Enhanced Differential Evolution Research Articles

Enhancing differential evolution through a modified mutation strategy for unimodal and multimodal problem optimization

<p>Amid a lot of evolutionary methods (EMs), differential evolution (DE) is broadly used for various optimization issues. Though, it has rare shortcomings such as slow convergence, stagnation etc. Likewise, mutation and its control factor choice for DE is extremely inspiring for enhanced optimization. To increase the exploration competence of DE, a modified-DE (M-DE) is advised in this paper. It implemented a new mutation system, thru the perception of particle swarm optimization, to further trade off the population diversity. Meanwhile, centered on time-varying structure, new mutant control parameters incorporated with the suggested mutation scheme, to escaping local optima and keep evolving. Using the features of memory and robustly altered control parameters, exploitation and exploration ability of M-DE is well-adjusted. Also, admitted features of M-DE algorithm follows to speeding up convergence significantly. Finally, to verify the effectiveness of M-DE, groups of assessments have been piloted on six unimodal and seven multimodal benchmark suites. Performance of M-DE compared with different peer DE algorithms. According the investigational results, efficiency of the suggested M-DE technique has been confirmed.</p>

Efficient power management optimization based on whale optimization algorithm and enhanced differential evolution

Daily increases in electricity prices accompany daily increases in energy consumption and use. An effective load-balancing scheduling system is necessary for the lowest cost of use and the lowest cost. Despite these devices having a significant capacity for power consumption, they must find a means to balance the load at a low price. Even if lowering the voltage is challenging, it is possible to do it at the lowest cost. Hybrid Whale Differential Evolution (HWDE) is a new optimization method that combines the well-known approaches of the Whale Optimization Algorithm (WOA) and Enhanced Differential Evolution (EDE). By balancing the required Real-Time Price (RTP) and Critical Peak Price (CPP) loads, WOA and EDE capabilities can save costs and ensure the device receives sufficient voltage. The three most recent performance indicators are kWh per charge, energy usage, and the maximum-average ratio. Existing models are evaluated according to their expenses (in rupees), energy consumption, cost per kilowatt-hour, and total cost. All simulation results indicate that HWDE is the optimal solution in every circumstance. In MATLAB simulations, HWDE consistently outperforms its rivals.

Elite levy spreading differential evolution via ABC shrink-wrap for multi-threshold segmentation of breast cancer images

Differential Evolution (DE) is a commonly used metaheuristic algorithm in different optimization scenarios. However, the original DE suffers from stagnation and premature convergence in solving complex problems. In this study, an Artificial Bee Colony (ABC)-inspired Shrink-wrap (SW) strategy is proposed by combining the idea of a restart operator in ABC. Furthermore, an Elite Levy Spreading (ELS) strategy is proposed, inspired by the ideas of dimensional variation in cuckoo search and linear reduction of the number of flames in the moth-flame optimization. Based on these two strategies, an Enhanced DE (EDE) is proposed, where the ABC-inspired SW strategy is used to enhance the global exploration capability, and the ELS strategy is dedicated to improving the optimal solution quality even further. Based on CEC 2017 test, scalability experiments were conducted on EDE, and performance was compared with state-of-the-art and champion algorithms. The results were analyzed using the Wilcoxon signed rank, Friedman test, and post-hoc statistical tests. Finally, Image Segmentation experiments were performed with some peers on nine breast cancer images to validate the performance of EDE. The above experimental results show that EDE performs satisfactorily in optimization cases and multi-threshold segmentation of breast cancer images.

Optimal Energy Consumption Scheduler Considering Real-Time Pricing Scheme for Energy Optimization in Smart Microgrid

Energy consumption schedulers have been widely adopted for energy management in smart microgrids. Energy management aims to alleviate energy expenses and peak-to-average ratio (PAR) without compromising user comfort. This work proposes an energy consumption scheduler using heuristic optimization algorithms: Binary Particle Swarm Optimization (BPSO), Wind Driven Optimization (WDO), Genetic Algorithm (GA), Differential Evolution (DE), and Enhanced DE (EDE). The energy consumption scheduler based on these algorithms under a price-based demand response program creates a schedule of home appliances. Based on the energy consumption behavior, appliances within the home are classified as interruptible, noninterruptible, and hybrid loads, considered as scenario-I, scenario-II, and scenario-III, respectively. The developed model based on optimization algorithms is the more appropriate solution to achieve the desired objectives. Simulation results show that the expense and PAR of schedule power usage in each scenario are less compared to the without-scheduling case.

Advanced biped gait generator using NARX-MLP neural model optimized by enhanced evolutionary algorithm

A novel biped walking pattern combining robust zero-moment-point ZMP technique and pre-determined foot-lifting value is proposed in this paper. The implementation of suggested approach contains following stages. Initially, a one-step ZMP curve for a small-sized humanoid is created using the 3rd-order interpolating equation, with pre-determined velocity responding the ZMP concept. The next step, biped gait planning is modeled as a non-linear MIMO plant including ten degree-of-freedom DOF. Then, the installation of a biped walking pattern generator (WPG) based on the new hybrid Neural-NARX model is completed. Eventually, the novel Enhanced Differential Evolution (EDE) technique is applied to optimally identify the weights of the hybrid Neural-NARX structure, for ensuring robust robot walking in terms of desired ZMP trajectories and pre-determined foot-lifting value. All case studies confirm that it is surely provide a biped WPG satisfying both of the effectiveness and high robustness. The verification of the newly proposed WPG is adequately tested via both simulation and experiment results.

Optimal Demand-Side Management Using Flat Pricing Scheme in Smart Grid

This work proposes a framework to solve demand-side management (DSM) problem by systematically scheduling energy consumption using flat pricing scheme (FPS) in smart grid (SG). The framework includes microgrid with renewable energy sources (solar and wind), energy storage systems, electric vehicles (EVs), and building appliances like time flexible, power flexible, and base/critical appliances. For the proposed framework, we develop an ant colony optimization (ACO) algorithm, which efficiently schedules smart appliances, and EVs batteries charging/discharging with microgrid and without (W/O) microgrid under FPS to minimize energy cost, carbon emission, and peak to average ratio (PAR). An integrated technique of enhanced differential evolution (EDE) algorithm and artificial neural network (ANN) is devised to predict solar irradiance and wind speed for accurate microgrid energy estimation. To endorse the applicability of the proposed framework, simulations are conducted. Moreover, the proposed framework based on the ACO algorithm is compared to mixed-integer linear programming (MILP) and W/O scheduling energy management frameworks in terms of energy cost, carbon emission, and PAR. The developed ACO algorithm reduces energy cost, PAR, and carbon emission by 23.69%, 26.20%, and 15.35% in scenario I, and 25.09%, 31.45%, and 18.50% in scenario II, respectively, as compared to W/O scheduling case. The results affirm the applicability of the proposed framework in aspects of the desired objectives.

Enhancing differential evolution with a target vector replacement strategy

Individuals find it difficult to avoid stagnation in the iterative process of the differential evolution (DE) algorithm, and the stagnant individuals have restricted improvement in the population, which will have a negative effect on its performance. This research put forward a target vector replacement strategy (TVRS) for reducing the impact of stagnant individuals on the DE algorithm's performance. For stagnant target vectors, while executing mutation operation and crossover operation, TVRS selects non-stagnant individuals in the population to replace the stagnant target vectors with a specific probability. Because improving stagnant individuals are difficult, TVRS provides more opportunities for improvement to those who are not stagnant, while the opportunities for stagnant individuals to be improved are decreased. For assessing the efficiency of TVRS, TVRS was implemented to six DE algorithms and compared to their original algorithms. Judging from the performance outcomes of TVRS in the CEC 2014 benchmark test set, TVRS can greatly increase the DE algorithm's performance. This study will show the evolutionary opportunity that is obtained by an individual should be related to the individual state. Adjusting the individual evolutionary opportunity based on the individual state is helpful for improving the stagnation problem of the differential evolution algorithm. This study will provide a new way for improving the stagnation problem of the differential evolution algorithm and other evolutionary algorithms.

Real-Time Energy Management and Load Scheduling with Renewable Energy Integration in Smart Grid

With the smart grid development, the modern electricity market is reformatted, where residential consumers can actively participate in the demand response (DR) program to balance demand with generation. However, lack of user knowledge is a challenging issue in responding to DR incentive signals. Thus, an Energy Management Controller (EMC) emerged that automatically respond to DR signal and solve energy management problem. On this note, in this work, a hybrid algorithm of Enhanced Differential Evolution (EDE) and Genetic Algorithm (GA) is developed, namely EDGE. The EMC is programmed based with EDGE algorithm to automatically respond to DR signals to solve energy management problems via scheduling three types of household load: interruptible, non-interruptible, and hybrid. The EDGE algorithm has critical features of both algorithms (GA and EDE), enabling the EMC to generate an optimal schedule of household load to reduce energy expense, carbon emission, Peak to Average Ratio (PAR), and user discomfort. To validate the proposed EDGE algorithm, simulations are conducted compared to the existing algorithms like Binary Particle Swarm Optimization (BPSO), GA, Wind Driven Optimization (WDO), and EDE. Results illustrate that the proposed EDGE algorithm outperforms benchmark algorithms in energy expense minimization, carbon emission minimization, PAR alleviation, and user discomfort maximization.

Load frequency control of time-delayed power systems using optimal IMC-PID design and model approximation approach

ABSTRACT In this paper, a new optimal and robust IMC-PID control design is proposed for the LFC of time-delayed power systems. The proposed design is a process reduction control approach. Primitively, a simple and approximate model (i.e. Reduced Order Model (ROM)) is determined for the large-scale power system by using the proposed Enhanced Differential Evolution (EDE) algorithm-based Model Order Reduction (MOR) approach. Further, by considering the ROM as an internal plant model, the unknown IMC filter time constant is tuned to attain the optimal performance by minimizing the integral of error between the reference input and the actual output responses of the power system by using the EDE algorithm. Finally, the finest PID controller gains are determined by the least-square model matching with the optimal IMC. The proposed design is illustrated by applying to various Single-Area Power Systems (SAPS) with a delay between the power system sensing device to the control centre. The simulation results demonstrate the efficacy of the proposed IMC-PID design in improving the dynamic stability against consistent and inconsistent delays and the robustness towards the load disturbances, parameter uncertainties and model mismatches.

Enhancing differential evolution algorithm through a population size adaptation strategy

As one of the three basic control parameters of the differential evolution algorithm (DE), the population size (PS) has attracted extensive attention. In general, the most appropriate population size varies for different types of problems and problems with different dimensions. As a result, the performance of an algorithm with a fixed population size is limited to some extent. In this paper, a new enhanced algorithm with a population entropy based population adaptation strategy has been proposed under the framework of SHADE (PE-SHADE). Firstly, a method to calculate the entropy of the population is introduced, through which the distribution state of the population is also characterized. Secondly, the population size is adapted according to the distribution state with a population increasing strategy and a population reduction strategy. In order to evaluate the performance of the proposed algorithm, experiments on the standard benchmark CEC2014 have been conducted, as well as the sensitivity experiments for the extra parameters. The performance comparisons with SHADE, L-SHADE, and some other well-known DE variants are analyzed, which statistically supports the effectiveness of the proposed algorithm.

Two Strategies to Improve the Differential Evolution Algorithm for Optimizing Design of Truss Structures

The performance of differential evolution (DE) mostly depends on mutation operator. Inappropriate configurations of mutation strategies and control parameters can cause stagnation due to over exploration or premature convergence due to over exploitation. Balancing exploration and exploitation is crucial for an effective DE algorithm. This work presents an enhanced DE (EDE) for truss design that utilizes two new strategies, namely, integrated mutation and adaptive mutation factor strategies, to obtain a good balance between the exploration and exploitation of DE. Three mutation strategies (DE/rand/1, DE/best/2, and DE/rand-to-best/1) are combined in the integrated mutation strategy to increase the diversity of random search and avoid premature convergence to a local minimum. The adaptive mutation factor strategy systematically adapts the mutation factor from a large value to a small value to avoid premature convergence in the early searching period and to increase convergence to the global optimum solution in the later searching period. The outstanding performance of the proposed EDE is demonstrated through optimization of five truss structures.

Optimal IMC-PID controller design for large-scale power systems via EDE algorithm-based model approximation method

In this paper, the authors propose an optimal IMC-PID controller design for the Load Frequency Control (LFC) of large-scale power system via model approximation method. The model approximation method uses the Enhanced Differential Evolution (EDE) algorithm to determine an optimal Reduced Order Model (ROM) for the considered large-scale power system by minimizing the performance measure called Integral Square Error (ISE) between their step responses. Later, the LFC design is carried out using an optimal ROM instead of processing with the large-scale power system model. Thus, this simplifies the design, reduces the computational efforts and also helps in determining the lower order controller. An optimal IMC design methodology is proposed by minimizing ISE between the actual output and the reference input responses of the large-scale power system using EDE algorithm. Further, PID controller gains are acquired by least square model matching with the optimal IMC transfer function. The proposed IMC-PID controller design allows a satisfied reference input tracking performance, robustness in disturbance rejection and improves the dynamic stability of the power system. The proposed method is validated by applying it to a single area power system of third-order SISO model and also extended to a centralized two-area thermal–thermal non-reheated power system of a seventh-order MIMO model. The simulation results and the comparison of error performance indices show the efficacy of the proposed method over the significant methods available in the literature.

Enhancing Differential Evolution on Continuous Optimization Problems by Detecting Promising Leaders

Due to that the performance of differential evolution (DE) significantly depends on offspring generation strategies, various DE variants have been reported with the improved mutation operators. However, on the one hand, the mutation operators in most DE variants are guided by the elites in terms of the fitness value, without considering their distribution information in the fitness landscape. It may lead to the population be evolving towards the unpromising areas more frequently if these elites are clustered in a locally optimal region. On the other hand, in most DE variants, the evolutionary information of the potential trial vectors is not fully utilized to guide the search, which will hamper the local exploitation in the promising regions that they are located in. To overcome these weaknesses, this article proposes an enhanced DE framework (DELDG) with a leaders-detection-and-guidance mechanism that consists of an adaptive leaders detection (ALD) and a neighborhood-based tournament selection (NTS). With these two novel operators, DELDG can not only guide the mutation process of each individual with multiple promising leaders detected by ALD, but also accelerate the convergence speed with the competition among the potential trial vectors by NTS. Therefore, DELDG is characterized by the explicit detection of the promising leaders according to their fitness values and distribution information and the effective use of the potential trial vectors in the neighborhood of each leader. Compared with 36 excellent DE variants and evolutionary algorithms (EAs), the experimental results on 28 IEEE CEC2013 real-parameter functions and 17 IEEE CEC2011 real-world problems have demonstrated the competitive performance of DELDG.

Enhanced Evolutionary Sizing Algorithms for Optimal Sizing of a Stand-Alone PV-WT-Battery Hybrid System

An increase in the world’s population results in high energy demand, which is mostly fulfilled by consuming fossil fuels (FFs). By nature, FFs are scarce, depleted, and non-eco-friendly. Renewable energy sources (RESs) photovoltaics (PVs) and wind turbines (WTs) are emerging alternatives to the FFs. The integration of an energy storage system with these sources provides promising and economical results to satisfy the user’s load in a stand-alone environment. Due to the intermittent nature of RESs, their optimal sizing is a vital challenge when considering cost and reliability parameters. In this paper, three meta-heuristic algorithms: teaching-learning based optimization (TLBO), enhanced differential evolution (EDE), and the salp swarm algorithm (SSA), along with two hybrid schemes (TLBO + EDE and TLBO + SSA) called enhanced evolutionary sizing algorithms (EESAs) are proposed for solving the unit sizing problem of hybrid RESs in a stand-alone environment. The objective of this work is to minimize the user’s total annual cost (TAC). The reliability is considered via the maximum allowable loss of power supply probability ( L P S P m a x ) concept. The simulation results reveal that EESAs provide better results in terms of TAC minimization as compared to other algorithms at four L P S P m a x values of 0%, 0.5%, 1%, and 3%, respectively, for a PV-WT-battery hybrid system. Further, the PV-WT-battery hybrid system is found as the most economical scenario when it is compared to PV-battery and WT-battery systems.

Enhancing differential evolution algorithm with repulsive behavior

In the real world, differential evolution (DE) algorithm can effectively solve optimization problems in engineering; thus, DE has been applied in various fields. However, in complex multimodal problems, DE may encounter stagnation during iterations. Thus, we propose an improved DE algorithm with repulsive behavior, named RBDE. The core idea of RBDE is that offsprings no longer simply learn from the current optima but continue to explore the direction in which the current optimal individual is repelled by poorer individuals. This mechanism increases the diversity of the learning direction of a population. RBDE includes two types of repulsive behaviors: In the first, RBDE selects two parents as the source of repulsion and generates two different repulsive forces to promote the offspring to explore the optimal individual; the other considers that the gradient of the repulsion between the parents is the learning direction of the offspring. The repulsive behavior can effectively alleviate the stagnation of DE when dealing with multimodal problems. To evaluate the performance of RBDE, we use CEC2017 benchmarks to test RBDE and nine other algorithms. The results show that the performance of RBDE is better than that of the other nine algorithms. In addition, RBDE is used to train an artificial neural network and is applied to the optimization problem of four-bar linkages, whose results indicate that the model obtained by RBDE is more accurate than those by the other algorithms.

Optimized semiblind sparse channel estimation algorithm for MU-MIMO OFDM system

In Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing (MIMO-OFDM) systems, the channel plays an imperative role as the multipath. The channel estimation frameworks specifically designed for the demanding channel conditions with faster time-varying characters are separately emphasized. The prevailing Channel Estimation (CE) methodologies are incredibly complex. To resolve such complexities, this paper proposed an Optimized Semi-Blind Sparse (OSBS) CE algorithm for MU-MIMO OFDM. On the transmitter block, initially, the QPSK modulation is implemented to modulate an input signal. Subsequently, the Pulse Shaping Algorithm (PSA) used for mitigating the ISI (Inter-Symbol Interferences). For symbol mapping, an IFFT (Inverse Fast Fourier Transforms) operation performed at each transmitter. Next, transmit the symbols over the Multipath channel via transmitter’s antennas towards the receiver’s antennas by adding AWGN (Additive White Gaussian Noise). The operations in the transmitter inversely done on the receiver block. Then CE is done by utilizing the OSBS algorithm, and the cost function is lessened by employing EDE (Enhanced Differential Evolution) algorithm. Lastly, the Channel Capacity (CC) is called gauge. Experiential result of the proposed system gives better results when contrasted with the other methods centered on Bit Error Rate (BER), PSNR, Symbol Error Rate (SER), LS, and MMSE.

Hybrid meta-heuristic optimization based home energy management system in smart grid

The emergence of the smart grid has empowered the consumers to manage the home energy in an efficient and effective manner. In this regard, home energy management (HEM) is a challenging task that requires efficient scheduling of smart appliances to optimize energy consumption. In this paper, we proposed a meta-heuristic based HEM system (HEMS) by incorporating the enhanced differential evolution (EDE) and harmony search algorithm (HSA). Moreover, to optimize the energy consumption, a hybridization based on HSA and EDE operators is performed. Further, multiple knapsacks are used to ensure that the load demand for electricity consumers does not exceed a threshold during peak hours. To achieve multiple objectives at the same time, hybridization proved to be effective in terms of electricity cost and peak to average ratio (PAR) reduction. The performance of the proposed technique; harmony EDE (HEDE) is evaluated via extensive simulations in MATLAB. The simulations are performed for a residential complex of multiple homes with a variety of smart appliances. The simulation results show that EDE performs better in terms of cost reduction as compared to HSA. Whereas, in terms of PAR, HSA is proved to be more efficient as compared to EDE. However, the proposed scheme outperforms the existing meta-heuristic techniques (HSA and EDE) in terms of cost and PAR.

Scavenging differential evolution algorithm for smart grid demand side management

Demand side management (DSM) has gained a lot of attention in recent years as a result of increased deployment of alternative renewable energy resources in electric power grids. This paper presents a novel scavenging differential evolution algorithm which reuses unfit population agents in previous generations of a genetic algorithm. The performance of the proposed algorithm is compared to another popular evolutionary algorithm in literature: enhanced differential evolution (EDE). The cost minimization model consists of parameters which describe consumer energy cost savings for weekdays in Johannesburg using home energy management system (HEMS). The HEMS is incorporated with solar photovoltaic (PV) panel and plug-in electric vehicle (PHEV). Preliminary results show that the proposed algorithm outperforms EDE with regard to flattening consumer energy usage profile and minimizing discomfort related to load scheduling.

A Novel Memetic Framework for Enhancing Differential Evolution Algorithms via Combination With Alopex Local Search

Differential evolution (DE) represents a class of population-based optimization techniques that uses differences of vectors to search for optimal solutions in the search space. However, promising solutions/regions are not adequately exploited by a traditional DE algorithm. Memetic computing has been popular in recent years to enhance the exploitation of global algorithms via incorporation of local search. This paper proposes a new memetic framework to enhance DE algorithms using Alopex Local Search (MFDEALS). The novelty of the proposed MFDEALS framework lies in that the behavior of exploitation (by Alopex local search) can be controlled based on the DE global exploration status (population diversity and search stage). Additionally, an adaptive parameter inside the Alopex local search enables smooth transition of its behavior from exploratory to exploitative during the search process. A study of the important components of MFDEALS shows that there is a synergy between them. MFDEALS has been integrated with both the canonical DE method and the adaptive DE algorithm L-SHADE, leading to the MDEALS and ML-SHADEALS algorithms, respectively.Both algorithms were tested on the benchmark functions from the IEEE CEC’2014 Conference. The experiment results show that Memetic Differential Evolution with Alopex Local Search (MDEALS) not only improves the original DE algorithm but also outperforms other memetic DE algorithms by obtaining better quality solutions. Further, the comparison between ML-SHADEALS and L-SHADE demonstrates that applying the MFDEALS framework with Alopex local search can significantly enhance the performance of L-SHADE.

Jaya based Optimization Method with High Dispatchable Distributed Generation for Residential Microgrid

This paper presents a model for optimal energy management under the time-of-use (ToU) and critical peak price (CPP) market in a microgrid. The microgrid consists of intermittent dispatchable distributed generators, energy storage systems, and multi-home load demands. The optimal energy management problem is a challenging task due to the inherent stochastic behavior of the renewable energy resources. In the past, medium-sized distributed energy resource generation was injected into the main grid with no feasible control mechanism to prevent the waste of power generated by a distributed energy resource which has no control mechanism, especially when the grid power limit is altered. Thus, a Jaya-based optimization method is proposed to shift dispatchable distributed generators within the ToU and CPP scheduling horizon. The proposed model coordinates the power supply of the microgrid components, and trades with the main grid to reduce its fuel costs, production costs, and also maximize the monetary profit from sales revenue. The proposed method is implemented on two microgrid operations: the standalone and grid-connected modes. The simulation results are compared with other optimization methods: enhanced differential evolution (EDE) and strawberry algorithm (SBA). Finally, simulation results show that the Jaya-based optimization method minimizes the fuel cost by up to 38.13%, production cost by up to 93.89%, and yields a monetary benefit of up to 72.78% from sales revenue.