Standard Differential Evolution Research Articles

Application of Big Data in College Student Education Management Based on Data Warehouse Technology and Integrated Learning

Integrated learning has attracted much attention from industry and academia. In the new era, colleges and universities need to discuss information management in light of actual conditions, integrate different data in each information system into the same database, so as to form a data warehouse based on the integrated database which can truly reflect the historical changes of data and provides support for managers' decision-making. This paper analyzes the clustering effect of standard differential evolution algorithm, improved differential evolution algorithm and K-means algorithm. The algorithm is tested using Iris and Wine database marts, the results show that the K-means algorithm is a relatively poor algorithm and its accuracy is significantly lower than the other two. Based on big data, multi-factor interactive variance analysis technology is used to analyze different data indicators and influencing factors. Therefore, colleges and universities can use the database to better understand the problems and advantages in management, thus to improve management efficiency and teaching level.

Optimized quantization parameter selection for video-based point cloud compression

Point clouds are sets of points used to visualize three-dimensional (3D) objects. Point clouds can be static or dynamic. Each point is characterized by its 3D geometry coordinates and attributes such as color. High-quality visualizations often require millions of points, resulting in large storage and transmission costs, especially for dynamic point clouds. To address this problem, the moving picture experts group has recently developed a compression standard for dynamic point clouds called video-based point cloud compression (V-PCC). The standard generates two-dimensional videos from the geometry and color information of the point cloud sequence. Each video is then compressed with a video coder, which converts each frame into frequency coefficients and quantizes them using a quantization parameter (QP). Traditionally, the QPs are severely constrained. For example, in the low-delay configuration of the V-PCC reference software, the quantization parameter values of all the frames in a group of pictures are set to be equal. We show that the rate-distortion performance can be improved by relaxing this constraint and treating the QP selection problem as a multi-variable constrained combinatorial optimization problem, where the variables are the QPs. To solve the optimization problem, we propose a variant of the differential evolution (DE) algorithm. Differential evolution is an evolutionary algorithm that has been successfully applied to various optimization problems. In DE, an initial population of randomly generated candidate solutions is iteratively improved. At each iteration, mutants are generated from the population. Crossover between a mutant and a parent produces offspring. If the performance of the offspring is better than that of the parent, the offspring replaces the parent. While DE was initially introduced for continuous unconstrained optimization problems, we adapt it for our constrained combinatorial optimization problem. Also, unlike standard DE, we apply individual mutation to each variable. Furthermore, we use a variable crossover rate to balance exploration and exploitation. Experimental results for the low-delay configuration of the V-PCC reference software show that our method can reduce the average bitrate by up to 43% compared to a method that uses the same QP values for all frames and selects them according to an interior point method.

Meta‐heuristic optimization techniques for scheduling in multiple‐input multiple‐output multiple‐access channel system

SummaryIn a highly dense multiple‐input multiple‐output (MIMO) communication system, proper resource allocation is exceedingly challenging. The simultaneous selection of antennas at the base‐station (BS) and scheduling of users in an uplink multiple access channel (MAC) system add up to the signal processing load in the MIMO wireless system. The method chosen for combining the user scheduling and antenna selection must have a very low computational complexity. However, the exhaustive search algorithm (ESA), which achieves the best sum‐rate capacity in a MIMO‐MAC system, has a very high level of complexity. In this paper, we use a metaheuristic‐based optimization algorithms to optimize the sum‐rate capacity in a MAC system with significantly less computational complexity. First, we use the beluga whale optimization (BWO) metaheuristic method to solve the optimization problem. The BWO is a swarm‐based algorithm that draws inspiration from beluga whale behavior. An improved BWO (iBWO) is also presented and is utilized for the same optimization challenge. The proposed iBWO scheme improves the search capability of the algorithm and thereby ensures better exploration and exploitation capabilities of the beluga whales. We compare the performance of these algorithms with a standard differential evolution (DE) algorithm. The simulation results demonstrate that the proposed iBWO is a very competitive meta‐heuristic algorithm for solving optimization problems. The proposed iBWO algorithm achieves near optimal throughput in a MIMO‐MAC system. Also, the computational complexity related to the suggested optimization technique in a MIMO‐MAC system is found to be very less compared with the complexity related to ESA.

The Importance of Being Constrained: Dealing with Infeasible Solutions in Differential Evolution and Beyond.

We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple bound constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours in terms of performance, disruptiveness, and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants, on a special test function and the BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem dimensionality. Differential Evolution is not at all special in this regard-there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the heuristic optimisation community to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we refer to as the strategy of dealing with infeasible solutions. This component needs to be consistently: (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on an algorithm's performance in a wider sense (i.e., convergence time, robustness, etc.), and (c) included in the (automatic) design of algorithms. All of these should be done even for problems with bound constraints.

Longitudinal vibration estimation of a mine hoist using a hybrid signal fusion method combining UKF, ND and improved DE

The monitoring of cage longitudinal vibration can directly indicate the operational status of mine hoists. However, it is always challenging to collect the sensor signals of moving cages with high dynamic characteristics in real time from complex working environments using traditional monitoring methods. In this study, a more practical hybrid signal fusion approach is proposed to realize estimation of cage longitudinal vibration from a low sampling rate acceleration acquisition signal and a low cost encoder signal for state estimation. A nonlinear differentiator is applied to extract encoder differential signals and expand observation variables. An unscented Kalman observer based on nonlinear mine hoist model is designed to estimate the unknown state. To overcome the influence of the uncertain parameters, an improved differential evolution (DE) algorithm combining parameter adaptive method, reverse learning competition scheme and multiple parallel populations strategy is proposed to find unknown parameters of the observation model and autotune the parameters of the algorithms by using low sampling rate acceleration. Sensor data of the simulated experiment platform were collected and processed by the xPC system to validate the effectiveness of the proposed strategy. The experimental results showed that the improved DE (IDE) algorithm had a faster mean time for parameter tuning and the smallest fitness value compared to the standard DE, the particle swarm optimization algorithm and the genetic algorithm. Moreover, the longitudinal vibration estimation system, after parameter tuning by the IDE optimization algorithm, could achieve the purpose of signal estimation, with a smaller estimation error and a better estimation effect.

An integrated differential evolution algorithm for reconfigurable manufacturing systems

Product platforms consider an effective strategy to empower mass customization (MC) in a reconfigurable manufacturing system (RMS) to have the capacity to reconfigure the hardware and manage resources at all organisational and functional levels. This enables quick modification of production functions in reaction to unforeseen changes in the market or regulatory requirements. Although several platform formation and assembly line techniques have emerged to satisfy the increased demand for MC and enable the manufacture of products with high variety, they also increase the system’s complexity and make it less cost-efficient as variety increases. This study aims to minimize the complexity of a production system by reducing the number of separate components in different production processes. An efficient approach that integrates the Median-Joining Phylogenetic Networks (MJPN) classification tool and differential evolution (DE) in one unified framework is developed to do that. The proposed framework uses the concept of the package to group separate components that are often employed jointly to produce particular products and allows the use of the ‘all-unit discount policy’, which applies discounts to the purchasing costs of a specific quantity of materials/components. Finally, two case studies are applied to validate the proposed MJPN-DE in different dimensions. The experimental results show that applying the proposed package model saves 57.5% of the purchasing costs of components and 41.35% average setup costs compared to MJPN- and non-platform-based models and increases the postponement effectiveness of the obtained layout by 41.51% and 74.11% compared with two other layout strategies. In algorithmic comparisons, the results of comparing MJPN-DE with standard DE and genetic algorithm (GA) show an enhanced performance of MJPN-DE where the total production cost is reduced in the small case study by 63.34% and 38.52%, and in the large case study by 16.90% and 11.51%, respectively.

Application of adaptive improved DE algorithm based on multi-angle search rotation crossover strategy in multi-circuit testing optimization

Abstract This study based on the standard differential evolution (DE) algorithm was carried out to address the issues of control parameter imprinting, mutation process, and crossover process in the standard DE algorithm as well as the issue of multidimensional circuit testing optimization. A rotation control vector was introduced to expand the search range in the poor strategy to the circumference range of the individual and the parent target individual, and a rotation crossover operator and a binomial poor operator were combined. Finally, an improved adaptive DE algorithm based on a multi-angle search rotation crossover strategy was obtained. The research will improve the DE algorithm to optimize the testing of multidimensional circuits. It can be noted that the improved average precision value is 0.9919 when comparing the precision recall curves of the DE algorithm before and after the change, demonstrating a significant improvement in accuracy and stability. The fitness difference of the 30-dimensional problem is discovered to be between 0.25 × 103 and 0.5 × 103 by comparing the box graphs of the 30-dimensional problem with that of the 50-dimensional problem. On the 50-dimensional problem, when calculating the F4–F10 function, the fitness difference of the improved DE algorithm is 0.2 × 104–0.4 × 104. In summary, the improved DE algorithm proposed in this study compensates for the shortcomings of traditional algorithms in complex problem calculations and has also achieved significant optimization results in multidimensional circuit testing.

Gene Targeting Differential Evolution: A Simple and Efficient Method for Large-Scale Optimization

Large-scale optimization problems (LSOPs) are challenging because the algorithm is difficult in balancing too many dimensions and in escaping from trapped bottleneck dimensions. To improve solutions, this paper introduces targeted modification to the certain values in the bottleneck dimensions. Analogous to gene targeting (GT) in biotechnology, we experiment on targeting the specific genes in candidate solution to improve its trait in differential evolution (DE). We propose a simple and efficient method, called GT-based DE (GTDE), to solve LSOPs. In the algorithm design, a simple GT-based modification is developed to perform on the best individual, comprising probabilistically targeting the location of bottleneck dimensions, constructing a homologous targeting vector, and inserting the targeting vector into the best individual. In this way, all the bottleneck dimensions of the best individual can be probabilistically targeted and modified to break the bottleneck and to provide global guidance for more optimal evolution. Note that the GT is only performed on the globally best individual and is just carried out as a simple operator that is added to the standard DE. Experimental studies compare the GTDE with some other state-of-the-art large-scale optimization algorithms, including the winners of CEC2010, CEC2012, CEC2013, and CEC2018 competitions on large-scale optimization. The results show that the GTDE is efficient and performs better than or at least comparable to the others in solving LSOPs.

Differential Evolution and Engineering Problems

In this paper, the performance of the Differential Evolution algorithm is evaluated when solving real-world problems. A Set of 13 engineering optimisation problems was selected from the fields of mechanics and industry to illustrate the usability of the Differential Evolution algorithm. Twelve variants of the standard Differential Evolution with various settings of the control parameters are compared with 19 state-of-the-art adaptive variants of this algorithm. The results are analysed statistically to achieve significant differences. Three variants of adaptive Differential Evolution provided better results compared to other algorithms. Some adaptive variants of Differential Evolution perform significantly worse than the original Differential Evolution with the fixed setting of the control parameters.

Joint decision-making of virtual module formation and scheduling considering queuing time

Formation and scheduling are the most important decisions in the virtual modular manufacturing system; however, the global performance optimization of the system may be sacrificed via the superposition of two independent decision-making results. The joint decision of formation and scheduling is very important for system design. Complex and discrete manufacturing enterprises such as shipbuilding and aerospace often comprise multiple tasks, processes, and parallel machines, resulting in complex routes. The queuing time of parts in front of machines may account for 90% of the production cycle time. This study established a weighted allocation model of a formation-scheduling joint decision problem considering queuing time in system. To solve this nondeterministic polynomial (NP) problem, an adaptive differential evolution-simulated annealing (ADE-SA) algorithm is proposed. Compared with the standard differential evolution (DE) algorithm, the adaptive mutation factor overcomes the disadvantage that the scale of DE’s differential vector is difficult to control. The selection strategy of the SA algorithm compensates for the deficiency that DE’s greedy strategy may fall into a local optimal solution. The comparison results of four algorithms of a series of random examples demonstrate that the overall performance of ADE-SA is superior to the genetic algorithm, and average iteration, maximum completion time, and move time are 24%, 11%, and 7% lower than the average of other three algorithms, respectively. The method can generate the joint decision-making scheme with better overall performance, and effectively identify production bottlenecks through quantitative analysis of queuing time.

Convolutional neural network optimized by differential evolution for electrocardiogram classification.

The Coronavirus disease 2019, or COVID-19, has shifted the medical paradigm from face-to-face to telehealth. Telehealth has become a vital resource to contain the virus spread and ensure the continued care of patients. In terms of preventing cardiovascular diseases, automating electrocardiogram (ECG) classification is a promising telehealth intervention. The healthcare service ensures that patient care is appropriate, comfortable, and accessible. Convolutional neural networks (CNNs) have demonstrated promising results in ECG categorization, which require high accuracy and short training time to ensure healthcare quality. This study proposes a one-dimensional-CNN (1D-CNN) arrhythmia classification based on the differential evolution (DE) algorithm to optimize the accuracy of ECG classification and training time. The performance of 1D-CNNs of different activation functions are optimized based on the standard DE algorithm. Finally, based on MIT-BIH and SCDH arrhythmia databases, the performances of optimized and unoptimized 1D-CNN are compared and analysed. Results show that the 1D-CNN optimized by the DE has higher accuracy in heartbeats classification. The optimized 1D-CNN improves from 97.6% to 99.5% on MIT-BIH and from 80.2% to 88.5% on SCDH. Therefore, the optimized 1D-CNN shows improvements of 1.9% and 8.3% in the two datasets, respectively. In addition, compared with the unoptimized 1D-CNN based on the same parameter settings, the optimized 1D-CNN has less training time. Under the conditions of ReLU function and 10 epochs, the training takes 9.22s on MIT-BIH and 10.35s on SCDH, reducing training time by 67.2% and 64.2%, respectively.

Research on PID Controller of Excavator Electro-Hydraulic System Based on Improved Differential Evolution

An electrical hydraulic control system (electro-hydraulic system) is thought to be a key component in excavator operation systems. Control methods with fixed parameters may not yield optimal system performances because a hydraulic system has various nonlinear uncertainties due to the leakage and compressibility of the fluid medium. Hence, a novel PID controller based on improved differential evolution (IDE) is introduced to excavator electro-hydraulic systems for interconnected hydraulic systems. The proposed algorithm not only adjusts the PID parameters of the different working conditions but also adjusts the scaling factor and crossover probability. Then, the proposed PID controller based on IDE and the excavator bucket control system are modeled and simulated on the MATLAB simulation platform. The simulation results demonstrate that the proposed controller has better performance in settling time, rise time, and convergence speed compared to the PID controller based on standard differential evolution and the Ziegler–Nichols (ZN) PID controller with a novel object function. Eventually, the IDE-PID controller is assessed on a 23-ton excavator, and good transient behavior and trajectory accuracy are obtained in comparison to the SDE-PID controller.

An optimal design of current conveyors using a hybrid-based metaheuristic algorithm

<span lang="EN-US">This paper focuses on the optimal sizing of a positive second-generation current conveyor (CCII+), employing a hybrid algorithm named DE-ACO, which is derived from the combination of differential evolution (DE) and ant colony optimization (ACO) algorithms. The basic idea of this hybridization is to apply the DE algorithm for the ACO algorithm’s initialization stage. Benchmark test functions were used to evaluate the proposed algorithm’s performance regarding the quality of the optimal solution, robustness, and computation time. Furthermore, the DE-ACO has been applied to optimize the CCII+ performances. SPICE simulation is utilized to validate the achieved results, and a comparison with the standard DE and ACO algorithms is reported. The results highlight that DE-ACO outperforms both ACO and DE.</span>

Cε-LDE: A lightweight variant of differential evolution algorithm with combined ε constrained method and Lévy flight for constrained optimization problems

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named Cε-LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed Cε-LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of Cε-LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that Cε-LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme.

RESEARCH ON FUZZY SCHEDULING OF CLOUD COMPUTING TASKS BASED ON HYBRID SEARCH ALGORITHMS AND DIFFERENTIAL EVOLUTION

In the process of task scheduling, due to the large search space of resources, it takes a long time to allocate appropriate resources for tasks, which results in the increase of execution time and execution cost of algorithms. For this reason, this paper proposes a cloud computing task fuzzy scheduling strategy based on hybrid search algorithm and differential evolution, which incorporates the classification based on normal distribution and a variety of mutation strategies on the basis of standard differential evolution algorithm. In mutation strategy, the individual difference vector assigns priority to each task and arranges tasks according to resource allocation rules. It improves the slow convergence speed and easy to fall into local optimum of standard difference algorithm, and can effectively solve the task scheduling problem of cloud computing. A cloud computing task scheduling algorithm with time and cost constraints is designed and tested in a simulation environment. The experimental results show that the algorithm can not only shorten the task processing time and reduce the execution cost, but also fully satisfy the users’ actual quality of service requirements by adjusting the weights of time and cost factors.

Adaptation of Population Size in Differential Evolution and Its Effects on Localization of Target Nodes

The differential evolution (DE) is a well known population-based evolutionary algorithm that has shown capabilities for solving real-world problems such as resource allocation, multicast routing, and localization of target nodes. However, the accuracy of the DE, like other evolutionary algorithms, depends on the settings of its control parameters. The localization of target nodes is highly nonlinear and multi-modal, which may trap the DE in a local optimum. A local optimum may be avoided by a proper selection of the control parameters. One of the key control parameters is the population size (PS), which affects directly the localization accuracy and computational complexity. Finding an adequate PS throughout the evolution process is a challenging task. Even if an adequate PS is found it may not be the adequate PS anymore when the scenario of a problem changes. Although several approaches have been proposed for adapting the PS, they have not been evaluated when solving the localization problem. In this paper, a comprehensive comparison in terms of accuracy and computational demand is conducted among the state-of-the-art PS adaptation techniques when employed with the DE for solving the localization problem of target nodes in various scenarios.We also propose three new PS adaptation techniques, namely, exponential, parabolic, and logistic reduction. The results from extensive numerical simulations show that, after setting the initial PS properly, there is no technique that outperforms the others in practically all the scenario of the localization problem. Additionally, the DE with the proposed techniques provides competitive localization accuracy with considerably less computational complexity. Specifically, The proposed approaches reduce the computational demand by approximately 50% over the standard DE in all the scenarios considered here.

Differential Evolution Algorithm with Hierarchical Fair Competition Model

This paper presents the study of differential evolution algorithm with hierarchical fair competition model (HFC-DE). HFC model is based on the fair competition of societal system found in natural world. In this model, the population is split into hierarchy and the competition is allowed between the hierarchical members. During evolution, the population members are allowed to move within the hierarchy levels. The standard differential evolution algorithm is used for population evolution. Experimentation has carried out to define the parameter for proposed model on test suit having unimodal problems and multi-model problems. After analyzing the results, the two variants of HFC-DE are proposed, named hierarchical fair competition model in differential evolution algorithm with replacement, I,e, HFCDE-R and hierarchical fair competition model in differential evolution algorithm without replacement, I,e, HFCDE-wR. The problem-solving capabilities of both algorithms are checked and the results are compared with differential evolution algorithm (DE) and other variants of DE. The early results are encouraging and motivating.

Overall Dynamic Optimization of Metal Mine Technical Indicators Considering Spatial Distribution of Ore Grade Using AADE

In optimizing the production of a metal mine, either the overall dynamic relations between technical indicators or the spatial distribution of the ore grade are usually considered, but few studies have considered both factors together. These two factors in combination have a greater effect on the optimization of mine production in terms of economic benefit and resource utilization than they do individually. We proposed an overall dynamic optimization model of technical indicators of metal mine production that considers the spatial distribution of the ore grade to better optimize the technical indicators and improve sustainable development of mineral resources. We incorporated an adaptive mutation strategy and adaptive control parameters into a differential evolution algorithm (AADE) in order to overcome the drawbacks of the differential evolution algorithm in solving this optimization model. The adaptive mutation strategy and adaptive control parameters were used to increase the rate of convergence and improve the search for a global maximum. To assess the performance of AADE, we used a real case and four test functions (the Sphere, Griewank, Rastrigin and Rosenbrock functions) in tests that compared AADE with a standard genetic algorithm, a standard differential evolution algorithm and the recently developed adaptive differential evolution algorithm. The results indicate that the optimization model we created is better aligned with mine production processes than current optimization models. In optimizing the technical indicators of metal mine production to maximize economic benefits, AADE performed significantly better than the other three algorithms tested in terms of convergence rate and global search ability.

Convergence Track Based Adaptive Differential Evolution Algorithm (CTbADE)

One of the challenging problems with evolutionary computing algorithms is to maintain the balance between exploration and exploitation capability in order to search global optima. A novel convergence track based adaptive differential evolution (CTbADE) algorithm is presented in this research paper. The crossover rate and mutation probability parameters in a differential evolution algorithm have a significant role in searching global optima. A more diverse population improves the global searching capability and helps to escape from the local optima problem. Tracking the convergence path over time helps enhance the searching speed of a differential evolution algorithm for varying problems. An adaptive powerful parameter-controlled sequences utilized learning period-based memory and following convergence track over time are introduced in this paper. The proposed algorithm will be helpful in maintaining the equilibrium between an algorithm's exploration and exploitation capability. A comprehensive test suite of standard benchmark problems with different natures, i.e., unimodal/multimodal and separable/non-separable, was used to test the convergence power of the proposed CTbADE algorithm. Experimental results show the significant performance of the CTbADE algorithm in terms of average fitness, solution quality, and convergence speed when compared with standard differential evolution algorithms and a few other commonly used state-of-the-art algorithms, such as jDE, CoDE, and EPSDE algorithms. This algorithm will prove to be a significant addition to the literature in order to solve real time problems and to optimize computational models with a high number of parameters to adjust during the problem-solving process.

Application of Improved Differential Evolution Algorithm in Solving Equations

The problem of finding roots of equations has always been an important research problem in the fields of scientific and engineering calculations. For the standard differential evolution algorithm cannot balance the convergence speed and the accuracy of the solution, an improved differential evolution algorithm is proposed. First, the one-half rule is introduced in the mutation process, that is, half of the individuals perform differential evolutionary mutation, and the other half perform evolutionary strategy reorganization, which increases the diversity of the population and avoids premature convergence of the algorithm; Second, set up an adaptive mutation operator and a crossover operator to prevent the algorithm from falling into the local optimum and improve the accuracy of the solution. Finally, classical high-order algebraic equations and nonlinear equations are selected for testing, and compared with other algorithms. The results show that the improved algorithm has higher solution accuracy and robustness, and has a faster convergence speed. It has outstanding effects in finding roots of equations, and provides an effective method for engineering and scientific calculations.