$\eta$ _CODE: A Differential Evolution With $\eta$ _Cauchy Operator for Global Numerical Optimization

Modified Teaching–Learning-Based Optimization algorithm for global numerical optimization—A comparative study

Differential Evolution (DE) is a simple, powerful and easy to use global optimization algorithm. DE has been studied in detail by many researchers in the past years. In DE algorithm trial vector generation strategies have a significant influence on its performance. This research studies that whether performance of DE algorithm can be improved by incorporating selection advancement in effective trial vector generation strategies. A novel advancement in DE trial vector generation strategies is proposed in this research to speeds up the convergence speed of DE algorithm. The proposed fitness proportion based random vector selection DE (FPRVDE) is based on the proportion of individual fitness mechanism. FPRVDE reduces the role of poor performing individuals to enhance it performance capability of DE algorithm. To form a trial vector using FPRVDE, individual based on the proportion of their fitness are selected. FPRVDE mechanism is applied to most commonly used set of DE variants. A comprehensive set of multidimensional function optimization problems is used to access the performance of FPRVDE. Experimental result shows that proposed approach accelerates DE algorithm.

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.

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.

High-speed 3D indoor localization system based on visible light communication using differential evolution algorithm

SummaryModern power systems are being shifted its attention towards distributed generations (DGs). DGs have allured more concern as an auspicious opportunity with considerable economic profits. To minimize the power generation costs of DGs, day‐to‐day operation scheduling is essential. The role of this study is to offer an optimal operation schedule for DG with several energy sources including renewable energy sources (RES), considering economic facets. In order to achieve the cost minimization along with optimal scheduling, an objection function has been formulated and solved using the optimization algorithms. This study aims to present the applications of differential evolution (DE) algorithm and its variants such as opposition‐based differential evolution (ODE), self‐adaptive differential evolution (SaDE), improved differential evolution (IDE), and cultivated differential evolution (CuDE) for scheduling DG optimally. A scheme for optimal scheduling of thermal, wind power, and solar PV generators has been evaluated. The simulations have been carried out on IEEE 14 bus system, IEEE 30 bus system, IEEE 57 bus system, and Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO), as a real part of 62 bus Indian utility system (IUS). The novelty of this study lies in simulating a real‐time system for solving optimal scheduling problem, in that way helping decision makers to choose the optimal operation points. The results indicate that the SaDE outperformed other DE variants by giving the best fitness value and convergence rate.

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.

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

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.

DE/EDA: A new evolutionary algorithm for global optimization

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.

Social learning differential evolution

Differential evolution (DE), as a class of biologically inspired and meta-heuristic techniques, has attained increasing popularity in solving many real world optimization problems. However, DE is not always successful. It can easily get stuck in a local optimum or an undesired stagnation condition. This paper proposes a new DE algorithm Differential Evolution with Alopex-Based Local Search (DEALS), for enhancing DE performance. Alopex uses local correlations between changes in individual parameters and changes in function values to estimate the gradient of the landscape. It also contains the idea of simulated annealing that uses temperature to control the probability of move directions during the search process. The results from experiments demonstrate that the use of Alopex as local search in DE brings substantial performance improvement over the standard DE algorithm. The proposed DEALS algorithm has also been shown to be strongly competitive (best rank) against several other DE variants with local search.

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.