Analysis of new differential evolution variants to solve multi-modal problems

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

In this paper, we propose a differential evolution (DE) algorithm variant with a combination of multiple mutation strategies based on roulette wheel selection, which we call MMRDE. We first propose a new, reflection-based mutation operation inspired by the reflection operations in the Nelder–Mead method. We design an experiment to compare its performance with seven mutation strategies, and we prove its effectiveness at balancing exploration and exploitation of DE. Although our reflection-based mutation strategy can balance exploration and exploitation of DE, it is still prone to premature convergence or evolutionary stagnation when solving complex multimodal optimization problems. Therefore, we add two basic strategies to help maintain population diversity and increase the robustness. We use roulette wheel selection to arrange mutation strategies based on their success rates for each individual. MMRDE is tested with some improved DE variants based on 28 benchmark functions for real-parameter optimization that have been recommended by the Institute of Electrical and Electronics Engineers CEC2013 special session. Experimental results indicate that the proposed algorithm shows its effectiveness at cooperative work with multiple strategies. It can obtain a good balance between exploration and exploitation. The proposed algorithm can guide the search for a global optimal solution with quick convergence compared with other improved DE variants.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

A self-competitive mutation strategy for Differential Evolution algorithms with applications to Proportional–Integral–Derivative controllers and Automatic Voltage Regulator systems

Regulation-based formulas and improved Differential Evolution(DE) algorithm is used to optimize PID parameters. In order to improve the global search ability and the convergence rate of the common DE algorithm, self-adaptive method is introduced to obtain DE parameters. On the other hand, initial population quality of DE algorithm has important influence on convergence of the algorithm. So the regulation-based formulas are used to guide the production of initial population, which is good to improve the convergence rate and realize obtaining of PID parameters completely adaptive without any personal experience. The simulation is developed on steam temperature system of cycle fluidized bed boiler with serious parameter uncertainties and many disturbance and long-time delay. The results show that the improved DE algorithm has higher optimal speed, small amount of calculation and effective optimization of parameters. The proposed method has better control quality and system robustness.

Differential evolution (DE) algorithm is a global optimization algorithm over continuous search space. DE also has been applied in many fields, such as artificial neural networks, chemical engineering, mechanical design, robotics, signal processing, biological information, and economics. At the same time, as a powerful evolutionary algorithm for solving global numerical optimization problems, the DE algorithm has drawn more and more attention. However, how to make a proper balance between the global and local search is a burning question and to limit the optimization performance of DE. In this paper, an improved algorithm η_CODE with a new η_Cauchy operator is proposed to enhance the global and local search ability of a well-known DE variant JADE. In order to guarantee the effective performance of the proposed operator, all the fitness values are ranked through a ranking scheme based on increasing order before a new η_Cauchy operator is conducted. The pNP individuals that have better fitness are selected and carried out Cauchy disturbance operation considering the complexity of the algorithm. The Dynamic parameter mechanism is utilized to select pNP individuals that number is also adjusted dynamically in each generation. The scale factor F and crossover probability CR are obtained with Lehmer mean without using determined parameter c in JADE, which aims to balance the exploration and exploitation of the algorithm during the running time. A total of sixty benchmark functions from CEC2014 and CEC2017 on real parameter optimization are employed to prove the validity of η_CODE for solving complex high-dimensional problems. The experiments indicate that η_CODE is better than or at least comparable with several state-of-the-art DE variants, including JADE, SinDE, TSDE, AGDE, and EFADE in the global numerical optimization problems. In order to further analyze the performance of η_CODE, we also select extra two high-powered modified algorithms called EBLSHADE and LSHADESPACMA based on LSHADE to discuss advantages and disadvantages of the proposed algorithm.

A differential evolution algorithm with intersect mutation operator

In response to the low accuracy exhibited by the Storm Water Management Model (SWMM), we propose an enhanced Differential Evolution and Bayesian Optimization Algorithm (DE-BOA) . This algorithm integrates the global search capability of the differential evolution algorithm with the local search capability of the Bayesian optimization algorithm, which enables a more comprehensive exploration of the vector solution space. A comparative analysis of various types of rainfall events is conducted. For model calibration and validation, a drainage subzone in Jinshazhou, Guangzhou City, is selected as the research subject. In total, 20 specific rainfall events are selected, and the DE-BOA algorithm outperforms the manual calibration, differential evolution algorithm, and Bayesian optimization algorithm regarding model calibration accuracy. Furthermore, the DE-BOA algorithm exhibits robust adaptability to rainfall events characterized by multiple peaks and higher precipitation levels, with Nash–Sutcliffe Efficiency coefficient values surpassing 0.90. This study’s findings could hold significant reference value for dynamically updating model parameters, thereby enhancing the model simulation performance and improving the accuracy of the urban intelligent water management platform.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Information utilization based modified Differential evolution algorithm (IUMDE) is an improved version of DE algorithm. In IUMDE, Mutation and Selection operation of basic Differential Evolution (DE) algorithm are modified. In proposed IUMDE initially modified mutation operation provides a selection criterion of base vector before performing the basic DE mutation operation. Further the modified selection operation utilizes the neglected trial vector and hence helps to improve the performance of DE algorithm. In this paper IUMDE algorithm is employed on 6 constrained benchmark optimization problems, selected from the literature. The numerical results expose that the IUMDE algorithm perform more accurately and significantly better than other algorithms with these constrained optimization problems.

Differential Evolution (DE) is a simple and fast population based Nature Inspired Algorithm (NIA). When it is experimented for benchmark problems as well as real world problems it outperformed other population based NIAs and other search metaheuristics in terms of rate of convergence. But it is not an exception in class of population based algorithms, it also show premature convergence and stagnates at suboptimal points. Therefore this paper tries to sustain a better convergence speed and keep away from stagnation by introducing levy flight random search process along with opposition based learning strategy in original DE algorithm. The proposed algorithm named as Opposition Based Levy Flight Search in DE (OLFDE) Algorithm. The newly proposed algorithm OLFDE tested over fourteen benchmark problems and three real world problems (Pressure Vessel Design, Parameter estimation for frequency modulated sound wave and Compression Spring problem) in order to prove its efficiency over some recent variants of DE.

Determining the optimal location of wells with the aid of an automated search algorithm is a significant and difficult step in the reservoir development process. It is a computationally intensive task due to the large number of simulation runs required. Therefore,the key issue to such automatic optimization is development of algorithms that can find acceptable solutions with a minimum number of function evaluations. In this study, the Differential Evolution (DE) algorithm is applied for the determination of optimal well locations. DE is a stochastic optimization algorithm that uses a population of solutions which evolve through generations to reach the global optimum. To investigate the performance of this algorithm, three example cases are considered which vary in dimension and complexity of the reservoir model. For each case, both DE algorithm and the widely used Genetic Algorithm (GA) are applied to maximize a Modified Net Present Value (MNPV) as the objective function. It is shown that DE outperforms GA in all cases considered, though the relative advantage of the DE vary from case to case. These results are very promising and demonstrate the applicability of DE for this challenging problem.

Differential evolution (DE), as an extremely powerful evolutionary algorithm, has recently been widely employed within complex reality optimisation problems. However, the DE algorithm mainly focuses on strengthening the adaptability of exploitation, which allows the sensitivity of the DE algorithm to be solved in cases where the effects of solving various types of problems are quite different. Moreover, the local search ability and population diversity have not been solved properly. Therefore, an adaptive DE algorithm using fitness distance correlation and a neighbourhood-based strategy (FNADE) is proposed. FNADE introduces the fitness distance correlation (FDC) as the basis for judging the difficulty of the problem, utilises a Voronoi diagram to increase the population diversity for complex multimodal problems and adopts the neighbourhood-based mutation strategy to strengthen the local search capability. FNADE is committed to solving unconstrained single-objective optimisation problems. The proposed algorithm is compared with six advanced DE algorithms in terms of CEC2017 benchmark functions. The experimental results show that the adaptive DE algorithm using FNADE is superior to other DE algorithms with regard to the accuracy and population diversity of the solution.