Classical Differential Evolution Algorithm Research Articles

Information sharing impact of stochastic diffusion search on differential evolution algorithm

This work details the research aimed at applying the powerful resource allocation mechanism deployed in stochastic diffusion search (SDS) to the differential evolution (DE), effectively merging a nature inspired swarm intelligence algorithm with a biologically inspired evolutionary algorithm. The results reported herein suggest that the hybrid algorithm, exploiting information sharing between the population elements, has the potential to improve the optimisation capability of classical DE algorithms. This claim is verified by running several experiments using state-of-the-art benchmarks. Additionally, the significance of the frequency within which SDS introduces communication and information exchange is also investigated.

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.

Adaptive Parameter Selection for Strategy Adaptation in Differential Evolution for Continuous Optimization

In order to automatically select the most suitable strategy for a specific problem without any prior knowledge, in this paper, we present an adaptive parameter selection technique for strategy adaptation in differential evolution (DE). First, a simple strategy adaptation mechanism is employed to implement the adaptive strategy selection in DE. Then, the probability- matching-based adaptive parameter selection method is proposed to select the best parameter of the strategy adaptation mechanism; in this way, it can accelerate the strategy adaptation mechanism to choose the most suitable strategy while solving a problem. To evaluate the performance of our approach, thirteen widely used benchmark functions are chosen as the test suite. The performance of our approach is compared with other DE variants, including two recently proposed DE with strategy adaptation. The results indicate that our approach is highly competitive to the compared algorithms. In addition, compared with the classical DE algorithms with single strategy, our method obtains better results in terms of the quality of the final solutions and the convergence speed.

Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

The classical Differential Evolution (DE) algorithm, one of population-based Evolutionary Computation methods, proved to be a successful approach for relatively simple problems, but does not perform well for difficult multi-dimensional non-convex functions. A number of significant modifications of DE have been proposed in recent years, including very few approaches referring to the idea of distributed Evolutionary Algorithms. The present paper presents a new algorithm to improve optimization performance, namely DE with Separated Groups (DE-SG), which distributes population into small groups, defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities. The performance of DE-SG is compared to that of eight algorithms belonging to the class of Evolutionary Strategies (Covariance Matrix Adaptation ES), Particle Swarm Optimization (Comprehensive Learning PSO and Efficient Population Utilization Strategy PSO), Differential Evolution (Distributed DE with explorative-exploitative population families, Self-adaptive DE, DE with global and local neighbours and Grouping Differential Evolution) and multi-algorithms (AMALGAM). The comparison is carried out for a set of 10-, 30- and 50-dimensional rotated test problems of varying difficulty, including 10- and 30-dimensional composition functions from CEC2005. Although slow for simple functions, the proposed DE-SG algorithm achieves a great success rate for more difficult 30- and 50-dimensional problems.

A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map

A technique for tuning of decoupled proportional-integral (PI) and proportional-integral-derivative (PID) multivariable controllers based on a chaotic differential evolution (DE) approach is presented in this paper. Due to the simple concept, easy implementation and quick convergence, nowadays DE has gained much attention and wide application in solving continuous non-linear optimization problems. However, the performance of DE greatly depends on its control parameters and it often suffers from being trapped in local optimum. The application of chaotic sequences based on chaotic Zaslavskii map instead of random sequences in DE is a powerful strategy to diversify the population and improve the DE’s performance in preventing premature convergence to local optima. The optimized PD and PID controllers shows good closed-loop responses in control of the binary Wood–Berry distillation column, a multivariable process with strong interactions between input and output pairs. Some comparison results of PD and PID tuning using chaotic DE, classical DE and genetic algorithm are presented and discussed.

Hybrid Differential Evolution with Convex Mutation

Differential evolution (DE) is a simple yet pow- erful evolutionary algorithm for global numerical opti- mization. In this paper, we propose a novel hybrid DE variant to accelerate the convergence rate of the classical DE algorithm. The proposed algorithm is hybridized with a convex mutation. The convex mutation is able to utilize the information of the parents, and hence, provides faster convergence speed. Our proposal is referred to as Convex- DE. In order to verify our expectation, we test our approach on 13 widely used benchmark functions. The results indicate that our approach is better than the classical DE algorithm in terms of the convergence speed and the quality of final solution. Furthermore, the potential of our approach for real-world applications is evaluated on three real-world problems.

Design of optimum gain pyramidal horn using self-adaptive differential evolution algorithms

In this work, we apply classical and new self-adaptive differential evolution (DE) algorithms to the design of optimum gain pyramidal horns. The application of DE algorithms to pyramidal horn design allows the accurate calculation of their physical dimensions in a short amount of time. Moreover, self-adaptive DE does not require the prespecified choice of control parameters reducing significantly the users' effort. Representative examples demonstrate the applicability of our proposal. Our study shows that self-adaptive DE algorithms outperform or produce similar results with other methods in the literature in terms of solution accuracy and convergence speed. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011. © 2011 Wiley Periodicals, Inc.

A new multi-objective technique for differential fuzzy clustering

This article presents a new multiobjective differential evolution based fuzzy clustering technique. Recent research has shown that clustering techniques that optimize a single objective may not provide satisfactory result because no single validity measure works well on different kinds of data sets. The fact motivated us to present a new multiobjective Differential Evolution based fuzzy clustering technique that encodes the cluster centres in its vectors and optimizes multiple validity measures simultaneously. In the final generation, it produces a set of non-dominated solutions, from which the user can relatively judge and pick up the most promising one according to the problem requirements. Superiority of the proposed method over its single objective versions, multiobjective version of classical differential evolution and genetic algorithm, well-known fuzzy C-means and average linkage clustering algorithms has been demonstrated quantitatively and visually for several synthetic and real life data sets. Statistical significance test has been conducted to establish the statistical superiority of the proposed multiobjective clustering approach. Finally, the proposed algorithm has been applied for segmentation of a remote sensing image to show its effectiveness in pixel classification.

Optimal coordination of over-current relays using modified differential evolution algorithms

Optimization of directional over-current relay (DOCR) settings is an important problem in electrical engineering. The optimization model of the problem turns out to be non-linear and highly constrained in which two settings namely time dial setting ( TDS) and plug setting ( PS) of each relay are considered as decision variables; the sum of the operating times of all the primary relays, which are expected to operate in order to clear the faults of their corresponding zones, is considered as an objective function. In the present study, three models are considered namely IEEE 3-bus model, IEEE 4-bus model and IEEE 6-bus model. To solve the problem, we have applied five newly developed versions of differential evolution (DE) called modified DE versions (MDE1, MDE2, MDE3, MDE4, and MDE5). The results are compared with the classical DE algorithm and with five more algorithms available in the literature; the numerical results show that the modified DE algorithms outperforms or perform at par with the other algorithms.

CIDE: Chaotically Initialized Differential Evolution

This paper proposes new Differential Evolution (DE) algorithm, named as Chaotically Initialized Differential Evolution (CIDE), that uses chaotic maps with certainty, ergodicity, unpredictability, non-periodicity, complex temporal behavior and the stochastic property for initial population generation. This has been done by using of different chaotic number generators each time a random number is needed by the classical DE algorithm in its initial step. Seven chaotic maps have been analyzed in the benchmark functions. It has been detected that coupling emergent results in different areas, like those of DE and complex dynamics, can improve the quality of results in some optimization problems and also that chaos may be a desired process. It has been also shown that, Sinus map and Circle map have somewhat increased the solution quality, that is in some cases they improved the global searching capability by escaping the local solutions.

Design of microwave broadband absorbers using a self-adaptive differential evolution algorithm

Microwave broadband absorber design for a desired frequency and angle range is presented. The design technique is based on a self-adaptive Differential Evolution (DE) algorithm. Numerical examples are compared with the existing in the literature and with those found by the other evolutionary algorithms. The results show that the new DE algorithm version outerperforms other global optimizers like Particle swarm optimization (PSO) variants and the classical DE algorithm. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.

Accelerating Differential Evolution Using an Adaptive Local Search

We propose a crossover-based adaptive local search (LS) operation for enhancing the performance of standard differential evolution (DE) algorithm. Incorporating LS heuristics is often very useful in designing an effective evolutionary algorithm for global optimization. However, determining a single LS length that can serve for a wide range of problems is a critical issue. We present a LS technique to solve this problem by adaptively adjusting the length of the search, using a hill-climbing heuristic. The emphasis of this paper is to demonstrate how this LS scheme can improve the performance of DE. Experimenting with a wide range of benchmark functions, we show that the proposed new version of DE, with the adaptive LS, performs better, or at least comparably, to classic DE algorithm. Performance comparisons with other LS heuristics and with some other well-known evolutionary algorithms from literature are also presented.