A Fuzzy Adaptive Differential Evolution Algorithm

The differential evolution algorithm is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. The algorithm has so far used empirically chosen values for its search parameters that are kept fixed through an optimization process. The objective of this paper is to introduce a new version of the Differential Evolution algorithm with adaptive control parameters – the fuzzy adaptive differential evolution algorithm, which uses fuzzy logic controllers to adapt the search parameters for the mutation operation and crossover operation. The control inputs incorporate the relative objective function values and individuals of the successive generations. The emphasis of this paper is analysis of the dynamics and behavior of the algorithm. Experimental results, provided by the proposed algorithm for a set of standard test functions, outperformed those of the standard differential evolution algorithm for optimization problems with higher dimensionality.     

On an evolutionary approach for constrained optimization problem solving

Over the last few decades, many different evolutionary algorithms have been introduced for solving constrained optimization problems. However, due to the variability of problem characteristics, no single algorithm performs consistently over a range of problems. In this paper, instead of introducing another such algorithm, we propose an evolutionary framework that utilizes existing knowledge to make logical changes for better performance. The algorithmic aspects considered here are: the way of using search operators, dealing with feasibility, setting parameters, and refining solutions. The combined impact of such modifications is significant as has been shown by solving two sets of test problems: (i) a set of 24 test problems that were used for the CEC2006 constrained optimization competition and (ii) a second set of 36 test instances introduced for the CEC2010 constrained optimization competition. The results demonstrate that the proposed algorithm shows better performance in comparison to the state-of-the-art algorithms.     

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.     

Differential evolution in constrained numerical optimization: An empirical study

Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches.     

A Memetic Chaotic Gravitational Search Algorithm for unconstrained global optimization problems

Metaheuristic optimization algorithms address two main tasks in the process of problem solving: i) exploration (also called diversification) and ii) exploitation (also called intensification). Guaranteeing a trade-off between these operations is critical to good performance. However, although many methods have been proposed by which metaheuristics can achieve a balance between the exploration and exploitation stages, they are still worse than exact algorithms at exploitation tasks, where gradient-based mechanisms outperform metaheuristics when a local minimum is approximated. In this paper, a quasi-Newton method is introduced into a Chaotic Gravitational Search Algorithm as an exploitation method, with the purpose of improving the exploitation capabilities of this recent and promising population-based metaheuristic. The proposed approach, referred to as a Memetic Chaotic Gravitational Search Algorithm, is used to solve forty-five benchmark problems, both synthetic and real-world, to validate the method. The numerical results show that the adding of quasi-Newton search directions to the original (Chaotic) Gravitational Search Algorithm substantially improves its performance. Also, a comparison with the state-of-the-art algorithms: Particle Swarm Optimization, Genetic Algorithm, Rcr-JADE, COBIDE and RLMPSO, shows that the proposed approach is promising for certain real-world problems.     

基于混沌理论的差异演化算法研究

差异演化算法（Differential Evolution,DE）足一种基于群体个体间差异的进化计算方法,可以对高维复杂空间进行有效搜索。利用混沌（Chaos）信号的遍历性与随机性,结合DE算法,提出了一种基于混沌的DE优化算法（CDE）。与DE相比,CDE减少了控制参数。通过典型高维非线性测试函数的验证,测试结果显示该方法在优化速度、搜索效率和避免陷入局部极值点方面,大大提高DE算法的性能,在不同情兜下几乎具有最佳的函数优化性能,从而具有一定的鲁棒性。     

Memetic algorithm using multi-surrogates for computationally expensive optimization problems

In this paper, we present a multi-surrogates assisted memetic algorithm for solving optimization problems with computationally expensive fitness functions. The essential backbone of our framework is an evolutionary algorithm coupled with a local search solver that employs multi-surrogate in the spirit of Lamarckian learning. Inspired by the notion of ‘blessing and curse of uncertainty’ in approximation models, we combine regression and exact interpolating surrogate models in the evolutionary search. Empirical results are presented for a series of commonly used benchmark problems to demonstrate that the proposed framework converges to good solution quality more efficiently than the standard genetic algorithm, memetic algorithm and surrogate-assisted memetic algorithms.     

DE-VNS: Self-adaptive Differential Evolution with crossover neighborhood search for continuous global optimization

In this paper, we suggest DE-VNS heuristic for solving continuous (unconstrained) nonlinear optimization problems. It combines two well-known metaheuristic approaches: Differential Evolution (DE) and Variable Neighborhood Search (VNS), which have, in the last decade, attracted considerable attention in both academic circles and among practitioners. The basic idea of our hybrid heuristic is the use of the neighborhood change mechanism in order to estimate the crossover parameter of DE. Moreover, we introduce a new family of adaptive distributions to control the distances among solutions in the search space as well as experimental evidence of finding the best probability distribution function for VNS parameter supported by its statistical estimation. This hybrid heuristic has shown excellent characteristics and it turns out that it is more favorable than the state-of-the-art DE approaches when tested on standard instances from the literature.     

基于二阶段差分演化的WSN节点定位优化

由于非测距的WSN节点定位算法DV-Hop定位精度不高,引入智能优化算法后有效提高了定位精度,但迭代次数过大,节点能耗相对过高,而在较少信标节点和较短的通讯信半径条件下,传统智能优化算法难以生效。针对这种情况,提出了基于二阶段的差分演化定位优化算法。仿真实验设计在100m×100m正方形的区域内,随机分布100个无线传感器节点,首先用DV-Hop算法进行第一阶段粗略定位,然后在第二阶段用差化演化算法对定位进行优化,为了对比各种算法在低能耗（很少迭代次数）下的表现,优化过程只迭代了10代,最后得到节点坐标。实验结果表明,算法能获得更好的定位精度和具有更好的稳定性。该算法在极少迭代次数的条件下,在信标节点稀疏和通信半径较短的特殊情况下,获得满意的定位精度和更好的稳定性。     

A hybrid particle swarm optimization algorithm for high-dimensional problems

In recent years, particle swarm optimization (PSO) emerges as a new optimization scheme that has attracted substantial research interest due to its simplicity and efficiency. However, when applied to high-dimensional problems, PSO suffers from premature convergence problem which results in a low optimization precision or even failure. To remedy this fault, this paper proposes a novel memetic PSO (CGPSO) algorithm which combines the canonical PSO with a Chaotic and Gaussian local search procedure. In the initial evolution phase, CGPSO explores a wide search space that helps avoid premature convergence through Chaotic local search. Then in the following run phase, CGPSO refines the solutions through Gaussian optimization. To evaluate the effectiveness and efficiency of the CGPSO algorithm, thirteen high dimensional non-linear scalable benchmark functions were examined. Results show that, compared to the standard PSO, CGPSO is more effective, faster to converge, and less sensitive to the function dimensions. The CGPSO was also compared with two PSO variants, CPSO-H, DMS-L-PSO, and two memetic optimizers, DEachSPX and MA-S2. CGPSO is able to generate a better, or at least comparable, performance in terms of optimization accuracy. So it can be safely concluded that the proposed CGPSO is an efficient optimization scheme for solving high-dimensional problems.     

一种新的混沌差分进化算法

提出一种新的混沌差分进化(CDE)算法,在每一代中通过差分进化(DE)算法找到最佳个体,在最佳个体附近用混沌方法进行局部搜索,通过引入调节因子加强其搜索能力。6个基本测试函数的优化结果表明,当误差函数精度为10-14时,与DE相比,CDE的寻优能力更强、收敛速度较快。     

Differential approximation results for the traveling salesman and related problems

This paper deals with the problem of constructing a Hamiltonian cycle of optimal weight, called TSP. We show that TSP is 2/3-differential approximable and cannot be differential approximable greater than 649/650. Next, we demonstrate that, when dealing with edge-costs 1 and 2, the same algorithm idea improves this ratio to 3/4 and we obtain a differential non-approximation threshold equal to 741/742. Remark that the 3/4-differential approximation result has been recently proved by a way more specific to the 1-, 2-case and with another algorithm in the recent conference, Symposium on Fundamentals of Computation Theory, 2001. Based upon these results, we establish new bounds for standard ratio: 5/6 for MaxTSP[a,2a] and 7/8 for MaxTSP[1,2]. We also derive some approximation results on partition graph problems by paths.     

A memory based differential evolution algorithm for unconstrained optimization

In optimization, the performance of differential evolution (DE) and their hybrid versions exist in the literature is highly affected by the inappropriate choice of its operators like mutation and crossover. In general practice, during simulation DE does not employ any strategy of memorizing the so-far-best results obtained in the initial part of the previous generation. In this paper, a new “Memory based DE (MBDE)” presented where two “swarm operators” have been introduced. These operators based on the pBEST and gBEST mechanism of particle swarm optimization. The proposed MBDE is employed to solve 12 basic, 25 CEC 2005, and 30 CEC 2014 unconstrained benchmark functions. In order to further test its efficacy, five different test system of model order reduction (MOR) problem for single-input and single-output system are solved by MBDE. The results of MBDE are compared with state-of-the-art algorithms that also solved those problems. Numerical, statistical, and graphical analysis reveals the competency of the proposed MBDE.     

改进的差异演化算法

针对差异演化算法求解复杂优化问题效率不高问题,提出一种改进的差异演化算法。该算法采用单种群机制提高全局搜索能力,利用二次局部变异操作使当前种群中的部分个体在当前最优个体附近寻优,增强局部搜索能力。利用不同类型的标准测试函数对该算法进行测试,并与差异演化算法、动态差异演化算法和粒子群优化算法进行比较。仿真结果表明,改进的差异演化算法显著提高了搜索效率。     

Moving object detection using Markov Random Field and Distributed Differential Evolution

In this article, we present an algorithm for detecting moving objects from a given video sequence. Here, spatial and temporal segmentations are combined together to detect moving objects. In spatial segmentation, a multi-layer compound Markov Random Field (MRF) is used which models spatial, temporal, and edge attributes of image frames of a given video. Segmentation is viewed as a pixel labeling problem and is solved using the maximum a posteriori (MAP) probability estimation principle; i.e., segmentation is done by searching a labeled configuration that maximizes this probability. We have proposed using a Differential Evolution (DE) algorithm with neighborhood-based mutation (termed as Distributed Differential Evolution (DDE) algorithm) for estimating the MAP of the MRF model. A window is considered over the entire image lattice for mutation of each target vector of the DDE; thereby enhancing the speed of convergence. In case of temporal segmentation, the Change Detection Mask (CDM) is obtained by thresholding the absolute differences of the two consecutive spatially segmented image frames. The intensity/color values of the original pixels of the considered current frame are superimposed in the changed regions of the modified CDM to extract the Video Object Planes (VOPs). To test the effectiveness of the proposed algorithm, five reference and one real life video sequences are considered. Results of the proposed method are compared with four state of the art techniques and provide better spatial segmentation and better identification of the location of moving objects.     

具有混沌局部搜索策略的差分进化全局优化算法

提出了一种具有混沌局部搜索策略的差分进化全局优化算法（CLSDE）,它是在每一代中通过DE/best/1/bin形式的差分进化算法找到最佳个体,然后在最佳个体的附近用混沌的方法进行局部搜索。8个基本的测试函数优化结果表明：若误差函数精度为10^-10,CLSDE寻优成功率比DE和SACDE都要高,而且收敛速度比DE和SACDE都要快。     

Learning behavior in abstract memory schemes for dynamic optimization problems

Integrating memory into evolutionary algorithms is one major approach to enhance their performance in dynamic environments. An abstract memory scheme has been recently developed for evolutionary algorithms in dynamic environments, where the abstraction of good solutions is stored in the memory instead of good solutions themselves to improve future problem solving. This paper further investigates this abstract memory with a focus on understanding the relationship between learning and memory, which is an important but poorly studied issue for evolutionary algorithms in dynamic environments. The experimental study shows that the abstract memory scheme enables learning processes and hence efficiently improves the performance of evolutionary algorithms in dynamic environments.     

基于差分算法的K-均值聚类分析

提出一种基于差分算法的聚类分析方法,采用结构体数组对聚类的中心进行编码,并用样本向量与相应聚类中心的欧氏距离的和来判断聚类划分的质量,通过变异、交叉和选择操作对聚类中心的编码进行优化,以获得最好的聚类中心.通过差分算法的全局搜索能力,来获取全局最优结果.实验结果显示,该方法的聚类划分效果明显优于传统的K-均值方法,也一般优于基于遗传算法的聚类算法和基于微粒群的聚类算法.     

Evolutionary algorithms for optimization problems with uncertainties and hybrid indices

Many optimization problems in real-world applications contain both explicit (quantitative) and implicit (qualitative) indices that usually contain uncertain information. How to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science. In this paper, we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices. To incorporate uncertainty in evolutionary algorithms, we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives; and then we transform the model into a precise one by employing the method of interval analysis; finally, we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms. The proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals. In our experiments, we apply the proposed algorithm to an interior layout problem, a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index. Our experimental results confirm the feasibility and efficiency of the proposed algorithm.     

Differential evolution for optimizing the positioning of prototypes in nearest neighbor classification

Nearest neighbor classification is one of the most used and well known methods in data mining. Its simplest version has several drawbacks, such as low efficiency, high storage requirements and sensitivity to noise. Data reduction techniques have been used to alleviate these shortcomings. Among them, prototype selection and generation techniques have been shown to be very effective. Positioning adjustment of prototypes is a successful trend within the prototype generation methodology.Evolutionary algorithms are adaptive methods based on natural evolution that may be used for searching and optimization. Positioning adjustment of prototypes can be viewed as an optimization problem, thus it can be solved using evolutionary algorithms. This paper proposes a differential evolution based approach for optimizing the positioning of prototypes. Specifically, we provide a complete study of the performance of four recent advances in differential evolution. Furthermore, we show the good synergy obtained by the combination of a prototype selection stage with an optimization of the positioning of prototypes previous to nearest neighbor classification. The results are contrasted with non-parametrical statistical tests and show that our proposals outperform previously proposed methods.