Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems

Evolutionary algorithms (EAs) are general-purpose stochastic search methods that use the metaphor of evolution as the key element in the design and implementation of computer-based problems solving systems. During the past two decades, EAs have attracted much attention and wide applications in a variety of fields, especially for optimization and design. EAs offer a number of advantages: robust and reliable performance, global search capability, little or no information requirement, and others. Among various EAs, differential evolution (DE), which characterized by the different mutation operator and competition strategy from the other EAs, has shown great promise in many numerical benchmark problems and real-world optimization applications. The potentialities of DE are its simple structure, easy use, convergence speed and robustness. To improve the global optimization property of DE, in this paper, a DE approach based on measure of population's diversity and cultural algorithm technique using normative and situational knowledge sources is proposed as alternative method to solving the economic load dispatch problems of thermal generators. The traditional and cultural DE approaches are validated for two test systems consisting of 13 and 40 thermal generators whose nonsmooth fuel cost function takes into account the valve-point loading effects. Simulation results indicate that performance of the cultural DE present best results when compared with previous optimization approaches in solving economic load dispatch problems.     

用演化算法求解抛物型方程扩散系数的识别问题

基于演化算法给出了一类求解参数识别反问题的一般方法,该方法表明只要找到好的、求解相应的正问题的数值方法,演化算法就可以用于求解此类反问题。设计有效的求解反问题的演化算法的关键是寻找一种适合反问题的解空间的编码表示形式、适当的适应值函数形式以及有效的计算正问题的数值方法。该文结合算法、传统的求解反问题的工方法和正则化技术,设计了一类求解参数识别反问题的方法。为验证此类方法,将其用于求解一维扩散方程的     

Solution of Jiles-Atherton vector hysteresis parameters estimation by modified Differential Evolution approaches

Differential Evolution (DE) is a simple and efficient stochastic global optimization algorithm of evolutionary computation field, which involves the evolution of a population of solutions using operators such as mutation, crossover, and selection. The basic idea of DE is to adapt the search during the evolutionary process. At the start of the evolution, the perturbations are large since parent populations are far away from each other. As the evolutionary process matures, the population converges to a small region and the perturbations adaptively become small. DE approaches have been successfully applied to solve a wide range of optimization problems. In this paper, the parameters set of the Jiles-Atherton vector hysteresis model is obtained with an approach based on modified Differential Evolution (MDE) approaches using generation-varying control parameters based on generation of random numbers with uniform distribution. Several evaluated MDE approaches perform better than the classical DE methods and a genetic algorithm approach in terms of the quality and stability of the final solutions in optimization of vector Jiles-Atherton vector hysteresis model from a workbench containing a rotational single sheet tester.     

A space search optimization algorithm with accelerated convergence strategies

Evolutionary algorithms (EAs), which have been widely used to solve various scientific and engineering optimization problems, are essentially stochastic search algorithms operating in the overall solution space. However, such random search mechanism may lead to some disadvantages such as a long computing time and premature convergence. In this study, we propose a space search optimization algorithm (SSOA) with accelerated convergence strategies to alleviate the drawbacks of the purely random search mechanism. The overall framework of the SSOA involves three main search mechanisms: local space search, global space search, and opposition-based search. The local space search that aims to form new solutions approaching the local optimum is realized based on the concept of augmented simplex method, which exhibits significant search abilities realized in some local space. The global space search is completed by Cauchy searching, where the approach itself is based on the Cauchy mutation. This operation can help the method avoid of being trapped in local optima and in this way alleviate premature convergence. An opposition-based search is exploited to accelerate the convergence of space search. This operator can effectively reduce a substantial computational overhead encountered in evolutionary algorithms (EAs). With the use of them SSOA realizes an effective search process. To evaluate the performance of the method, the proposed SSOA is contrasted with a method of differential evolution (DE), which is a well-known space concept-based evolutionary algorithm. When tested against benchmark functions, the SSOA exhibits a competitive performance vis-a-vis performance of some other competitive schemes of differential evolution in terms of accuracy and speed of convergence, especially in case of high-dimensional continuous optimization problems.     

Diversity-maintained differential evolution embedded with gradient-based local search

Differential evolution (DE) has been used to solve real-parameter optimization problems with nonlinear and multimodal functions for more than a decade of years. However, it is pointed out that this classical DE harbors restricted efficiency and limited local search ability. Inspired by that gradient-based algorithms have powerful local search ability, we propose a new algorithm, which is diversity-maintained DE based on gradient local search (namely, DMGBDE), by incorporating approximate gradient-based algorithms into the DE search while maintaining the diversity of the population. The primary novelties of the proposed DMGBDE are the following: (1) the gradient-based algorithm is embedded into DE in a different manner and (2) a diversity-maintained mutation is introduced to slow down the learning procedure from the searched best individual. We conduct numerical experiments with a number of benchmark problems to measure the performance of the proposed DMGBDE. Simulation results show that the proposed DMGBDE outperforms classical DE and variant without gradient local search or diversity-based mutation. Moreover, comparison with some other recently reported approaches indicates that our proposed DMGBDE is rather competitive.     

Repairing the crossover rate in adaptive differential evolution

Differential evolution (DE) is a simple yet powerful evolutionary algorithm (EA) for global numerical optimization. However, its performance is significantly influenced by its parameters. Parameter adaptation has been proven to be an efficient way for the enhancement of the performance of the DE algorithm. Based on the analysis of the behavior of the crossover in DE, we find that the trial vector is directly related to its binary string, but not directly related to the crossover rate. Based on this inspiration, in this paper, we propose a crossover rate repair technique for the adaptive DE algorithms that are based on successful parameters. The crossover rate in DE is repaired by its corresponding binary string, i.e. by using the average number of components taken from the mutant. The average value of the binary string is used to replace the original crossover rate. To verify the effectiveness of the proposed technique, it is combined with an adaptive DE variant, JADE, which is a highly competitive DE variant. Experiments have been conducted on 25 functions presented in CEC-2005 competition. The results indicate that our proposed crossover rate technique is able to enhance the performance of JADE. In addition, compared with other DE variants and state-of-the-art EAs, the improved JADE method obtains better, or at least comparable, results in terms of the quality of final solutions and the convergence rate.     

Auto-tuning strategy for evolutionary algorithms: balancing between exploration and exploitation

Genetic Algorithms (GAs) and other Evolutionary Algorithms (EAs), as powerful and broadly applicable stochastic search and optimization techniques have been successfully applied in the area of management science, operations research and industrial engineering. In the past few years, researchers gave lots of great idea for improvement of evolutionary algorithms, which include population initialization, individual selection, evolution, parameter setting, hybrid approach with conventional heuristics etc. However, though lots of different versions of evolutionary computations have been created, all of them have turned most of its attention to the development of search abilities of approaches. In this paper, for improving the search ability, we focus on how to take a balance between exploration and exploitation of the search space. It is also very difficult to solve problem, because the balance between exploration and exploitation is depending on the characteristic of different problems. The balance also should be changed dynamically depend on the status of evolution process. Purpose of this paper is the design of an effective approach which it can correspond to most optimization problems. In this paper, we propose an auto-tuning strategy by using fuzzy logic control. The main idea is adaptively regulation for taking the balance among the stochastic search and local search probabilities based on the change of the average fitness of parents and offspring which is occurred at each generation. In addition, numerical analyses of different type optimization problems show that the proposed approach has higher search capability that improve quality of solution and enhanced rate of convergence.     

An evolving surrogate model-based differential evolution algorithm

Differential evolution (DE) is a simple and effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of mutation and crossover strategies and their associated control parameters. Therefore, to achieve optimal performance, a time-consuming parameter tuning process is required. In DE, the use of different mutation and crossover strategies with different parameter settings can be appropriate during different stages of the evolution. Therefore, to achieve optimal performance using DE, various adaptation, self-adaptation, and ensemble techniques have been proposed. Recently, a classification-assisted DE algorithm was proposed to overcome trial and error parameter tuning and efficiently solve computationally expensive problems. In this paper, we present an evolving surrogate model-based differential evolution (ESMDE) method, wherein a surrogate model constructed based on the population members of the current generation is used to assist the DE algorithm in order to generate competitive offspring using the appropriate parameter setting during different stages of the evolution. As the population evolves over generations, the surrogate model also evolves over the iterations and better represents the basin of search by the DE algorithm. The proposed method employs a simple Kriging model to construct the surrogate. The performance of ESMDE is evaluated on a set of 17 bound-constrained problems. The performance of the proposed algorithm is compared to state-of-the-art self-adaptive DE algorithms: the classification-assisted DE algorithm, regression-assisted DE algorithm, and ranking-assisted DE algorithm.     

一种改进的微分进化算法

相对于其他优化算法来说,微分进化算法具有控制参数少、易于使用以及鲁棒性强等特点,但在搜索过程中存在着局部搜索能力弱的缺点。针对微分进化算法局部搜索能力弱的缺点,提出了一种基于局部变异的微分进化算法,该算法使个体具有良好快速收敛能力。使用典型优化函数对比较算法进行了测试,算法分析和仿真结果表明,改进以后的算法具有寻优能力...     

基于最优高斯随机游走和个体筛选策略的差分进化算法

针对差分进化算法开发能力较差的问题, 提出一种具有快速收敛的新型差分进化算法. 首先, 利用最优高斯随机游走策略提高算法的开发能力; 然后, 采用基于个体优化性能的简化交叉变异策略实现种群的进化操作以加强其局部搜索能力; 最后, 通过个体筛选策略进一步提高算法的探索能力以避免陷入局部最优. 12 个标准测试函 数和两种带约束的工程优化问题的实验结果表明, 所提出的算法在收敛速度、算法可靠性及收敛精度方面均优于EPSDE、SaDE、JADE、BSA、CoBiDE、GSA和ABC等算法, 在加强算法探索能力的同时能够有效地提高算法的开发能力.

     

C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization

In recent years, evolutionary algorithms (EAs) have been extensively developed and utilized to solve multi-objective optimization problems. However, some previous studies have shown that for certain problems, an approach which allows for non-greedy or uphill moves (unlike EAs), can be more beneficial. One such approach is simulated annealing (SA). SA is a proven heuristic for solving numerical optimization problems. But owing to its point-to-point nature of search, limited efforts has been made to explore its potential for solving multi-objective problems. The focus of the presented work is to develop a simulated annealing algorithm for constrained multi-objective problems. The performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems. A comparison with other established multi-objective optimization algorithms, such as infeasibility driven evolutionary algorithm (IDEA), Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective Scatter search II (MOSS-II) has been included to highlight the benefits of the proposed approach.     

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.     

Self-adaptive population sizing for a tune-free differential evolution

The study and research of evolutionary algorithms (EAs) is getting great attention in recent years. Although EAs have earned extensive acceptance through numerous successful applications in many fields, the problem of finding the best combination of evolutionary parameters especially for population size that need the manual settings by the user is still unresolved. In this paper, our system is focusing on differential evolution (DE) and its control parameters. To overcome the problem, two new systems were carried out for the self-adaptive population size to test two different methodologies (absolute encoding and relative encoding) in DE and compared their performances against the original DE. Fifty runs are conducted for every 20 well-known benchmark problems to test on every proposed algorithm in this paper to achieve the function optimization without explicit parameter tuning in DE. The empirical testing results showed that DE with self-adaptive population size using relative encoding performed well in terms of the average performance as well as stability compared to absolute encoding version as well as the original DE.     

Remote sensing image subpixel mapping based on adaptive differential evolution

In this paper, a novel subpixel mapping algorithm based on an adaptive differential evolution (DE) algorithm, namely, adaptive-DE subpixel mapping (ADESM), is developed to perform the subpixel mapping task for remote sensing images. Subpixel mapping may provide a fine-resolution map of class labels from coarser spectral unmixing fraction images, with the assumption of spatial dependence. In ADESM, to utilize DE, the subpixel mapping problem is transformed into an optimization problem by maximizing the spatial dependence index. The traditional DE algorithm is an efficient and powerful population-based stochastic global optimizer in continuous optimization problems, but it cannot be applied to the subpixel mapping problem in a discrete search space. In addition, it is not an easy task to properly set control parameters in DE. To avoid these problems, this paper utilizes an adaptive strategy without user-defined parameters, and a reversible-conversion strategy between continuous space and discrete space, to improve the classical DE algorithm. During the process of evolution, they are further improved by enhanced evolution operators, e.g., mutation, crossover, repair, exchange, insertion, and an effective local search to generate new candidate solutions. Experimental results using different types of remote images show that the ADESM algorithm consistently outperforms the previous subpixel mapping algorithms in all the experiments. Based on sensitivity analysis, ADESM, with its self-adaptive control parameter setting, is better than, or at least comparable to, the standard DE algorithm, when considering the accuracy of subpixel mapping, and hence provides an effective new approach to subpixel mapping for remote sensing imagery.     

求解高维多模优化问题的自适应差分进化算法

在基变量选择方差理论分析的基础上,提出一种自适应差分进化算法(ADE).ADE算法通过设计自适应收敛因子构建自调整的权重质心变异策略,同时在交叉策略中引入发射、收缩两种单纯形操作算子,保证算法全局搜索能力的同时,能钉效提高算法后期的局部增强能力.30个优化问题的数值研究结果表明ADE算法具有比DE、DERL以及DERB三种算法更快的收敛速度和可靠性,尤其适合于高维多模优化问题的求解.     

Self-adaptive differential evolution with multi-trajectory search for large-scale optimization

In this paper, self-adaptive differential evolution (DE) is enhanced by incorporating the JADE mutation strategy and hybridized with modified multi-trajectory search (MMTS) algorithm (SaDE-MMTS) to solve large-scale continuous optimization problems. The JADE mutation strategy, the “DE/current-to-pbest” which is a variation of the classic “DE/current-to-best”, is used for generating mutant vectors. After the mutation phase, the binomial (uniform) crossover, the exponential crossover as well as no crossover option are used to generate each pair of target and trial vectors. By utilizing the self-adaptation in SaDE, both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, suitable offspring generation strategy along with associated parameter settings will be determined adaptively to match different phases of the search process. MMTS is applied frequently to refine several diversely distributed solutions at different search stages satisfying both the global and the local search requirement. The initialization of step sizes is also defined by a self-adaption during every MMTS step. The success rates of both SaDE and the MMTS are determined and compared; consequently, future function evaluations for both search algorithms are assigned proportionally to their recent past performance. The proposed SaDE-MMTS is employed to solve the 19 numerical optimization problems in special issue of soft computing on scalability of evolutionary algorithms for large-scale continuous optimization problems and competitive results are presented.     

Optimal short-term hydro-thermal scheduling using quasi-oppositional teaching learning based optimization

This paper presents a new approach for solving short-term hydrothermal scheduling (HTS) using an integrated algorithm based on teaching learning based optimization (TLBO) and oppositional based learning (OBL). The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydro reservoirs, water transport delay and scheduling time linkage that make the problem of optimization difficult using standard optimization methods. To overcome these problems, the proposed quasi-oppositional teaching learning based optimization (QOTLBO) is employed. To show its efficiency and robustness, the proposed QOTLBO algorithm is applied on two test systems. Numerical results of QOTLBO are compared with those obtained by two phase neural network, augmented Lagrange method, particle swarm optimization (PSO), improved self-adaptive PSO (ISAPSO), improved PSO (IPSO), differential evolution (DE), modified DE (MDE), fuzzy based evolutionary programming (Fuzzy EP), clonal selection algorithm (CSA) and TLBO approaches. The simulation results reveal that the proposed algorithm appears to be the best in terms of convergence speed, solution time and minimum cost when compared with other established methods. This method is considered to be a promising alternative approach for solving the short-term HTS problems in practical power system.     

Parameter control system of evolutionary algorithm that is aided by the entire search history

In solving problems with evolutionary algorithms (EAs), the performance of the EA will be affected by its properties. As the properties of EA depend on the parameter setting, users need to tune the parameters to optimize the performance on different problems. In the case that the user does not have any prior knowledge of the problem, parameter tuning is very difficult and time consuming. One needs to try different combinations of parameter values to find the best setting. To solve this problem, one way is to control the parameters during the EA run. This paper proposes a new adaptive parameter control system, called Parameter Control system using entire Search History (PCSH). It is a general add-on system which is not restricted to a specific class of EA. Users are only required to know the range of the parameters. It automatically adjusts the parameters of an EA according to the entire search history, in a parameter-less manner. To illustrate the performance of PCSH, it is applied to control the parameters of three common classes of EAs: (1) canonical Genetic Algorithm (GA), (2) Particle Swarm Optimization (PSO) and (3) Differential Evolution (DE). For GA, we show that PCSH can automatically control the crossover operator, crossover values (uniformly sampled from the range) and mutation operator. For DE, we show that PCSH can automatically control the crossover operator, crossover values and the differential amplification factor (uniformly sampled from the ranges). For PSO, we show that PCSH can automatically control the two learning factors and the inertia weight (uniformly sampled from the range). Moreover, no special provision is needed at the initialization. 34 benchmark functions are used to evaluate the performance comprehensively. The test results show that, in most of the benchmark functions, the performance of the test EAs are improved or similar after adopting PCSH. It shows that PCSH keeps or improves the performance of the test EAs while relieving the heavy burden of the algorithm designer on the setting of some parameters.     

Differential evolution based on covariance matrix learning and bimodal distribution parameter setting

Differential evolution (DE) is an efficient and robust evolutionary algorithm, which has been widely applied to solve global optimization problems. As we know, crossover operator plays a very important role on the performance of DE. However, the commonly used crossover operators of DE are dependent mainly on the coordinate system and are not rotation-invariant processes. In this paper, covariance matrix learning is presented to establish an appropriate coordinate system for the crossover operator. By doing this, the dependence of DE on the coordinate system has been relieved to a certain extent, and the capability of DE to solve problems with high variable correlation has been enhanced. Moreover, bimodal distribution parameter setting is proposed for the control parameters of the mutation and crossover operators in this paper, with the aim of balancing the exploration and exploitation abilities of DE. By incorporating the covariance matrix learning and the bimodal distribution parameter setting into DE, this paper presents a novel DE variant, called CoBiDE. CoBiDE has been tested on 25 benchmark test functions, as well as a variety of real-world optimization problems taken from diverse fields including radar system, power systems, hydrothermal scheduling, spacecraft trajectory optimization, etc. The experimental results demonstrate the effectiveness of CoBiDE for global numerical and engineering optimization. Compared with other DE variants and other state-of-the-art evolutionary algorithms, CoBiDE shows overall better performance.     

Differential evolution with Gaussian mutation for combined heat and power economic dispatch

This paper presents differential evolution with Gaussian mutation to solve the complex non-smooth non-convex combined heat and power economic dispatch (CHPED) problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. Differential evolution (DE) is a simple yet powerful global optimization technique. It exploits the differences of randomly sampled pairs of objective vectors for its mutation process. This mutation process is not suitable for complex multimodal optimization. This paper proposes Gaussian mutation in DE which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the simplicity of the structure of DE. The effectiveness of the proposed method has been verified on five test problems and three test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed differential evolution with Gaussian mutation-based approach is able to provide better solution.