Differential Evolution Algorithm Research Articles

Application of Metaheuristics for Multi-Trip Capacitated Vehicle Routing Problem with Time Window

Abstract This study focuses on the delivery routing problem faced by a transport company located in Phuket, Thailand. The goal of this study is to find a daily optimum route in order to minimize the total transportation cost, which comprises fixed costs associated with vehicle rental and variable costs calculated based on factors of travel distance, fuel prices, and fuel consumption. The complexity of this problem is compounded by the fact that customer demand often exceeds a vehicle capacity, in terms of weight and volume. In addition, delivery must be made within specific time windows. To tackle this issue, the delivery routing problem is classified as a multi-trip capacitated vehicle routing problem with time window (MTCVRPTW). Since the problem is NP-hard, an application of metaheuristic is more practical to determine the delivery routing of the company within a reasonable computing time. In this study, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm are applied to solve MTCVRPTW. The numerical results show that DE provides better solution quality compared to those obtained from PSO and company current practices.

AdaGuiDE: An adaptive and guided differential evolution for continuous optimization problems

Differential evolution (DE) has been proven as a simple yet powerful meta-heuristic algorithm on tackling continuous optimization problems. Nevertheless most existing DE methods still suffer from certain drawbacks including the use of ineffective mechanisms to adjust mutation strategies and their control parameters that may possibly mislead the search directions, and also the lack of intelligent guidance and reset mechanisms to escape from local optima. Therefore, to enhance the adaptability of DE-based search frameworks and the robustness on optimizing complex problems full of local optima, an adaptive and guided differential evolution (AdaGuiDE) algorithm is proposed. Essentially, the adaptability of the AdaGuiDE search framework is enhanced by three schemes to iteratively refine the search behaviour at two different levels. At the macroscopic level, the AdaGuiDE search framework revises the existing adaptive mechanism for selecting appropriate DE search strategies by counting the actual contributions in terms of solution quality. In addition, the adaption strategy is extended to the microscopic level where a penalty-based guided DE search is employed to guide the search escaping from local optima through temporarily penalizing the local optima and their neighborhood. Furthermore, a systematic boundary revision scheme is introduced to dynamically adjust the search boundary for locating any potential regions of interest during the search. For a rigorous evaluation of the proposed search framework, the AdaGuiDE algorithm is compared against other well-known meta-heuristic approaches on three sets of benchmark functions involving different dimensions in which the AdaGuiDE algorithm attained remarkable results especially on the high-dimensional and complex optimization problems. More importantly, the proposed AdaGuiDE framework shed lights on many possible directions to further enhance the adaptability of the underlying DE-based search strategies in tackling many challenging real-world applications.

Multi-population multi-strategy differential evolution algorithm with dynamic population size adjustment

Multi-population multi-strategy differential evolution algorithm with dynamic population size adjustment

Joint differential evolution algorithm in RIS-assisted multi-UAV IoT data collection system

This paper investigates a Reconfigurable Intelligent Surface (RIS)-assisted multi-UAV data collection system, in which unmanned aerial vehicles (UAVs) collect data from Internet of Things (IoT) devices. The RIS, mounted on building surfaces, plays a vital role in preventing obstruction and improving the communication quality of the IoT-UAV transmission link. Our aim is to minimize the energy consumption of this system, including the transmission energy consumption of IoT devices and the hovering energy consumption of UAVs, by optimizing the deployment of UAVs and the phase shifts of RIS. To achieve this goal, a multi-UAV deployment and phase shift of RIS optimization algorithm (MUDPRA) is proposed that consists of two phases. In the first phase, a joint differential evolution (DE) algorithm with a two-layer structure featuring a variable population size, namely DEC-ADDE, is proposed to optimize the UAV deployment. Specifically, each UAV’s location is encoded as an individual, with the whole UAV deployment is considered as the population in DEC-ADDE. Thus, a differential evolution clustering (DEC) algorithm is employed initially to initialize the population, which allows for obtaining better initial UAV deployment without the need for a predefined number of UAVs. Subsequently, an adaptive and dynamic DE algorithm (ADDE) is employed to produce offspring population to further optimize UAV deployment. Finally, an adaptive updating strategy is adopted to adjust the population size to optimize the number of UAVs. In the second phase, a low-complexity method is proposed to optimize the phase shift of RIS with the aim of enhancing the IoT-UAV data transmission rate. Experimental results conducted on eight instances involving IoT devices ranging from 60 to 200 demonstrate the effectiveness of MUDPRA in minimizing energy consumption of this system compared to six alternative algorithms and three benchmark systems.

Cluster Heat Selection Optimization in Wsn Via Genetic Based Evolutionary Algorithm and Secure Data Transmission Using Paillier Homomorphic Cryptosystem

Introduction: Wireless Sensor Networks (WSNs) consist of sensor nodes requiring energy-saving measures to extend their lifespan. Traditional solutions often lead to premature node failure due to non-adaptive network setups. Differential Evolution (DE) and Genetic Algorithms (GA) are two key evolutionary algorithms used for optimizing cluster head (CH) selection in WSNs to enhance energy efficiency and prolong network lifetime.Methods: This study compares DE and GA for CH selection optimization, focusing on energy efficiency and network lifespan. It also introduces an improved decryption method for the Paillier homomorphic encryption system to reduce decryption time and computational cost.Results: Experiments show GA outperforms DE in the number of rounds for the first node to die (FND) and achieves a longer network lifespan, despite fewer rounds for the last node to die (LND). GA has slower fitness convergence but higher population fitness values and significantly faster decoding speeds.Conclusion: GA is more effective than DE for CH selection in WSNs, leading to an extended network lifespan and better energy efficiency. Despite slower fitness convergence, GA's higher fitness values and improved decoding speeds make it a superior choice. The enhancements to the Paillier encryption system further increase its efficiency, offering a robust solution for secure and efficient WSN operation

Recovery Model of Electric Power Data Based on RCNN-BiGRU Network Optimized by an Accelerated Adaptive Differential Evolution Algorithm

Recovery Model of Electric Power Data Based on RCNN-BiGRU Network Optimized by an Accelerated Adaptive Differential Evolution Algorithm

A triple population adaptive differential evolution

The Differential Evolution (DE) algorithm is one of the most efficient algorithms for complex numerical optimization. However, the nature of differential mutation and crossover hinders the individuals from a major change and always guides them toward their superior neighbors. There's a lack of useful directional information to help the population escape from early convergence. To solve the above problem, this paper proposes a novel Triple-population-based Adaptive Differential Evolution (TPADE) to enhance the evolutionary efficiency in solving various complex numerical optimization problems. First, a population division method with symmetrical linear reduction is designed to divide the parent population of each iteration into three sub-populations of different sizes, i.e., superior sub-population, medium sub-population, and inferior sub-population. Each sub-population adopts distinct differential mutation and crossover operators to maintain balanced search directions. Second, a superior-trial-preserved selection mechanism is proposed to screen useful directional information to guide the next iteration of evolution. Third, an effective parameter adaptation strategy is designed with the linear population size reduction strategy to avoid redundant search. Experiments are then conducted to show that the TPADE exhibits well performance compared with eleven state-of-the-art DE variants, CEC winners, and their variants on the CEC'2014, CEC'2017, and CEC'2022 benchmark suites. The C++ source code of TPADE can be downloaded from https://github.com/DoubleGong/TPADE.

Optimal Reconfiguration of Bipolar DC Networks Using Differential Evolution

The search for more efficient power grids has led to the concept of microgrids, based on the integration of new-generation technologies and energy storage systems. These devices inherently operate in DC, making DC microgrids a potential solution for improving power system operation. In particular, bipolar DC microgrids offer more flexibility due to their two voltage levels. However, more complex tools, such as optimal power flow (OPF) analysis, are required to analyze these systems. In line with these requirements, this paper proposes an OPF for bipolar DC microgrid reconfiguration aimed at minimizing power losses, considering dispersed generation (DG) and asymmetrical loads. This is a mixed-integer nonlinear optimization problem in which integer variables are associated with the switch statuses, and continuous variables are associated with the nodal voltages in each pole. The problem is formulated based on current injections and is solved by a hybridization of the differential evolution algorithm (to handle the integer variables) and the interior point method-based OPF (to minimize power losses). The results show a reduction in power losses of approximately 48.22% (33-bus microgrid without DG), 2.87% (33-bus microgrid with DG), 50.90% (69-bus microgrid without DG), and 50.50% (69-bus microgrid with DG) compared to the base case.

A new strategy for manufacturing, modeling, and optimization of 3D printed polylactide based on multiple nonlinear neuro regression analysis and stochastic optimization methods

Although there are many studies related to design, modeling, and optimization of fused deposition modeling (FDM) process parameters in the literature, the absence of a systematic approach to increase the reliability of model selection and optimization results is an important shortcoming that must be addressed. To make up for this deficiency, a new strategy was proposed to obtain desired quality on mechanical properties by adjusting FDM process parameters. This attempt involves manufacturing, modeling, and optimization point of view. The D-optimal method was employed to form experiment set, including process parameters. A hybrid approach neuro regression combining artificial neural network (ANN) and regression analysis together was used for modeling of FDM process. The most significant advantage of the neuro-regression approach compared to ANN is that the mathematical models can be used directly without needing any transformation. This is not possible in neural networks and, therefore, significantly limits and complicates the use of models obtained using ANN. The present study aims at optimization of the FDM process parameters, including infill density, infill pattern, layer thickness, and print speed on ultimate strength, fracture strength, and fracture strain for polylactide (PLA). In this regard, modified versions of the optimization algorithms Differential Evolution, Nelder Mead, and Simulated Annealing were used to find the best or elite designs. Linear or nonlinear models consisting of polynomial, trigonometric, and logarithmic expressions and their hybrid forms were employed to define the strength and strain behavior of PLA. It is concluded that (a) implementations of the optimization algorithms provide a 19% improving the minimum strain value if it is compared with the experimental results, (b) infill pattern types ( x2) were found as honeycomb, triangle, and cubic for the designs in terms of maximum fracture strength, minimum strain, and maximum ultimate tensile strength respectively, (c) many alternatives near optimum local designs could be obtained based on Nelder Mead algorithm for fracture strength and ultimate strength parameters. Thus, this allows work in a wide range of applications without depending on a single result for production.

A New Perspective for Scientific Modelling: Sparse Reconstruction Based Approach for Learning Time-Space Fractional Differential Equations

Abstract This paper studies a sparse reconstruction based approach to learn time-space fractional differential equations, i.e. to identify parameter values and particularly the order of the fractional derivatives. The approach uses a generalized Taylor series expansion to generate, in every iteration, a feature matrix which is used to learn the fractional orders of both, temporal and spatial derivatives by minimizing the LASSO operator using Differential Evolution algorithm. To verify the robustness of the method, numerical results for time-space fractional diffusion equation, wave equation, and Burgers? equation at different noise levels in the data are presented. Finally, the methodology is applied to a realistic example where underlying fractional differential equation associated to published experimental data obtained from an in-vitro cell culture assay is learned.

A novel hybrid adaptive differential evolution for global optimization

Differential Evolution (DE) stands as a potent global optimization algorithm, renowned for its application in addressing a myriad of practical engineering issues. The efficacy of DE is profoundly influenced by its control parameters and mutation strategies. In light of this, we introduce a refined DE algorithm characterized by adaptive parameters and dual mutation strategies (APDSDE). APDSDE inaugurates an adaptive switching mechanism that alternates between two innovative mutation strategies: DE/current-to-pBest-w/1 and DE/current-to-Amean-w/1. Furthermore, a novel parameter adaptation technique rooted in cosine similarity is established, with the derivation of explicit calculation formulas for both the scaling factor weight and crossover rate weight. In pursuit of optimizing convergence speed whilst preserving population diversity, a sophisticated nonlinear population size reduction method is proposed. The robustness of each algorithm is rigorously evaluated against the CEC2017 benchmark functions, with empirical evidence underscoring the superior performance of APDSDE in comparison to a host of advanced DE variants.

Hybrid differential evolution algorithm for Falkner-Skan flow with rotation

A hybrid differential evolution algorithm is used in this work to study the rotating transport of Falkner-Skan flow. The problem is modeled as an equivalent optimization problem by using Padé rational approximation functions. The primary model of the governing partial differential equations is imposed to subjugate the error between profiles. A hybrid evolutionary algorithm based on differential evolution and a convergent version of Nelder-Mead direct search algorithm is employed to perform global exploratory search along with an enhanced exploitation to improve the accuracy of the proposed solution scheme. The resulting scheme is named as evolutionary Padé approximation (EPA) scheme. The performance of the proposed EPA scheme on the Falkner-Skan boundary value problem is investigated by considering various values of the rotation parameters. The developed optimizer in EPA scheme was able to minimize the residuals up to10−10. Results are displayed graphically in order to study the effect of various types of parameters. EPA scheme determined that angular velocity increases or decreases accordingly as fluid parameter (β) and the rotation parameter (λ) but shows inverse behavior with respect to power law index(n). Similarly, the response of velocity profile along y−axis was decreasing function of β as well as n but increasing function of λ. The performance of the proposed EPA scheme has been demonstrated by comparing results with a hybrid neural network scheme and found in excellent agreement.

Energy efficient multi-user task offloading through active RIS with hybrid TDMA-NOMA transmission

In this paper, we address the challenge of minimizing system energy consumption for task offloading within non-line-of-sight (NLoS) mobile edge computing (MEC) environments. Our approach integrates an active reconfigurable intelligent surface (RIS) and employs a hybrid transmission scheme combining time division multiple access (TDMA) and non-orthogonal multiple access (NOMA) to enhance the quality of service (QoS) for user task offloading. The formulation of this problem as a non-convex optimization issue presents significant challenges due to its inherent complexity. To overcome this, we introduce an innovative method termed element refinement-based differential evolution (ERBDE). Initially, through rigorous theoretical analysis, we optimally determine the allocation of local computation resources, computation resources at the base station (BS), and transmit power of users, while maintaining fixed values for the offloading ratio, amplification factor, phase of the reflecting element, and the transmission period. Subsequently, we employ the differential evolution (DE) algorithm to iteratively fine-tune the offloading ratio, amplification factor, phase of the reflecting element, and transmission period towards near-optimal configurations. Our simulation results demonstrate that the implementation of active RIS-supported task offloading utilizing the hybrid TDMA-NOMA scheme results in an average system energy consumption reduction of 80.3%.

Optimized the locations and sizes of FACTS devices on electrical network involving wind power using a new hybrid stochastic algorithm

This article focuses on utilizing a new hybrid optimization algorithm called the Fitness-Distance Balance-based Archimedes Optimization Algorithm (FDB-AOA) to solve the Optimal Power Flow (OPF) problems within a recently adopted electrical transmission grid, specifically the modified IEEE-30 bus system. This system integrates thermal and wind -based generating units, including various types of Flexible AC Transmission System (FACTS) devices. Several tests are performed where the stochastic wind energy is modeled using probability density functions. The optimization goal takes into account the cost of thermal generation, the direct cost of scheduled wind power, and the penalty cost for underestimating wind power. The locations and sizing of FACTS devices are optimized with aim of reducing several fitness functions. The optimization results achieved by the proposed method in solving single objective functions were more effective in finding the optimal solution compared to several well-known algorithms. The results show the superiority of the proposed method in the majority of case studies, as it achieved a better optimum solution with a total generation cost ( Cgen ) value of 806.9817 $/h, and a real power loss ( Ploss ) value 1.7619 MW, also yields a competitive gross cost ( Cgross ) value of 1104.6652 $/h compared to those obtained by the other algorithms. In contrast, the statistical analysis proven the superiority of this algorithm where the standard deviations (SD) required in solving the single objective problem ( Cgen ) is 0.0996, which are better compared to other techniques. the simulation results demonstrate that the FDB-AOA optimizer is robust than other approaches, like the Success history based-adaptive differential evolution (SHADE) algorithm, MSA (Moth Swarm Algorithm), and ABC (artificial bee colony) integrated with the SF (superiority of feasible solutions) approach, in solving OPF problems involving the integration of both thermal and wind power plants along with FACTS devices.

Three-dimensional DV-Hop based on improved adaptive differential evolution algorithm

Three-dimensional DV-Hop based on improved adaptive differential evolution algorithm

Parameter identification method of load modeling based on improved dung beetle optimizer algorithm

The role of load modeling in power systems is crucial for both operational and regulatory considerations. It is essential to develop an effective and reliable method for optimizing load modeling parameter identification. In this paper, the dung beetle algorithm is improved by using the good point set, and a load model parameter identification strategy based on the good point set dung beetle optimization algorithm (GDBO) within the framework of the measurement-based load modeling method. The proposed parameter identification strategy involves utilizing PMU voltage data as input, selecting a comprehensive load model, and refining the initialization process based on the good point set to mitigate the influence of local maxima. Through iterative optimization of the objective function using the Dung Beetle Optimizer (DBO) algorithm, the optimal parameters for the comprehensive load model are determined, enhancing the model’s ability to accurately capture the power curve. Analysis of examples pertaining to PMU-measured modeling parameter identification reveals that the proposed GDBO algorithm, which incorporates a good point set, outperforms alternative methods such as the improved differential evolution algorithm (IDE), particle swarm optimization algorithm (PSO), grey wolf optimization algorithm (GWO), and conventional DBO algorithm. This demonstrates the superior performance of the introduced approach in the context of load model parameter identification.

A pointwise weighting prediction variance–high-dimensional model representation model-based global optimization approach for ship hull parametric design

Ship hull optimization techniques based on computer-aided design/computational fluid dynamics can effectively enhance the efficiency and stability of ship designs, with significant application prospects. To enhance the potential of ship hull optimization, increasing design variable dimensionality is essential, but can cause a significant increase in hydrodynamic simulations. To reduce simulations required for high-dimensional ship hull optimization, a new surrogate method, pointwise weighting prediction variance–high-dimensional model representation (PWPV-HDMR), which uses pointwise weighting prediction variance (PWPV) to aggregate different a priori assumptions, is developed. Moreover, a differential evolution algorithm is used to identify promising hull design parameters, using the PWPV-HDMR model instead of costly simulation as the fitness function. The proposed approach is tested on the hydrostatic resistance optimization of KRISO Container Ship. The results show that PWPV-HDMR outperforms kriging-HDMR, with a better resistance optimization effect, illustrating the effectiveness of the PWPV-HDMR-based global optimization approach in discovering promising ship hull parameters.

Modeling and identification of hysteresis of marine damper considering shock environment based on evolutionary sparrow search algorithm

The mechanical properties of marine dampers are usually highly nonlinear in order to adapt to dynamic and shock environments. The dampers are subjected to dynamic and shock tests and the hysteresis curves are found to be rate-dependent and asymmetric. To be able to describe the dynamic hysteresis and shock hysteresis, a rate-dependent generalized Prandtl-Ishlinskii (RDGPI) model is proposed based on the generalized Prandtl-Ishlinskii (GPI) model, which is a hybrid of the GPI model and the radial basis function (RBF) neural network. Due to the large number of parameters in the model, thus aiming to improve the effect of parameter identification, an evolutionary sparrow search algorithm mixed with sparrow search algorithm and differential evolutionary algorithm is proposed. Compared with other algorithms, sparrow search algorithm is verified to have ideal optimization effect and convergence speed, and it is not easy to fall into the local optimum. Finally, the RDGPI model is experimentally verified, and the results show that the prediction error of the RDGPI model for dynamic hysteresis is within 0.06 kN, and the prediction error for shock hysteresis is within 0.8 kN, which is capable of describing the rate-dependent characteristics of the damper hysteresis. And it has a very good generalization ability, which makes it very suitable to be used in the modeling of the mechanical characteristics of the marine damper.

HAPI-DE: Differential evolution with hierarchical archive based mutation strategy and promising information

Differential Evolution (DE), as a population-based meta-heuristic global optimization technique, has shown excellent performance in handling optimization problems in continuous spaces. Despite its effectiveness, the DE algorithm suffers from shortcomings such as complexity of parameter selection and limitations of the mutation strategy. Therefore, this paper presents a new strategy for generating trial vectors based on a hierarchical archive, which integrates promising information during evolution with current populations to obtain a good perception of the objective landscape. Moreover, to mitigate mis-scaling by scale factor, an adaptive parameter generation mechanism with hierarchical selection (APSH) is proposed. Furthermore, a novel population diversity metric technique and a restart mechanism based on wavelet functions is introduced in this paper. Comparative experiments were conducted to evaluate the performance of the proposed algorithm using 100 benchmark functions from the CEC2013, CEC2014, CEC2017, and CEC2022 test suites. The results demonstrate that the HAPI-DE algorithm outperforms or is on par with 6 recent powerful DE variants. Additionally, HAPI-DE was utilized in parameter extraction for the photovoltaic model STP6-120/36. The findings suggest that our algorithm, HAPI-DE, demonstrates competitiveness when compared to the 6 other DE variants.

Intelligent distribution network fault monitoring integrating differential evolution and chaos whale optimization algorithm

Faced with rapid development and increasingly complex power grid structure structure of the power grid, it is necessary to accurately locate faults in modern intelligent distribution networks in order to ensure power supply reliability and improve power supply service quality. Aiming at the low positioning accuracy, long time consumption, and limited coverage types in existing positioning algorithms, a new intelligent distribution network fault positioning algorithm is designed by combining two algorithms to complete the monitoring task. Firstly, intelligent distribution network fault location methods under different distributed power grid connection methods are analyzed. Then, considering the distributed power grid connection, a fault location algorithm is designed by combining differential evolution algorithm, Sine chaotic mapping, and whale algorithm. The research results indicated that the designed method had good benchmark performance, with accuracy and recall values as high as 0.98 and 0.97, respectively. During the training process, it only required 175 iterations to reach a stable state. In practical applications, the accuracy of this algorithm in testing three types of faulty power grids was 98.90%, 98.41%, and 98.25%, respectively. The method can effectively improve the fault location accuracy, providing better positioning technology for fault monitoring problems in power systems.