Mean‐Guided Elite Selection Genetic Algorithm for Multi‐Objective Optimization of Operational Costs and Voltage Control in Grid‐Connected Microgrids

We present a differential particle swarm evolution (DPSE) algorithm which combines the basic idea of velocity and position update rules from particle swarm optimization (PSO) and the concept of differential mutation from differential evolution (DE) in a new way. With the goal of optimizing within a limited number of function evaluations, the algorithm is tested and compared with the standard PSO and DE methods on 14 benchmark problems to illustrate that DPSE has the potential to achieve a faster convergence and a better solution. Simulation results show that, on the average, DPSE outperforms DE by 39.20% and PSO by 14.92% on the 14 benchmark problems. To show the feasibility of the proposed strategy on a real-world optimization problem, an application of DPSE to optimize the parameters of active disturbance rejection control (ADRC) in PUMA-560 robot is presented. I. INTRODUCTION The particle swarm optimization (PSO) algorithm was originally introduced in (1) as an alternative to the standard genetic algorithm (GA). The PSO was inspired by insect swarms and has since proven to be a competitor to the standard GA when it comes to function optimization. Since then several researchers have analyzed the PSO performance and disadvantages (2-4) and their research indicates that it performs well in the early iterations but has problems reaching a near optimal solution in several real-valued function optimization problems. Differential evolution (DE) is a simple yet powerful evolutionary algorithm (EA) for global optimization introduced by Price and Storn (5). Both PSO and DE received great interest from the evolutionary computation community, and showed great promise in several real-world applications (6-9). As a result, a lot of effort has been spent recently in combining both methods to achieve better optimization result. One method proposed in 2003 (10) applies to the modeling of gene regulator networks in 2007 (11). In this algorithm, the mutations provided by DE operator are applied, and only applied on the personal best individual to prevent the swarm from disorganizing by unexpected fluctuations. Later in 2008, (12) also presents a method of hybrid PSO with DE and its application to a high-frequency transformer can be seen in (13). In this algorithm, the DE mutations are applied to update both personal best and global best. At the same time, Swagatam Das et al. (14) proposed a hybridization of PSO and DE for continuous optimization in 2008. Based on that idea, (15) apply this algorithm for the black-box optimization benchmarking for noisy functions.

The differential evolution (DE) algorithm has been received some attention recently in terms of water distribution system (WDS) optimization. The DE is potentially becoming an alternative optimization tool for WDS design due to its satisfactory search performance. This paper presents a systematic performance comparison between the DE algorithm and the frequently used genetic algorithms (GAs). Two DE variants and two GA variants are compared in this paper in terms of optimizing the design of WDSs. These include the traditional DE, the dither DE algorithm, the traditional GA and the creeping mutation GA. Two well-known benchmark water distribution case studies are used in this study, which are the New York Tunnels Problem and the Hanoi Problem. The results show that the DE variants significantly outperform the GA variants in terms of both the solution quality and efficiency.

This paper proposed to discuss the complexity of scheduling by comparing two optimization methods between genetic algorithms with differential Evolution. Genetic Algorithms can solve the simplest to complex problems as well. Therefore, the Genetic algorithm is precisely applied to the scheduling of subjects. Then another appropriate optimization method for completing optimization is the Differential Evolution (DE) algorithm. DE algorithm is a fast and effective search algorithm in solving numerical and finding optimal global solutions. The steps of the two algorithms are initialization, participation, mutation, crossover, and selection. The scheduling system produces non-optimal schedules for teacher conflicts and empty slot schedules. After the genetic algorithm and differential evolution are applied, an analysis of the results of the subject scheduling is then performed by comparing the fitness values and the execution speed of the two algorithms. the genetic algorithm found only 2 perfect schedules out of 10 experiments, whereas in the implementation of differential algorithms, there are 7 perfect schedules out of 10 experiments. Thus, it can be concluded that by determining the value of the producing parameters 5, generation 50, mutation 0.6, and crossover 0.2, the differential evolution produces better output or conformity values using genetics.

The increase in global power demand has caused most of today's power networks to become overloaded especially in Sub-Saharan Africa. The increased load demand can be met through expansion of existing generation and transmission system. However, construction of new power infrastructure is limited by financing and technical constraints. Thus, power networks have been left to operate at overload conditions with high power losses and many power quality (PQ) problems. Flexible AC Transmission System (FACTS) devices can improve the power transfer capability of the existing transmission networks without the need of constructing new power infrastructure. In this paper, a multi-objective function comprising of minimization of power loss (PL), voltage deviation (VD) and operational cost (OC) was formulated and solved using a novel algorithm. A novel Genetic Algorithm-Improved Particle Swarm Optimization (GA-IPSO) technique is proposed in this paper for optimization of size and location of FACTS devices. Static Synchronous Compensator (STATCOM), Thyristor Controlled Series Capacitor (TCSC) and Unified Power Flow Controller (UPFC) are the three FACTS devices considered. The proposed technique was validated using IEEE-33 Bus Test System, which is a popular benchmark Radial Distribution System (RDS). The three FACTS devices were optimized separately and also in a combined manner. Under the separate optimization, the size and location of individual FACTS devices were optimized. For combined optimization, the sizes and locations of more than one device were optimized in the same test system. For separate optimization, UPFC produced the best results by reducing the active power losses by 38.44 % and OC from $1.59×105 to $ 1.15×105. Under the combined optimization, combination of TCSC, STATCOM and UPFC gave better results by achieving active power loss reduction of 56.09 % and reducing OC from $1.59×105 to $ 1.03×105. Comparison of GA-IPSO technique with other algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Improved Grey Wolf Optimization (IGWO) and Differential Evolution Algorithm (DEA) showed that the proposed hybrid technique was superior and more efficient in solving the FACTS optimization problem.

Differential evolution algorithm for nonlinear inversion of high-frequency Rayleigh wave dispersion curves

The differential evolution (DE) algorithm has been received increasing attention in terms of optimizing the design for the water distribution systems (WDSs). This paper aims to carry out a comprehensive performance comparison between the new emerged DE algorithm and the most popular algorithm—the genetic algorithm (GA). A total of six benchmark WDS case studies were used with the number of decision variables ranging from 8 to 454. A preliminary sensitivity analysis was performed to select the most effective parameter values for both algorithms to enable the fair comparison. It is observed from the results that the DE algorithm consistently outperforms the GA in terms of both efficiency and the solution quality for each case study. Additionally, the DE algorithm was also compared with the previously published optimization algorithms based on the results for those six case studies, indicating that the DE exhibits comparable performance with other algorithms. It can be concluded that the DE is a newly promising optimization algorithm in the design of WDSs.

Evolutionary algorithms (EAs) have recently been successfully applied in optimization problems and engineering disciplines. They can solve complex optimization problems without specialized information such as gradient or smoothness of objective functions. Although pure EAs such as genetic algorithm (GA), evolutionary strategies (ES) and evolutionary programming (EP) are easy to implement and offer fair performance in many applications, experimental results have shown that a variant of evolutionary method namely Differential Evolution (DE) has good convergence properties and outperforms other well known EAs (Ilonen et al., 2003). This variation was first introduced by Storn and Price (Storn & Price, 1997) and has an increasing interest as an optimization technique in recent years due to its achievement for a global minimum. It has several important differences from the traditional genetic optimization especially in the nature of the mutation, in which instead of taking a random perturbation, DE randomly selects a pair of individuals and computes the difference between their parameter vectors. This vector of difference is then added to the individual being mutated after multiplying by a constant. Another important difference is that the DE does not require the selection of parents based on fitness. Instead, fitness determines which children are kept for the next generation. Advantages of these approaches are shown in (Storn & Price, 1997). Using DE for training neural networks was first introduced in (Masters & Land, 1997). It was reported that the DE algorithm is particularly suitable for training general regression neural networks (GRNN), and it outperforms other training methods such as gradient and Hessian on applications which have the presence of multiple local minima in the error space. Recently, the combination of the DE and other training algorithms has also been investigated. Subudhi and Jena (Subudhi & Jena, 2008) proposed a combination of DE and Levenberg Marquardt (LM) to train neural network for nonlinear system identification. It was shown that this combination can offer better identification results than neural networks trained by ordinary LM algorithm. More comprehensive studies for using DE in the training neural networks are presented in (Ilonen et al., 2003). Although there are many network architectures proposed for different problems and applications, it was shown that single hidden-layer feedforward neural networks (SLFNs) can form boundaries with arbitrary shape and approximate any function with arbitrarily small error if the activation functions are chosen properly (Huang et al., 2000). An efficient training algorithm namely extreme learning machine (ELM) was proposed for SLFNs. It O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

A robust and efficient parameter identification method of the stress relaxation model based on Altenbach-Gorash-Naumenko creep equations is discussed. The differential evolution (DE) algorithm with a modified forward-Euler scheme is used in the identification procedure. Besides its good convergence properties and suitability for parallelization, initial guesses close to the solutions are not required for the DE algorithm. The parameter determination problem of the stress relaxation model is based on a very broad range specified for each parameter. The performance of the proposed DE algorithm is compared with a step-by-step model parameter determination technology and the genetic algorithm (GA). The model parameters of 12Cr-1Mo-1W-1/4V stainless steel bolting material at 550°C have been determined, and the creep and stress relaxation behaviors have been calculated. Results indicate that the optimum solutions can be obtained more easily by DE algorithm than others.

Differential Evolution (DE) algorithm is a new heuristic approach which has been proposed particulary for numeric optimization problems. It is a population based algorithm like genetic algorithms using the similar operators; crossover, mutation and selection. In this work, DE algorithm has been applied to the design of fixed point digital Finite Impuls Response (FIR) filters and its performance has been compared to that of Genetic Algorithm (GA) and Least Squares Algorithm (LSQ).

With the emergence of smart grid, which presents the next generation of electrical power systems, residential and commercial buildings have the opportunities to manage their offices energy usage to reduce energy expenditure. This paper presents a differential evolution algorithm to optimize the energy production and consumption systems in a smart office with the integration of renewable energy resources, and battery storage systems. The aim of the study is to optimize energy management in buildings by integrating a photovoltaic (PV) system with a battery storage system, using the Differential Evolution (DE) algorithm to minimize operational costs while ensuring efficient energy utilization and system reliability. To achieve this, energy model using PV, battery, and grid data over 24 hours in 1- hour steps was developed; also, energy cost was minimized by optimizing PV battery and grid usage. Moreover, power balance was kept at equilibrium to meet load demand and enable grid export while battery limits is applied to state of charge (SOC), discharge rate and capacity. In addition, an heuristic differential evolution algorithm was used to solve the energy optimization problem. Three scenarios were evaluated to minimize costs of energy in the offices. Scenario I explored grid supply only, scenario II looked at electricity equilibrium of the micro grid with the PV and grid supply while scenario III considered equilibrium of the micro grid with PV, BESS and grid supply. Moreover, actual time-of-use tariffs for electricity prices is evaluated. The simulation results of the devised model are given for different case studies and the effectiveness of the system is demonstrated via a comparative study. As a result, it was found that the operational costs are decreased nearly by integrating only photovoltaic production according to the case which has no additional sources. Also, a substantial reduction of is achieved by considering both and . Results find the global optimum solution for the horizon with important reduction of execution time and by achieving significant energy cost savings of the considered scenarios. To improve modeling and optimization of energy in smart buildings considering the benefits of PV and BESS on the power sector, genetic algorithm is a powerful optimization tool recommended for finding solutions to optimization of energy management decision variables like cost functions, power and so on. It gives the exact solution of micro grid energy management problems which converge as fast as possible as exemplified in this research study.

Differential evolution (DE) algorithm is presented and applied to global optimization in this research. DE suggested initially for the solution to Chebychev polynomial fitting problem is similar to genetic algorithm (GA) including crossover, mutation and selection process. However, differential evolution algorithm is simpler than GA because it uses a vector concept in populating process. And DE turns out to be converged faster than GA, since it employs the difference information as pseudo-sensitivity. In this paper, a trial vector and its control parameters of DE are examined and unconstrained optimization problems of highly nonlinear multimodal functions are demonstrated. To illustrate the efficiency of DE, convergence rates and robustness of global optimization algorithms are compared with those of simple GA.

Differential Evolution (DE) algorithm is a new heuristic approach mainly having three advantages; finding the true global minimum of a multi modal search space regardless of the initial parameter values, fast convergence, and using a few control parameters. DE algorithm which has been proposed particulary for numeric optimization problems is a population based algorithm like genetic algorithms using the similar operators; crossover, mutation and selection. In this work, DE algorithm has been applied to the design of digital Finite Impulse Response filters and compared its performance to that of genetic algorithm.

We studied the joint replenishment problem with deterministic resource restriction. A differential evolution (DE) algorithm that uses indirect grouping strategy to solve constrained joint replenishment is presented. The procedure and structure of the DE algorithm is proposed. Extensive computational experiments are performed to compare the performances of the DE algorithm with results of genetic algorithm (GA) and heuristic algorithm CRAND. The experimental results indicate that the DE algorithm performs relative to CRAND and superior to GA.

Particles swarm optimization (PSO) and differential evolution (DE) algorithms based on optimization are employed to estimate low atmospheric refractivity profiles from radar sea clutter. Low atmospheric refractivity profiles are modeled as evaporation ducts. The objective functions, which are used to evaluate the fit of simulated and measured power in estimation procedures, are also investigated at different frequencies such as L-, S-, C- and X-frequency at 10 m/s wind speeds. The results show that all the objective functions are multi-peak functions. The Adjusted Barton Model of radar cross section (RCS) is adopted. PSO and DE algorithms are compared with genetic algorithm (GA) by 200 Monte Carlo simulation estimations. Simulation results indicate that DE has the best global search ability, and PSO has the highest success probability. According to the statistical results, PSO algorithm with the population size 30 is the appropriate way for evaporation duct estimation.

Differential evolution (DE) algorithm has been proven to be a simple and efficient evolutionary algorithm for global optimization over continuous spaces, which is widely used in both benchmark test functions and real-world applications. Like genetic algorithms, differential evolution algorithm uses three typical operators to search the solution space: crossover, mutation and selection. Among these operators, mutation plays a key role in the performance of differential evolution algorithm and there are several mutation variants often used, which constitute several corresponding differential evolution strategies. By means of experiments, this paper investigates the relative performance of different differential evolution algorithms for global optimization under different differential evolution strategies respectively. In simulation studies, De Jong’s test functions have been employed, and some conclusions are drawn.