Differential Evolution Algorithm Research Articles

Population diversity control based differential evolution algorithm using fuzzy system for noisy multi-objective optimization problems

The objective measurements of the real-world optimization problems are mostly subject to noise which occurs due to several reasons like human measurement or environmental factors. The performance of the optimization algorithm gets affected if the effect of noise is higher than the negligible limit. The previous noise handling optimization algorithms use a large population size or multiple sampling at same region which increases the total count of function evaluations, and few methods work for a particular problem type. To address the above challenges, a Differential Evolution based Noise handling Optimization algorithm (NDE) to solve and optimize noisy bi-objective optimization problems is proposed. NDE is a Differential Evolution (DE) based optimization algorithm where the strategies for trial vector generation and the control parameters of DE algorithm are self-adapted using fuzzy inference system to improve the population diversity along the evolution process. In NDE, explicit averaging based method for denoising is used when the noise level is higher than negligible limit. Extending noise handling method enhances the performance of the optimization algorithm in solving real world optimization problems. To improve the convergence characteristics of the proposed algorithm, a restricted local search procedure is proposed. The performance of NDE algorithm is experimented using DTLZ and WFG problems, which are benchmark bi-objective optimization problems. The obtained results are compared with other SOTA algorithm using modified Inverted Generational Distance and Hypervolume performance metrics, from which it is confirmed that the proposed NDE algorithm is better in solving noisy bi-objective problems when compared to the other methods. To further strengthen the claim, statistical tests are conducted using the Wilcoxon and Friedman rank tests, and the proposed NDE algorithm shows significance over the other algorithms rejecting the null hypothesis.

Wireless sensor localization based on distance optimization and assistance by mobile anchor nodes: a novel algorithm.

Wireless sensor networks (WSNs) have wide applications in healthcare, environmental monitoring, and target tracking, relying on sensor nodes that are joined cooperatively. The research investigates localization algorithms for both target and node in WSNs to enhance accuracy. An innovative localization algorithm characterized as an asynchronous time-of-arrival (TOA) target is proposed by implementing a differential evolution algorithm. Unlike available approaches, the proposed algorithm employs the least squares criterion to represent signal-sending time as a function of the target position. The target node's coordinates are estimated by utilizing a differential evolution algorithm with reverse learning and adaptive redirection. A hybrid received signal strength (RSS)-TOA target localization algorithm is introduced, addressing the challenge of unknown transmission parameters. This algorithm simultaneously estimates transmitted power, path loss index, and target position by employing the RSS and TOA measurements. These proposed algorithms improve the accuracy and efficiency of wireless sensor localization, boosting performance in various WSN applications.

Advanced differential evolution for gender-aware English speech emotion recognition

Speech emotion recognition (SER) technology involves feature extraction and prediction models. However, recognition efficiency tends to decrease because of gender differences and the large number of extracted features. Consequently, this paper introduces a SER system based on gender. First, gender and emotion features are extracted from speech signals to develop gender recognition and emotion classification models. Second, according to gender differences, distinct emotion recognition models are established for male and female speakers. The gender of speakers is determined before executing the corresponding emotion model. Third, the accuracy of these emotion models is enhanced by utilizing an advanced differential evolution algorithm (ADE) to select optimal features. ADE incorporates new difference vectors, mutation operators, and position learning, which effectively balance global and local searches. A new position repairing method is proposed to address gender differences. Finally, experiments on four English datasets demonstrate that ADE is superior to comparison algorithms in recognition accuracy, recall, precision, F1-score, the number of used features and execution time. The findings highlight the significance of gender in refining emotion models, while mel-frequency cepstral coefficients are important factors in gender differences.

Improved multi-objective differential evolution algorithm and its application in the capacity configuration of urban rail photovoltaic hybrid energy storage systems

With the rapid expansion of urban rail transit, energy demand is continuously increasing. Integrating photovoltaic (PV) systems into hybrid energy storage systems (HESS) to form a rail transit PV hybrid energy storage system (RTPHESS) is an effective energy-saving and emission reduction measure. However, the integration changes the energy composition of the rail power supply system, making traditional HESS capacity configuration schemes inadequate to meet the stability requirement. In light of this, an RTPHESS model was established aiming at suppressing traction network voltage fluctuations and minimizing the total life-cycle cost of HESS. The model introduces traction network voltage fluctuation rate and HESS total life-cycle cost as evaluation objectives. Based on this, an improved multi-objective differential evolution algorithm (IMODE) was proposed to optimize HESS capacity. Optimal point set theory was used for population initialization to enhance the uniformity and diversity of the initial population, thereby improving global optimization capabilities. During the mutation phase, a hybrid Gaussian-Cauchy mutation strategy was introduced to improve both global and local search capabilities. The proposed algorithm's effectiveness was evaluated using IGD, SP, MS, and ER metrics on eight benchmark test functions with different characteristics, and compared with SaMODE_LS, MODE, MOPSO, MOALO, and MOMGA. Finally, IMODE was applied to the capacity configuration of RTPHESS. The results demonstrate that IMODE outperforms traditional algorithms in terms of accuracy and stability, reducing traction network voltage fluctuations by approximately 4.1 % and lowering the total life-cycle cost to 3,201,100 yuan.

Metaheuristic optimization algorithms-based prediction modeling for titanium dioxide-Assisted photocatalytic degradation of air contaminants

Airborne contaminants pose significant environmental and health challenges. Titanium dioxide (TiO2) has emerged as a leading photocatalyst in the degradation of air contaminants compared to other photocatalysts due to its inherent inertness, cost-effectiveness, and photostability. To assess its effectiveness, laboratory examinations are frequently employed to measure the photocatalytic degradation rate of TiO2. However, this approach involves time-consuming requirements, labor-intensive tasks, and high costs. In literature, ensemble or standalone models are commonly used for assessing the performance of TiO2 photocatalytic degradation of water and air contaminants. Nonetheless, the application of metaheuristic hybrid models has the potential to be more effective in predictive accuracy and efficiency. Accordingly, this research utilized hybrid machine learning (ML) algorithms to estimate the photo-degradation rate constants of organic air pollutants using TiO2 nanoparticles and exposure to ultraviolet light. Six metaheuristics optimization algorithms, namely, nuclear reaction optimization (NRO), differential evolution algorithm (DEA), human felicity algorithm (HFA), lightning search algorithm (LSA), Harris hawks algorithm (HHA), and tunicate swarm algorithm (TSA) were combined with random forest (RF) technique to establish the hybrid models. A database of 200 data points was acquired from experimental studies for model training and testing. Furthermore, multiple statistical indicators and 10-fold cross-validation were employed to examine the established hybrid model's accuracy and robustness. The TSA-RF model demonstrated superior prediction accuracy among the six suggested models, achieving an impressive correlation (R) of 0.90 and a lower root mean square error (RMSE) of 0.25. In contrast, the HFA-RF, HHA-RF, and NRO-RF models exhibited a slightly lower R-value of 0.88, with RMSE scores of 0.32. The DEA-RF and LSA-RF models, while effective, showed a marginally lower R-value of 0.85, with RMSE values of 0.45 and 0.44, respectively. Moreover, the SHapley Additive exPlanation (SHAP) results indicated that the degradation rates of air contaminants through photocatalysis were most notably influenced by factors such as the reactor sizes, photocatalyst dosage, humidity, and intensity.

Performance analysis of the temperature-upgraded flash-driven low-temperature advanced natural circulation heating reactor system

To address the current deficiencies in outlet temperature and thermal power of low-temperature heating reactors while ensuring safety and economic viability, this study introduces the Temperature-Upgraded Flash-driven Low-temperature Advanced Natural Circulation Heating Reactor (TU-FLANC). The FLANC system innovatively utilizes the flashing phenomenon of the coolant in the rising channel to significantly increase the coolant circulation flow rate and thus enhance thermal power at atmospheric pressure. The TU system employs an Absorption Heat Pump (AHP) to upgrade the temperature of the reactor’s output heat. The two systems are interconnected via a Coupled System Heat Exchanger (CSHEX), achieving an upgrade in reactor thermal power and outlet temperature at atmospheric pressure. To evaluate the performance of the TU-FLANC system, a mathematical model of the system was established, and a computational program was developed. The impact of key parameters such as evaporator temperature, condenser temperature, and solution concentration on system performance was analyzed. The results indicate that the evaporator temperature and solution concentration have the most significant impact on the system’s coefficient of performance (COP) and the coefficient of performance considering pump work (COPW). Through Differential Evolution (DE) algorithm optimization, the optimal solution concentration combinations were determined to maximize COP and COPW under different temperature upgrade demands. For a temperature upgrade demand of 50 °C, the optimal solution concentration combinations are 40.02 % and 57.48 %, with corresponding COP and COPW values of 0.5282 and 0.4886, respectively. The research findings highlight the significant innovative potential of the TU-FLANC system in enhancing heat power and outlet temperature.

Knowledge-assisted differential evolution based non-contact voltage measurement for multiconductor systems in smart grid

Multiconductor systems, such as overhead lines and multicore cables, are widely used in smart grids for their reliable power transmission capabilities. However, measuring the voltage of individual conductors in these systems has been challenging despite their promising applications. This paper proposes a novel framework to address this issue by utilizing a low-cost electric field (EF) sensor array and a knowledge-assisted differential evolution algorithm. The framework involves designing an annular EF sensor array to capture EF information around the multiconductor systems while ensuring its anti-interference capabilities through grounding and balanced electrodes. Furthermore, an optimization problem is formulated to reflect the model accuracy, and a knowledge-assisted differential evolution algorithm is proposed to optimize the voltage values and conductor positions by leveraging knowledge about the conductor positions and EF distribution. The use of this knowledge is expected to generate promising initial solutions for accelerating the optimization process. The proposed framework is experimentally validated, and the results demonstrate the robustness and accuracy of the EF sensor array and algorithm in obtaining the voltage of individual conductors in multiconductor systems.

A multi-task evolutionary algorithm for solving the problem of transfer targets

In recent years, multi-task optimisation, aimed at handling multiple optimisation problems simultaneously, has received great attention in the field of evolutionary algorithms. Research on multi-task evolutionary algorithms mostly focuses on solving the problem of effective transfer, which usually transfers the extracted effective knowledge to the matching selection stage or environment selection stage. However, the impact of these transfer targets on algorithm performance is rarely studied. To solve the problem of transfer targets, we propose a multi-task evolutionary algorithm with a hybrid knowledge transfer strategy (MTEA-HKTS). Firstly, we determined three transfer targets and designed knowledge transfer strategies for each stage by analysing the population changes in the differential evolution algorithm. Secondly, a knowledge transfer strategy is devised to control the transfer targets. Finally, we designed a new archive update strategy that uses a distribution model constructed for recent generations of populations to calculate gene similarity. The experimental results on the multi-task benchmark problems show that the transfer targets affect the performance of the multi-task optimisation algorithm, and verify the superiority of the proposed MTEA-HKTS algorithm.

Memetic discrete differential evolution with domain knowledge for blocking scheduling distributed flow shop with lot-streaming constraints

This article addresses the blocking distributed flow shop scheduling problem with lot-streaming (BDFSPL) with the objective of minimizing the maximum completion time, or makespan. In many realistic conditions, a job is divided into multiple continuous processed sublots. This pattern achieves operation overlap on consecutive machines and decreases the completion time of the whole job. Moreover, there are no buffers between machines, potentially causing finished sublots to be blocked on the current machine until the downstream machine is available. This is the first study to consider distributed production, blocking constraints, and lot-streaming together. To address this problem, we formulate a mathematical model for BDFSPL and propose a memetic discrete differential evolution (MDDE) algorithm. First, the MDDE algorithm partitions the entire population into three subpopulations based on solution quality, and each subpopulation evolves independently through adaptive scale and parameter adjustment. Second, four discrete mathematical operators are proposed to generate new individuals, and based on these operators, discrete mutation, crossover, and selection operations of MDDE are designed. Additionally, a crucial path-based local search strategy, informed by the domain knowledge of the best individual, is embedded into MDDE to enhance the exploitation capacity. To validate MDDE’s effectiveness, comprehensive experiments with several related algorithms on extensive testing instances are carried out, and the parameters of the MDDE algorithm are calibrated by employing a design of experiments. The comparison results demonstrate the effectiveness and efficiency of the proposed MDDE algorithm for the BDFSPL.

Differential Evolution Algorithm with Three Mutation Operators for Global Optimization

Differential evolution algorithm is a very powerful and recently proposed evolutionary algorithm. Generally, only a mutation operator and predefined parameter values of differential evolution algorithm are utilized to solve various optimization problems, which limits the performance of the algorithm. In this paper, six commonly used mutation operators are divided into three categories according to their own features. A mutation pool is established based on the three categories. A parameter pool with three predefined values is designed. During evolution, three mutation operators are randomly chosen from the three categories, and three parameter values are also randomly selected from the parameter pool. The three groups of mutation operators and parameter values are employed to produce trial vectors. The proposed algorithm makes good use of different mutation operators. Three recently proposed differential evolution variants and three non-differential evolution algorithms are used to make comparisons on the 29 testing functions from CEC. The experimental results have demonstrated that the proposed algorithm is very competitive. The proposed algorithm is utilized to solve three real applications, and the results are superior.

A modified dispersed frequency and phase consensus algorithm based on differential evolution and credibility weighting matrix

In distributed antenna array systems, accurate synchronization of the frequency and phase of the transmission signals among subarrays is a premise for beamforming. To solve this problem, a modified dispersed frequency and phase consensus (MDFPC) algorithm, which is based on differential evolution (DE) and the credibility weighting matrix, is proposed in this paper. DE algorithm is adopted to optimize the mixing matrix of MDFPC algorithm, and the convergence speed of consensus algorithm can be improved. Moreover, Lanczos method is adopted to calculate the fitness of individuals during optimization, thus the computation amount of the eigenvalue decomposition of the large-scale, sparse and symmetric mixing matrix can be effectively reduced. In addition, the influence of the transmission distance between subarrays on the received Signal-to-Noise Ratio (SNR) is considered, and the credibility weighting matrix can be obtained. Then the contribution of low-credible frequency and phase messages to the iterative updated values can be decreased by the credibility weighting matrix, thus more accurate frequency and phase updated values can be obtained in each iteration. It is shown from simulation results that the proposed algorithm can further reduce the phase synchronization error by at least 8% and achieve at least 18% convergence speed improvement compared to dispersed frequency and phase consensus (DFPC) algorithm.

Research on Distortion Control in Off-Axis Three-Mirror Astronomical Telescope Systems

With off-axis reflection systems with specific distortion values serving as objectives or collimators, it is possible to compensate and correct for spectral line bending in spectroscopic instruments. However, there is limited research on the precise control of distortion, which poses particular challenges in large field-of-view optical systems. This paper presents a method for controlling distortion in off-axis reflection systems. Based on Seidel aberration theory and the relationship between distortion wavefront error and primary ray error, we construct objective functions with structural constraints and aberration constraints. The initial structure with specific distortion values is then solved using a differential evolution algorithm. The effectiveness and reliability of this method are verified through the design of an off-axis three-reflection system. The method provided in this study facilitates the design of remote sensing instruments.

Enhanced Pansharpening Using Curvelet Transform Optimized by Multi Population Based Differential Evolution

In this study, a pansharpening process was conducted to merge the color information of low-resolution RGB images with the details of high-resolution panchromatic images to obtain higher quality images. During this process, weight optimization was performed using the Curvelet Transform method and the Multi Population Based Differential Evolution (MDE) algorithm. The proposed method was tested on Landsat ETM satellite image. For Landsat ETM data, the RGB images have a resolution of 30m, while the panchromatic images have a resolution of 15m. To evaluate the performance of the study, the proposed MDE-optimized Curvelet Transform-based pansharpening method was compared with classical IHS, Brovey, PCA, Gram-Schmidt and Simple Mean methods. The comparison process employed metrics such as RMSE, SAM, COC, RASE, QAVE, SID, and ERGAS. The results indicate that the proposed method outperforms classical methods in terms of both visual quality and numerical accuracy.

Parameters Estimation of Photovoltaic Modules Using Differential Evolution Metaheuristic Method

This paper presents the analysis of the differential evolution (DE) metaheuristic method, which is used to estimate some parameters employed in the equivalent electrical circuit that represents the photovoltaic (PV) cell model. The DE algorithm is an evolutionary algorithm that can be designed to search global optimal points with fast convergence time and present accurate results, requiring few control variables to be set. The accuracy of reproducing the characteristics of the PV module depends on the knowledge of some PV cell model parameters, such as series and shunt resistances, diode ideality factor, and diode reverse saturation current. Once the referred parameters are not usually given in the manufacturers' datasheet, their determination can be achieved by the DE algorithm, employing data and the current-voltage (I-V) characteristic curve provided by the PV module manufacturers. The technique is designed to minimize the error between the reference I-V curve and the I-V curve reproduced by the DE algorithm. Through simulation results, the feasibility of the DE algorithm to estimate the desired parameters of a PV cell is validated, and the algorithm's performance to reach the best solution with fast convergence and a small iteration number is evaluated.

Research on Active Disturbance Rejection Control of Small Modular Reactor Once-Through Steam Generator Based on Differential Evolution Optimization Algorithm

The pressure control of once-through steam generator (OTSG) is critical for the operation and safety of small modular reactors. However, the dynamics of the OTSG are quite nonlinear, time varying, and uncertain. Classical control methods face significant challenges in keeping the pressure within acceptable limits in an environment with frequent load variations and multiple sources of external disturbances. In this paper, a robust control strategy based on active disturbance rejection control (ADRC) optimized by the differential evolution (DE) algorithm is proposed to satisfy the requirements of steam pressure control in an optimum and efficient way. First, a lumped parameter model for the OTSG is developed based on the notion of moving boundaries and linearized to introduce a transfer function model for control design purposes. Then a feedforward cascade control system based on an ADRC controller and a proportional integral differential (PID) controller is designed, which mainly consists of a pressure ADRC controller, a feedwater PID controller, and a feedforward compensator. To improve the pressure control performance and parameter tuning efficiency of the OTSG control system, a DE algorithm is applied to optimize the ADRC parameters, and the frequency domain and time domain characteristics are compared with particle swarm optimization and the genetic algorithm. Transient simulation experiments were used to evaluate the control performance at 100%, 50%, and 25% power levels, respectively. Moreover, a performance robustness criterion is proposed to demonstrate the robust stability of the ADRC, and the robustness metric is compared with that of the PID control schemes. The simulation results show that DE-ADRC control strategy has better set point tracking, interference rejection, and robust stability than DE-PID control strategy.

Experimental, modeling and optimisation of adipic acid reactive extraction using ionic liquids

Adipic acid (hexanedioic acid, AA) can be utilised as an essential monomer in the production of nylon-6,6 (75 %), but also for urethane foams, fibers, elastomers, tire reinforcements, and synthetic lubricants. Considerable work has been done to develop sustainable biosynthetic processes for its manufacture, especially for adipic acid efficient separation (one of the main challenges for industrialisation). As for scale-up, process optimisation, and thorough engineering mathematical models that describe the system efficiently are required, this study proposes mathematical models for a reactive extraction using ionic liquids as extractants for adipic acid separation to improve the biosynthetic route’s sustainability, efficiency, and environmental performance. Heptane as the solvent and 117.8 g/L [P6,6,6,14][Phos] as the extractant at 2.8 pH of the aqueous phase were the optimum mixture for reactive extraction, resulting in an extraction yield of 97.55 % for adipic acid. The process was modeled using an artificial neural network optimised with a differential evolution algorithm. The optimal model structure had one hidden layer with 20 neurons, and its performance in the testing phase was: explained variance score of 0.974, mean absolute error of 1.917, and coefficient of determination of 0.974.

Intelligent Indoor Layout Design Based on Interactive Genetic and Differential Evolution Algorithms

Intelligent Indoor Layout Design Based on Interactive Genetic and Differential Evolution Algorithms

Novel Hybrid Crayfish Optimization Algorithm and Self-Adaptive Differential Evolution for Solving Complex Optimization Problems

This study presents the Hybrid COASaDE Optimizer, a novel combination of the Crayfish Optimization Algorithm (COA) and Self-adaptive Differential Evolution (SaDE), designed to address complex optimization challenges and solve engineering design problems. The hybrid approach leverages COA’s efficient exploration mechanisms, inspired by crayfish behaviour, with the symmetry of SaDE’s adaptive exploitation capabilities, characterized by its dynamic parameter adjustment. The balance between these two phases represents a symmetrical relationship wherein both components contribute equally and complementary to the algorithm’s overall performance. This symmetry in design enables the Hybrid COASaDE to maintain consistent and robust performance across a diverse range of optimization problems. Experimental evaluations were conducted using CEC2022 and CEC2017 benchmark functions, demonstrating COASaDE’s superior performance compared to state-of-the-art optimization algorithms. The results and statistical analyses confirm the robustness and efficiency of the Hybrid COASaDE in finding optimal solutions. Furthermore, the applicability of the Hybrid COASaDE was validated through several engineering design problems, where COASaDE outperformed other optimizers in achieving the optimal solution.

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.

Monitoring soil nutrients using machine learning based on UAV hyperspectral remote sensing

ABSTRACT Unmanned aerial vehicles (UAV) are rapidly evolving experimental platforms that play an important role in remote sensing. In this study, we investigated a machine learning method for monitoring soil nutrient content using UAV hyperspectral remote sensing. We employed machine learning techniques for feature extraction and soil hyperspectral information modelling. In contrast to traditional mathematical transformation methods, we adopted a combination of random forest and differential evolution algorithms to rank the weights of individual hyperspectral data, thereby obtaining a series of spectral feature subsets for soil organic matter, total nitrogen and available phosphorus and potassium. Furthermore, the analytic hierarchy process was used for weight analysis, and the characteristic bands of the four soil nutrients were successfully extracted. Next, a quantitative inversion model based on a back-propagation (BP) neural network was established to estimate soil nutrient content, with determination coefficients higher than 0.7 and 0.6 for the modelling and verification sets, respectively. The relative percent difference values were greater than 2, among which the highest was for available potassium, with determination coefficients of 0.95 and 0.84 for the modelling and verification sets, respectively. In addition, visualization distribution maps of soil nutrients were obtained by combining the BP model and original reflectance hyperspectral images, and the comparisons of content histograms showed a relatively consistent distribution between the sampling and inversion points. The results verified the effectiveness of the combined machine learning method for large-scale and high-precision monitoring and visualization of soil nutrient contents.