一种新型的差分演化算法及其应用研究

提出了一种新的基于简单多样性规则的改进差分演化算法,并把它运用于约束全局最优化问题的求解中。新算法的特征是: 1)提出一种新的混合自适应交叉变异算子,以增强算法的搜索能力; 2)采用具有保持群体多样性的约束函数处理技术; 3)简化基本差分演化算法的缩放因子,尽量减少算法的控制参数,方便工程人员的使用。通过对13个标准测试函数进行测试,并与其他演化算法结果进行比较。实验结果表明,新算法在求解精度和稳定性具有很好的性能,而且其函数平均评价次数要低于所比较的其他演化算法。     

一种求解动态优化问题的改进自适应差分进化算法

针对原始动态自适应差分进化（SADE）算法局部搜索能力弱和寻优精度低的问题,提出一种求解动态优化问题的邻域搜索差分进化（NSDE）算法。通过引入邻域搜索机制,在划分种群最优个体的邻域空间范围内产生候选解,选取候选解集合中的最优解并对种群最优个体进行迭代,增强算法局部搜索能力。在传统基于距离的排斥方案中,引入hill-valley函数追踪邻近峰,提高算法寻优精度。实验结果表明,与SADE、人工免疫网络动态优化、多种群竞争差分进化和改进差分进化算法相比,NSDE算法在49个测试问题中分别有28、38、29和38个测试问题的平均误差更小,综合性能表现更好。     

Identification of tumor region parameters using evolutionary algorithm and multiple reciprocity boundary element method

In the paper the inverse problems consisting in the simultaneous estimation of unknown thermophysical and/or geometrical parameters (thermal conductivity, perfusion coefficient, metabolic heat source, location, size) of the tumor region are solved. The additional information concerning the knowledge of local skin surface temperature at the selected set of points is assumed to be known. The problem of thermal processes proceeding in the domain considered is described by the system of the Pennes equations and boundary conditions given on the outer and contact surfaces. On the stage of numerical solution the evolutionary algorithm coupled with the multiple reciprocity boundary element method has been applied.     

A novel kinematic parameters calibration method for industrial robot based on Levenberg-Marquardt and Differential Evolution hybrid algorithm

The poor absolute positioning accuracy of industrial robots is the main obstacle for its further application in precision grinding of complex surfaces, such as blisk, blade, etc. Based on the established kinematic error model of a typical industrial robot FANUC M710ic/50, a novel kinematic parameters calibration method is proposed in this paper to improve the absolute positioning accuracy of robot. The pre-identification of the kinematic parameter deviations of robot was achieved by using the Levenberg-Marquardt algorithm. Subsequently, these identified suboptimal values of parameter deviations were defined as central values of the components of initial individuals to complete accurate identification by using Differential Evolution algorithm. The above two steps, which were regarded as the core of this Levenberg-Marquardt and Differential Evolution hybrid algorithm, were used to obtain the preferable values for kinematic parameters of the robot. On this basis, the experimental investigations of kinematic parameters calibration were conducted by using a laser tracker and numerical simulation method. The results revealed that the robot positioning error decreased from 0.994 mm, initial positioning error measured by laser tracker, to 0.262 mm after calibration with this proposed hybrid algorithm. The absolute positioning accuracy has increased by 40.86% than that of the Levenberg-Marquardt algorithm, increased by 40.31% than that of the Differential Evolution algorithm, and increased by 25.14% than that of the Simulated Annealing algorithm. This work shows that the proposed kinematic parameters calibration method has a significant improvement on the absolute positioning accuracy of industrial robot.     

一种改进的基于差分进化的多目标进化算法

近年来运用进化算法（EAs）解决多目标优化问题（Multi-objective Optimization Problems MOPs）引起了各国学者们的关注。作为一种基于种群的优化方法,EAs提供了一种在一次运行后得到一组优化的解的方法。差分进化（DE）算法是EA的一个分支,最开始是用来解决连续函数空间的问题。提出了一种改进的基于差分进化的多目标进化算法（CDE）,并且将它与另外两个经典的多目标进化算法（MOEAs）NSGA-II和SPEA2进行了对比实验。     

A parameterized model of heat storage by lake sediments

A model of seasonal heat storage by lake sediments is proposed oriented at applications in climate modeling and at lake parameterization in numerical weather prediction. The computational efficiency is achieved by reformulating of the heat transfer problem as a set of ordinary differential equations for evolution of the temperature wave inside the upper sediment layer. Arising temperature and depth scales completely replace the conductivity of the sediment in the heat transfer equation and can be easily achieved from the lake water temperature observations without any data on the sediment thermal properties. The method is proposed for the scales estimation from the inverse solution of the model equations in special case of the constant water-sediment heat flux in ice-covered lakes. The method is tested on data from sediments of Lake Krasnoye, North-Western Russia. The long-term (1961–2002) modeling of temperature in German lakes Müggelsee and Heiligensee with a coupled one-dimensional model of lake water column and sediments has demonstrated an appreciable effect of the sediment heat storage on near-bottom temperatures in both lakes. Thus, incorporation of the sediment layer into lake temperature models can essentially improve, at low computational costs, the model performance, especially for shallow lakes. In addition, a better forecast of near-bottom temperature evolution on climatic scales can provide a better understanding of the response of lake benthic communities to global warming.     

Disturbed Exploitation compact Differential Evolution for limited memory optimization problems

This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles its statistical model. This evolutionary framework is based on a Differential Evolution which cooperatively employs two exploitative search operators: the first is based on a standard Differential Evolution mutation and exponential crossover, and the second is the trigonometric mutation. These two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions. The action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population, which has the role of “disturbing” the excessively exploitative action of the framework and thus inhibits its premature convergence. The proposed algorithm, namely Disturbed Exploitation compact Differential Evolution, is a simple and memory-wise cheap structure that makes use of the Memetic Computing paradigm in order to solve complex optimization problems. The proposed approach has been tested on a set of various test problems and compared with state-of-the-art compact algorithms and with some modern population based meta-heuristics. Numerical results show that Disturbed Exploitation compact Differential Evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms, including some memetic approaches and complex modern Differential Evolution based algorithms. In order to show the potential of the proposed approach in real-world applications, Disturbed Exploitation compact Differential Evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro-controller. Numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature.     

RBF网络的微分进化正交最小二乘算法

研究用于径向基函数（RBF）网络训练的一种微分进化正交最小二乘（DEOLS）算法。把微分进化（DE）算法的种群作为正交最小二乘（OLS）算法的候选径向基函数集合,利用OLS对DE的种群个体进行评断,以确定RBF网络的隐结点的数目、中心和宽度。该算法融合了DE的强大搜索能力和OLS的高效评断能力,隐结点的选择比OLS要合理,同时避免DE的复杂性。最后使用实验验证了该算法的优越性。     

Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration

Recently an interesting evolutionary mechanism, sensibility, inherited from a concept model of Free Search (FS) was introduced and used for solving network problems. Unfortunately, the original FS is not easy to implement because it requires key knowledge that is not clearly defined in the existing literature to determine the neighborhood space that profoundly affects the performance of the original FS. This paper thus designs a new implementation for the concept model of FS, and proposes a new algorithm, called Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration (ADEQFS) to address this issue. In ADEQFS, we focus on designing a new mutation strategy by employing adaptive differential evolution techniques as well as concepts and principles from real-coded quantum-inspired evolutionary algorithm. In addition, we use the crossover operation from the traditional Differential Evolution scheme to alleviate the premature convergence for the proposed algorithm. Furthermore, we employ the greedy mechanism to preserve the best solutions found at each generation. The convergence analysis of the proposed algorithm is also presented in this paper. We give the proof of convergence by using the Markov chain model. Thirty-four optimization test functions with different mathematical characteristics are employed as benchmark set to test the performance of ADEQFS. The numerical results highlight the improved convergence rate and computation reliability.     

Optimization methodology based on neural networks and self-adaptive differential evolution algorithm applied to an aerobic fermentation process

The determination of the optimal neural network topology is an important aspect when using neural models. Due to the lack of consistent rules, this is a difficult problem, which is solved in this paper using an evolutionary algorithm namely Differential Evolution. An improved, simple, and flexible self-adaptive variant of Differential Evolution algorithm is proposed and tested. The algorithm included two initialization strategies (normal distribution and normal distribution combined with the opposition based principle) and a modified mutation principle. Because the methodology contains new elements, a specific name has been assigned, SADE-NN-1. In order to determine the most influential inputs of the models, a sensitivity analysis was applied. The case study considered in this work refer to the oxygen mass transfer coefficient in stirred bioreactors in the presence of n-dodecane as oxygen vector. The oxygen transfer in the fermentation broths has a significant influence on the growth of cultivated microorganism, the accurate modeling of this process being an important problem that has to be solved in order to optimize the aerobic fermentation process.The neural networks predicted the mass transfer coefficients with high accuracy, which indicates that the proposed methodology had a good performance. The same methodology, with a few modifications, and with the best neural network models, was used for determining the optimal conditions for which the mass transfer coefficient is maximized.A short review of the differential evolution methodology is realized in the first part of this article, presenting the main characteristics and variants, with advantages and disadvantages, and fitting in the modifications proposed within the existing directions of research.     

Differential evolution algorithm as a tool for optimal feature subset selection in motor imagery EEG

One of the challenges in developing a Brain Computer Interface (BCI) is dealing with the high dimensionality of the data when extracting features from EEG signals. Different feature selection algorithms have been proposed to overcome this problem but most of them involve complex transformed features, which require high computation and also result in increasing size of the feature set. In this paper, we present a new hybrid method to select features that involves a Differential Evolution (DE) optimization algorithm for searching the feature space to generate the optimal feature subset, with performance evaluated by a classifier. We provide a comprehensive study of the significance of evolutionary algorithm in selecting the best features for EEG signals. The BCI competition III, dataset IVa has been used to evaluate the method. Experimental results demonstrate that the proposed method performs well with Support Vector Machine (SVM) classifier, with an average classification accuracy of above 95% with a minimum of just 10 features. We also present a comparison of Differential Evolution (DE) with other evolutionary algorithms, and the results show the superiority of DE which implies that, with the selection of a good searching algorithm, a simple Common Spatial Pattern filter features can produce good results.     

基于差异演化算法和郭涛算法的文化算法

针对数值优化问题,对差异演化算法进行改进,获得多子差异演化算法。将多子差异演化算法和基于自适应搜索子空间的郭涛算法融合到文化算法的框架中,提出一种新的文化算法。实验结果表明,与多子差异演化算法、差异演化算法和基于自适应搜索子空间的郭涛算法相比,该算法收敛速度快,不易陷入局部最优,所得解的质量更好。     

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.     

Discretization error due to the identity operator in surface integral equations

We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving well-tested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao-Wilton-Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the identity operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly.     

Parameter estimation of a pressure swing adsorption model for air separation using multi-objective optimisation and support vector regression model

In order to successfully estimate parameters of a numerical model, multiple criteria should be considered. Multi-objective Differential Evolution (MODE) and Multi-objective Genetic Algorithm (MOGA) have proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. We describe the performance of two population based search algorithms (Nondominated Sorting Differential Evolution (NSDE) and Nondominated Sorting Genetic Algorithm (NGAII)) when applied to parameter estimation of a pressure swing adsorption (PSA) model. Full PSA mode is a complicated dynamic processing involving all transfer phenomena (mass, heat and momentum transfer) and has proven to be successful in a wide of applications. The limitation of using full PSA models is their expensive computational requirement. The parameter estimation analysis usually needs to run the numerical model and evaluate the performance thousands of times. However, in real world applications, there is simply not enough time and resources to perform such a huge number of model runs. In this study, a computational framework, known as v-support vector regression (v-SVR) PSA model, is presented for solving computationally expensive simulation problems. Formulation of an automatic parameter estimation strategy for the PSA model is outline. The simulations show that the NSDE is able to find better spread of solutions and better convergence near the true Pareto-optimal front compared to NSGAII-one elitist MOGA that pays special attention to creating a diverse Pareto-optimal front.     

解0—1背包问题的混合编码贪婪DE算法

提出一种混合编码差异演化算法来求解0—1背包问题。通过增加边界约束处理算子和编码映射函数,构建混合编码差异演化算法,求解离散优化问题,并利用贪婪变换方法对演化过程中的不可行解进行修复。仿真实验结果表明了该算法求解0-1背包问题的有效性与适用性。     

A two-step splitting algorithm in heat and mass transfer problems

An efficient finite-difference algorithm for multisequencing of the computational process excluding the solution of systems of finite-difference equations is proposed to solve heat and mass transfer problems on multiprocessor computers. The total approximation of the algorithm is established and its unconditional stability is proved.     

双种群差分进化规划算法

标准差分进化算法（SDE）具有算法简单,控制参数少,易于实现等优点。但在难优化问题中,算法存在收敛速度较慢和容易早熟等缺陷。为克服此缺点,提出一种改进算法--双种群差分进化规划算法（BGDEP）。该算法将种群划分为两个子群独立进化,分别采用DE/rand/1/bin和DE/best/2/bin版本生成变异个体。每隔δt（取5~10）代,将两个子群合并为一个种群,再应用混沌重组算子将之划分为两个子群,以实现子群间的信息交流。在双种群协同差分进化的同时,应用非均匀变异算子对其最优个体执行进化规划操作,使得算法具有较快的收敛速度和较强的全局寻优能力。为测试BGDEP的性能,给出了4个30维benchmark函数优化问题的对比数值实验。结果表明,BGDEP的求解精度、收敛速度、鲁棒性等性能优于SDE、双种群差分进化（BGDE）和非均匀变异进化规划（NUMEP）等4种算法。     

Multi-Cohort Intelligence algorithm: an intra- and inter-group learning behaviour based socio-inspired optimisation methodology

ABSTRACT

A Multi-Cohort Intelligence (Multi-CI) metaheuristic algorithm in emerging socio-inspired optimisation domain is proposed. The algorithm implements intra-group and inter-group learning mechanisms. It focusses on the interaction amongst different cohorts. The performance of the algorithm is validated by solving 75 unconstrained test problems with dimensions up to 30. The solutions were comparing with several recent algorithms such as Particle Swarm Optimisation (PSO), Covariance Matrix Adaptation Evolution Strategy, Artificial Bee Colony, Self-Adaptive Differential Evolution Algorithm, Comprehensive Learning Particle Swarm Optimisation, Backtracking Search Optimisation Algorithm, and Ideology Algorithm. The Wilcoxon signed-rank test was carried out for the statistical analysis and verification of the performance. The proposed Multi-CI outperformed these algorithms in terms of the solution quality including objective function value and computational cost, i.e. computational time and functional evaluations. The prominent feature of the Multi-CI algorithm along with the limitations is discussed as well. In addition, an illustrative example is also solved and every detail is provided.