multiple domains has posed a great challenge for data processing and analysis techniques. In particular, the traditional record maintenance strategy has been replaced in the healthcare system. It is vital to develop a model that is able to handle the huge amount of e-healthcare data efficiently. In this paper, the challenging tasks of selecting critical features from the enormous set of available features and diagnosing heart disease are carried out. Feature selection is one of the most widely used pre-processing steps in classification problems. A modified differential evolution (DE) algorithm is used to perform feature selection for cardiovascular disease and optimization of selected features. Of the 10 available strategies for the traditional DE algorithm, the seventh strategy, which is represented by DE/rand/2/exp, is considered for comparative study. The performance analysis of the developed modified DE strategy is given in this paper. With the selected critical features, prediction of heart disease is carried out using fuzzy AHP and a feed-forward neural network. Various performance measures of integrating the modified differential evolution algorithm with fuzzy AHP and a feed-forward neural network in the prediction of heart disease are evaluated in this paper. The accuracy of the proposed hybrid model is 83%, which is higher than that of some other existing models. In addition, the prediction time of the proposed hybrid model is also evaluated and has shown promising results.

Hybrid differential evolution algorithm combined with heuristic correction and chaotic search for online energy-efficient optimization of server cluster

Server cluster has been widely used to improve the performance of various servers. How to optimize the deployment of each server in a cluster so as to minimize cluster’s power consumption while satisfying load capacity requirement is an urgent problem to be resolved. In this paper, we first formula te a typical energy-efficient optimization problem of server cluster as a constrained MIP (Mixed Integer Programming) problem. Then, aimed at the traits of the problem, we propose a hybrid DE (Differential Evolution) algorithm combined with heuristic correction and chaotic search to solve the problem. We introduce a correction operation to traditional DE algorithm, which bases on greedy idea to correct the individuals that do not satisfy constraints. Besides, we generate the initial population based on chaotic sequence so as to enhance population diversity, and implement chaotic search around the best individual of each generation so as to improve solving accuracy and accelerate convergence speed. The algorithm has high solving efficiency and can run online even when applied in large-scale server clusters. Simulation results verify the feasibility and effectiveness of the algorithm.