Differential Evolution Method Research Articles

Design, simulation and energy dissipation evaluating of a new lead shear damper

This study presents a novel design for a lead shear damper (LSD) that features lead blocks encased in laminated steel and rubber plates, intersected by X-shaped steel sticks. It combines the excellent energy dissipation and fatigue resistance of lead with the uniform yielding capabilities of X-shaped steel sticks along their height. Cyclic loading testing and fatigue tests are conducted in order to determine the mechanical properties of the LSD. The test results reveal that the LSD has a variable yielding force, and exhibits stiffness hardening when the damper's deformation direction deviates from the origin. However, when the deformation direction returns to the origin, there is no stiffness hardening observed, and the resistant force remains constant. Furthermore, this LSD can work effectively despite the failure of energy dissipation parts, which improves hysteretic energy dissipation under large deformation. In order to replicate the hysteretic behaviour, a uniaxial constitutive model is formulated and its parameters are determined by the utilization of the differential evolution approach, based on test data. The observed strong concurrence between the experimental and simulated hysteresis curves serves as compelling evidence for the efficacy of the differential evolution method. Meanwhile, a three-story building from the third-generation benchmark problem is employed as the testbed structure to examine the energy dissipation capacity of the developed dampers. Nonlinear seismic analysis on the benchmark model equipped with the proposed dampers is also conducted, and the results are compared to those fitted with conventional dampers, such as mild dampers and friction dampers. The findings of this study indicate that the performance of the LSD in reducing structural displacements is superior to that of mild dampers and friction dampers.

A metaheuristic algorithm for regulating virtual inertia of a standalone microgrid incorporating electric vehicles

AbstractModern electrical networks, particularly microgrids, have seen a sharp rise in acquiring non‐conventional sources. The inertia of the microgrid decreases drastically because RESs have been used in place of traditional synchronous generators. The reduced inertia negatively impacts the dynamics and performance of the microgrid with RESs, which decreases the microgrid's stability, especially in operation on an island. The primary purpose of this research study is to enhance the dynamic security of an island microgrid by merging an electric vehicle with a frequency control technique based on virtual inertia control. A Proportional Integral Derivative Filter Constant (PIDFN) controller optimally created using the Modified Differential Evolution (MDE) method served as the foundation for control in the virtual inertia control loop. The effectiveness of the MDE‐based PIDFN controller was examined considering the diverse operational scenarios are compared and contrasted with those of traditional methods Differential Evolution (DE) and Teaching Learning Based Optimization (TLBO)‐based PIDFN controllers. Real‐time wind and solar power statistics and random load fluctuations were incorporated to provide realistic simulation settings. The outcomes demonstrate that the MDE‐based PIDFN controller performs better in reference frequency tracking and reducing frequency disturbances than the other optimization strategies.

Reliable and adaptive computation offload strategy with load and cost coordination for edge computing

There are several important factors to consider in edge computing systems including latency, reliability, power consumption, and queue load. Task replication requires additional energy costs in mobile edge offloading scenarios based on master-slave replication for fault tolerance. Excessive task offloading may lead to a sharp increase in the total energy consumption of the system including replication costs. Conversely, new tasks cannot enter the waiting queue and are lost, resulting in reliability issues. This paper proposes an adaptive task offloading strategy for balancing the edge node queue load and offloading cost (Lyapunov and Differential Evolution based Offloading schedule strategy, LDEO). The LDEO strategy innovatively customizes the Lyapunov drift-plus-penalty function by incorporating replication redundancy offloading costs to establish a balance model between the queue load and offloading cost. The LDEO strategy computes the optimal offloading decisions with dynamic adjustment characteristics by integrating a low-complexity differential evolution method, aiming to find the optimal balance point that minimizes the offloading cost while maintaining reliability performance. The experimental results show that compared with the existing strategies, LDEO strategy effectively reduces the redundancy of fault tolerance cost and the waiting time under the condition of ensuring that the task will not be discarded over time. It stabilizes the queue length in a reasonable range, controls the waiting time and loss rate of tasks, reduces the extra energy consumption paid by replication redundancy, and effectively realizes the optimal balance under multiple conditions.

A hybrid optimization algorithm for multi-agent dynamic planning with guaranteed convergence in probability

The paper aims to solve the problem of multi-agent path planning in complex environment using optimization algorithm. To address the issue of local optimum and premature convergence, a new method is proposed based on the whale optimization algorithm, combining the chaotic initialization, the reverse search and the differential evolution methods. It is theoretically proved that this algorithm is globally convergent in probability. When applied to path planning problems, the proposed optimization algorithm can effectively find a globally optimal and smoother path. Through simulation experiments with multi-UAVs, it is demonstrated that the proposed algorithm has better performance than the state-of-the-art methods in environment with both static and dynamic obstacles, reflecting the global convergence and robustness of the proposed algorithm.

Calibration of horizontal seismic design spectra of offshore earthquake ground motions by applying improved differential evolution method

Design Response Spectrum (DRS) serves as a crucial cornerstone for seismic design, encapsulating the characteristic parameters of the design spectrum. To investigate the offshore design spectrum required for seismic design of offshore structures, improved differential evolution (DE) methods are first used to determine the characteristic parameters of the horizontal design spectra of offshore ground motions. In assessing the stability and precision of the chosen improved DE methods, we scrutinize the applicability of various renowned DE methodologies in the calibration process. Our findings indicate that differential evolution with global and local neighborhoods (GLDE) exhibits superior stability and accuracy compared to other DE methods, rendering it suitable for calibrating the design spectrum to delineate optimal characteristic parameters of the DRS. Subsequently, the properties of the offshore horizontal design spectra are investigated by applying the recommended GLDE to 6756 seismic data collected from three offshore regions. The site conditions of water depth and sedimentary thickness of the ocean-bottom stations were investigated by the finely divided seismic data with classified earthquake types. The ocean-bottom stations are classified as A-D by the water depth and sedimentary thickness, and the offshore DRS for four site classes with different earthquake types are presented in this study. According to the observed offshore response spectra with different water depth groups, it is found that the water depth should be considered in the offshore design spectra mainly due to the differences between buried and unburied seafloor stations, and the spectral values with deep water layer are considerably larger than those with shallow water. Offshore DRSs are compared with onshore DRSs of seismic codes and different peak ground acceleration (PGA) groups are presented in this study.

Adjustment of mutant vector elements in the differential evolution method for solving the problem of power shortage minimization in electric power systems

The article is aimed at increasing the effectiveness of numerical optimization methods in calculations of problems concerning power shortage minimization in electric power systems, specifically the differential evolution (DE) method and its variations–aDE and jDE. Experimental studies and testing of the proposed adjustments were carried out on complex electric power systems of different order. These systems are represented and realized by means of mathematical models of power shortage minimization with the possibility of their analysis using the developed software package as part of adequacy assessment. The performed analysis of the DE method elements and the existing variants of the mutation process revealed that the existing approaches can be further modified. This can subsequently increase the speed of problem-solving. It is shown that the main changes include an additional check that the mutant vectors meet the upper and lower bounds, and if they fail to do so, three adjustment options are considered. Existing approaches propose to generate new vector elements beyond the bounds by applying random numbers within the bounds. The present authors propose to use the “projections” of the found vector elements, i.e., to use the values of upper or lower bounds when they are exceeded for a particular element as mutant vector values. The implemented method involving the adjustment of mutant vector elements is shown to offer an advantage of a 47% reduction in problem-solving time over existing adjustment methods while maintaining the same accuracy. It is noted that aDE and jDE are the most effective variations for solving stated problems. The obtained results of experimental studies confirm the effectiveness and advantages of applying the proposed adjustment method in mutation process of in the form of “projections”, as well as using aDE and jDE variations of the DE method to solve the problems of power shortage minimization in electric power systems.

A Multi-level Surrogate-assisted Algorithm for Expensive Optimization Problems

With the development of computer science, more and more complex problems rely on the help of computers for solving. When facing the parameter optimization problem of complex models, traditional intelligent optimization algorithms often require multiple iterations on the target problem. It can bring unacceptable costs and resource costs in dealing with these complex problems. In order to solve the parameter optimization of complex problems, in this paper we propose a multi-level surrogate-assisted optimization algorithm (MLSAO). By constructing surrogate models at different levels, the algorithm effectively explores the parameter space, avoiding local optima and enhancing optimization efficiency. The method combines two optimization algorithms, differential evolution (DE) and Downhill simplex method. DE is focused on global level surrogate model optimization. Downhill simplex is concentrated on local level surrogate model update. Random forest and inverse distance weighting (IDW) are constructed for global and local level surrogate model respectively. These methods leverage their respective advantages at different stages of the algorithm. The MLSAO algorithm is evaluated against other state-of-the-art approaches using benchmark functions of varying dimensions. Comprehensive results from the comparisons showcase the superior performance of the MLSAO algorithm in addressing expensive optimization problems. Moreover, we implement the MLSAO algorithm for tuning precipitation parameters in the Community Earth System Model (CESM). The outcomes reveal its effective enhancement of CESM's simulation accuracy for precipitation in the North Indian Ocean and the North Pacific region. These experiments demonstrate that MLSAO can better address parameter optimization problems under complex conditions.

The Differentiated Creative Search (DCS): Leveraging differentiated knowledge-acquisition and creative realism to address complex optimization problems

This article introduces differentiated creative search (DCS), a groundbreaking optimization algorithm that revolutionizes traditional decision-making systems in complex environments. In contrast to conventional differential evolution methods, DCS integrates a unique knowledge-acquisition process with a creative realism paradigm, thereby transforming optimization strategies. The primary aim of DCS is to enhance decision-making efficacy by employing a newly proposed dual-strategy approach that balances divergent and convergent thinking within a team-based framework. High-performing members apply divergent thinking via the DCS/Xrand/Linnik(α,σ) strategy, which incorporates existing knowledge and Linnik flights. Conversely, the remaining team harnesses convergent thinking through the DCS/Xbest/Current-to-2rand strategy, which combines insights from both the team leader and fellow members. This division of labor, coupled with a strategy tailored to the performance levels of team members, allows for a dynamic and effective decision-making process. The methodology of DCS involves iterative cycles of divergent and convergent thinking, supported by a differentiated knowledge-acquisition process and retrospective assessments. The algorithm's novelty lies in its differentiated knowledge-acquisition, adjusted based on individual team member performance, fostering an environment of continuous learning and adaptation. The paper's contributions are demonstrated through rigorous testing of DCS on various benchmark functions, including CEC2017, classical, and sensor selection problems, as well as real-world applications such as car side impact design, gear train design, and FM sound wave parameter estimation. The results showcase the promising performance of DCS compared to that of existing algorithms, attributable to its innovative approach to problem solving and decision making in complex scenarios. The results and impact section highlights that DCS considerably outperforms traditional optimization algorithms, offering a robust and versatile tool for complex decision-making systems. Its impact is particularly notable in scenarios requiring a balance between innovative solutions and practical decision-making, making DCS a valuable asset in strategic planning and execution across various industries.

A two-stage frequency-domain generation algorithm based on differential evolution for black-box adversarial samples

Adversarial sample generation problem is a hot issue in the security field of deep learning. Evolutionary algorithm has been widely used to solve this problem in recent years because of its good global search ability. However, existing methods still suffer from the “curse of dimensionality” when attacking high-resolution images. In this paper, a two-stage frequency domain generation algorithm of black-box adversarial samples based on differential evolution is proposed. In the first stage, a representative image-guided differential evolution method is proposed to quickly generate a universal adversarial perturbation with a high attack success rate in the frequency-domain. In the second stage, a space reduction strategy based on frequency-domain pixel blocks is designed to reduce the search space and alleviate the problem of “curse of dimensionality”. In addition, a new space–frequency interaction sensitivity measure is introduced to evaluate the similarity between the adversarial samples and the original images. The adversarial perturbations obtained by the measure are more in line with the subjective perception of the human eye. Finally, compared with several typical black-box adversarial sample generation algorithms, experimental results show that the proposed algorithm can achieve higher attack success rate with less prediction times.

Explainable prediction of surface roughness in multi-jet polishing based on ensemble regression and differential evolution method

Surface roughness is a critical parameter for quantifying the surface quality of a workpiece. Accurate surface roughness prediction can significantly influence the overall quality of the final components by reducing costs and enhancing productivity. Although various prediction methods have been explored in previous research, less attention has been given to explainable prediction methods for surface roughness. This paper proposes a surface roughness prediction model based on the Differential Evolution (DE) algorithm with ensemble learning. It aims to elucidate the intrinsic correlation between processing parameters and surface roughness values in Multi-Jet Polishing (MJP) using explainable analysis methods. The proposed Ensemble Regression with Differential Evolution (ERDE) algorithm comprises two main modules: data processing and analytics, and ensemble model prediction. These modules investigate the surface roughness of MJP from the data and model levels, respectively. To validate the effectiveness of ERDE, MJP experiments were conducted on three-dimensional printed components of 316L stainless steel. The experimental data indicated that ERDE outperforms other existing algorithms, reducing the mean absolute percentage error by approximately 42 %.

Improved Differential Evolution Algorithm Guided by Best and Worst Positions Exploration Dynamics.

The exploration of premium and new locations is regarded as a fundamental function of every evolutionary algorithm. This is achieved using the crossover and mutation stages of the differential evolution (DE) method. A best-and-worst position-guided novel exploration approach for the DE algorithm is provided in this study. The proposed version, known as "Improved DE with Best and Worst positions (IDEBW)", offers a more advantageous alternative for exploring new locations, either proceeding directly towards the best location or evacuating the worst location. The performance of the proposed IDEBW is investigated and compared with other DE variants and meta-heuristics algorithms based on 42 benchmark functions, including 13 classical and 29 non-traditional IEEE CEC-2017 test functions and 3 real-life applications of the IEEE CEC-2011 test suite. The results prove that the proposed approach successfully completes its task and makes the DE algorithm more efficient.

Perbandingan Performansi Antara Differential Evolution dan Bat Algorithm pada Tuning PID Untuk Optimasi Kontrol Kecepatan Paralell Hybrid Electric Vehicle

In the last decade, there have been many means of transportation that use fuel oil (Internal Combustion Engine (ICE)). This has a serious impact on the environment due to the emission of pollutant gases. One solution is the use of a hybrid electric vehicle (HEV) as a substitute for vehicles that use ICE. One of the performance that must be owned by the HEV is to have a stable speed when driving. In this study, several methods used in the metaheuristic algorithm in the disturbance observer have the advantage of describing the inverse model of the plant without making a mathematical model. The test is carried out by comparing the two methods of the metaheuristic algorithm, namely Differential Evolution and Bat Algirthm. The simulation results show that the method used in this HEV is to maintain its speed, so according to the test results it shows that the Differential Evolution method is the best method for controlling the speed of the Parallel Hybrid Electric Vehicle.

Optimization of parameters for a fringe projection measurement system by use of an improved differential evolution method.

Fringe projection 3D measurement is widely used for object surface reconstruction. While improving measurement accuracy is a crucial task. Measurement accuracy is profoundly affected by various optical structural parameters. However, the current practice of system construction lacks theoretical guidelines and often relies on the experience of the operator, inevitably leading to unpredictable error. This paper investigates a theoretical optimization model and proposes an automatic optimization method for qualitatively determining the multiple optimal optical structural parameters in fringe projection measurement system. The aim is to enhance measurement accuracy conducting a rational comprehensive optimal structural parameters design prior to the system construction. Firstly, the mathematical model of the measurement system is established based on the principle of optical triangulation, and the phase sensitivity criterion is defined as the optimization norm. Within the full measurement range, the optimization merit function is formulated by combing three positions: the center position, the left and right boundary of the CCD. The imaging effectiveness criteria and sensor geometric dimensions are taken into account as the constraint boundaries. Subsequently, a combined improved differential evolution and Levy flight optimization algorithm is applied to search for the optimal parameters. The optimal structural parameters of the system were designed based on the optimization process. Experimental results validated the improvement in measurement accuracy achieved by the optimized structural parameters.

Идентификация математической модели экономического развития двух регионов мира

This paper is devoted to solving the inverse problem (determining the parameters of a system of ordinary differential equations based on additional information determined at discrete points in time) and analyzing its solution for a mathematical model describing the dynamics of changes in the population and capital of two regions of the world. The inverse problem is reduced to the problem of minimizing the target functional and is solved by the method of differential evolution. A numerical method for solving direct and inverse problems is implemented. The developed method was tested on model and real data for countries such as Russia, China, India and the USA.

Application of the evolutionary approach to structural and parametric identification of dynamic objects

The paper examines the evolutionary approach to structural and parametric identification of dynamic systems in the form of differential equations. The approach is based on a genetic programming algorithm to determine a structure of the equation and differential evolution method for parameters selection. The author proposed approach based on such evolutionary algorithms as genetic programming and differential evolution. The search for the structure is carried out by genetic programming. The selection of numerical parameters and initial conditions is implemented by a method of differential evolution. The problem of finding a model that describes changes in the efficiency of a hydraulic system is solved with the help of this approach. The proposed approach is compared with a recurrent neural network and a nonparametric kernel regression estimation.

Online Active Fault Detection for Over-Actuated Systems With Prescribed Control Performance

In the field of fault detection, active fault detection for dynamic systems is an emerging research topic. By redesigning the control input, active fault detection can enhance fault detection performance. In this study, the online active fault detection problem is investigated for over-actuated systems, where the control input is designed by considering both the prescribed control performance and the fault detection performance. A two-stage input design architecture is constructed, where the first stage is a virtual controller design and the second stage is a control allocation design. In the first stage, the virtual control input is designed by utilizing a prescribed performance function to fulfill the control requirement. In the second stage, a differential evolution method is adopted to obtain an optimal control allocation algorithm for improving the fault detection performance. The designed control input can both improve fault detection performance and achieve the prescribed control performance. Two cases, including a numerical example and a manned submersible propulsion system, are studied to support theoretical results. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In this study, the aim is to design a control input for over-actuated systems to obtain better fault detection performance while achieving prescribed control performance. To achieve it, a two-stage control input design architecture is constructed, where the first stage is a virtual controller design and the second stage is a control allocation design. In the first stage, choose a proper prescribed performance function and a sliding mode function to accomplish the transient and steady behavioral bounds on the tracking errors. In the second stage, design a special observer to generate the system residual signal, which is used for indicating system faults. Based on the residual signal, construct an index for the control allocation algorithm. Differential evolution algorithm is applied to obtain the optimal control allocation algorithm by maximizing the index. Thus the control allocation algorithm which can improve fault detection performance is designed. In this way, the input can improve fault detection performance without affecting system behavior. The proposed technique of this study can be applied to dynamic systems with input redundancy.

A framework of evolutionary optimized convolutional neural network for classification of shang and chow dynasties bronze decorative patterns.

As a UNESCO World Cultural Heritage, the aesthetic value of bronze artifacts from the Shang and Chow Dynasties has had a profound influence on Chinese traditional culture and art. To facilitate the digital preservation and protection of these Shang and Chow bronze artifacts (SCB), it becomes imperative to categorize their decorative patterns. Therefore, a SCB pattern classification method of differential evolution called Shang and Chow Bronze Convolutional Neural Network (SCB-CNN) is proposed. Firstly, the original bronze decorative patterns of Shang and Chow dynasties are collected, and the samples are expanded through image augmentation technology to form a training dataset. Secondly, based on the classical convolutional neural network structure, the recognition and classification of bronze patterns are implemented by adjusting the network parameters. Then, the initial parameters of the convolutional neural network are optimized by differential evolution algorithm, and the optimized SCB-CNN is simulated. Finally, comparative experiments were conducted between the optimized SCB-CNN, the unoptimized model, VGG-Net, and GoogleNet. The experimental results indicate that the optimized SCB-CNN significantly reduces training time while maintaining fast prediction speed, convergence speed, and high accuracy. This study provides new insights for the inheritance and innovation research of SCB patterns.

An Interactive Differential Evolution Method with Human Auditory Perception for Sound Composition

An Interactive Differential Evolution Method with Human Auditory Perception for Sound Composition

Triple competitive differential evolution for global numerical optimization

As optimization problems become more and more complex in real-world scenarios, the effectiveness of many existing differential evolution (DE) methods is critically challenged. To circumvent this predicament, this paper proposes a triple competitive DE (TCDE) to tackle increasingly complicated optimization problems. Specifically, a triple competition mechanism is devised to first randomly arrange individuals into exclusive triples and then let individuals in each triple compete with each other. Subsequently, heterogeneous mutation schemes are designed to update the three individuals in each triple based on the competition results. With the cooperation between these two techniques, on the one hand, better individuals in the triples tend to exploit the areas where they lie to find high-accuracy solutions, while worse individuals in the triples prefer to explore the intricate problem space to locate promising regions. On the other hand, different individuals are mutated by following the guidance of different leading exemplars, which ensures that individuals traverse the sophisticated solution space in diverse directions along with slight intensification to optimal regions. Furthermore, a modified adaptive parameter adjustment scheme is designed for individuals in each triple by considering their differences so as to meet the expectation that better individuals focus on exploitation while worse individuals concentrate on exploration. Finally, experiments are performed to first compare TCDE with totally 10 advanced DE variants and then further compare it with totally 10 CEC winners and their latest variants on the CEC'2014 and the CEC'2017 problem suites with totally 4 different dimensionality settings. Experimental results prove that TCDE achieves highly competitive or even much better performance than the totally 20 compared methods. Particularly, TCDE is demonstrated to be especially capable of solving complicated optimization problems. Furthermore, the efficacy of TCDE in tackling real-world optimization problems is substantiated through experiments conducted on the CEC'2011 real-world optimization problem set.

A HYBRID DIFFERENTIAL EVOLUTION FOR NON-SMOOTH OPTIMIZATION PROBLEMS

Solving high dimentional, multimodal, non-smooth global optimization problems faces challenges concerning quality of solution, computational costs or even the impossibility of solving the problem. Evolutionary algorithms, in particular, differential evolution algorithm proved itself as good method of global optimization. On the other side, approach based on subgradient methods are good for optimizing non-smooth functions. Combination of these two approaches enables to improve the quality of the algorithm, using the best features of both methods. In this paper, a new hybrid evolutionary approach based on differential evolution and subgradient algorithm as the local search procedure is proposed. Behavior of the proposed SSGDE algorithm was studied in a numerical experiment on three groups of generated tests. Comparison of the new hybrid algorithm with the pure DE approach showed the advantage of the SSGDE. It has been experimentally established that the proposed method finds the global minimum in the best way for all considered dimensions of the problem with respect to the differential evolution method. The SSGDE algorithm showed the best results with a significant increase in the number of functions.