物件導向軟體之架構(Object-Oriented Software Construction)探討

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which 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, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants.

Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization

Aspect] is a simple and practical aspect-oriented extension to Java With just a few new constructs, AspectJ provides support for modular implementation of a range of crosscutting concerns. In AspectJ's dynamic join point model, join points are well-defined points in the execution of the program; pointcuts are collections of join points; advice are special method-like constructs that can be attached to pointcuts; and aspects are modular units of crosscutting implementation, comprising pointcuts, advice, and ordinary Java member declarations. AspectJ code is compiled into standard Java bytecode. Simple extensions to existing Java development environments make it possible to browse the crosscutting structure of aspects in the same kind of way as one browses the inheritance structure of classes. Several examples show that AspectJ is powerful, and that programs written using it are easy to understand.

An overview of AspectJ

A new differential evolution (DE) algorithm, JADE, is proposed to improve optimization performance by implementing a new mutation strategy ldquoDE/current-to-p bestrdquo with optional external archive and updating control parameters in an adaptive manner. The DE/current-to-pbest is a generalization of the classic ldquoDE/current-to-best,rdquo while the optional archive operation utilizes historical data to provide information of progress direction. Both operations diversify the population and improve the convergence performance. The parameter adaptation automatically updates the control parameters to appropriate values and avoids a user's prior knowledge of the relationship between the parameter settings and the characteristics of optimization problems. It is thus helpful to improve the robustness of the algorithm. Simulation results show that JADE is better than, or at least comparable to, other classic or adaptive DE algorithms, the canonical particle swarm optimization, and other evolutionary algorithms from the literature in terms of convergence performance for a set of 20 benchmark problems. JADE with an external archive shows promising results for relatively high dimensional problems. In addition, it clearly shows that there is no fixed control parameter setting suitable for various problems or even at different optimization stages of a single problem.

JADE: Adaptive Differential Evolution With Optional External Archive

We describe an efficient technique for adapting control parameter settings associated with differential evolution (DE). The DE algorithm has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters, which are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE. We present an algorithm-a new version of the DE algorithm-for obtaining self-adaptive control parameter settings that show good performance on numerical benchmark problems. The results show that our algorithm with self-adaptive control parameter settings is better than, or at least comparable to, the standard DE algorithm and evolutionary algorithms from literature when considering the quality of the solutions obtained

Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems

Differential Evolution (DE) has been shown to be a powerful evolutionary algorithm for global optimization in many real problems. Self-adaptation has been found to be high beneficial for adjusting control parameters during evolutionary process, especially when done without any user interaction. In this paper we investigate a self-adaptive differential evolution algorithm where more DE strategies are used and control parameters F and CR are self-adapted. The performance of the self-adaptive differential evolution algorithm is evaluated on the set of 24 benchmark functions provided for the CEC2006 special session on constrained real parameter optimization.

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Self-Adaptive Differential Evolution Algorithm in Constrained Real-Parameter Optimization

In this paper we investigate a Self-Adaptive Differential Evolution algorithm (jDE) where F and CR control parameters are self-adapted and a multi-population method with aging mechanism is used. The performance of the jDE algorithm is evaluated on the set of benchmark functions provided for the CEC 2009 special session on evolutionary computation in dynamic and uncertain environments.

https://www.cs.le.ac.uk/people/syang/ECiDUE/Competition09-Papers/4982976.pdf

Dynamic optimization using Self-Adaptive Differential Evolution

In this paper we investigate a self-adaptive differential evolution algorithm (jDEdynNP-F) where F and CR control parameters are self-adapted and a population size reduction method is used. Additionally the proposed jDEdynNP-F algorithm uses a mechanism for sign changing of F control parameter with some probability based on the fitness values of randomly chosen vectors, which are multiplied by the F control parameter (scaling factor) in the mutation operation of DE algorithm. The performance of the jDEdynNP-F algorithm is evaluated on the set of 7 benchmark functions provided for the CECpsila2008 special session on high-dimensional real-parameter optimization.

/pdf/high-dimensional-real-parameter-optimization-using-self-10vypcyq3o.pdf

High-dimensional real-parameter optimization using Self-Adaptive Differential Evolution algorithm with population size reduction

In this paper, an optimization algorithm is formulated and its performance assessment for large scale global optimization is presented. The proposed algorithm is named DEwSAcc and is based on Differential Evolution (DE) algorithm, which is a floating-point encoding evolutionary algorithm for global optimization over continuous spaces. The original DE is extended by log-normal self-adaptation of its control parameters and combined with cooperative co-evolution as a dimension decomposition mechanism. Experimental results are given for seven high-dimensional test functions proposed for the Special Session on Large Scale Global Optimization at 2008 IEEE World Congress on Computational Intelligence.

Viljem Zumer

Papers

Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems

Self-Adaptive Differential Evolution Algorithm in Constrained Real-Parameter Optimization

Dynamic optimization using Self-Adaptive Differential Evolution

High-dimensional real-parameter optimization using Self-Adaptive Differential Evolution algorithm with population size reduction

Large Scale Global Optimization using Differential Evolution with self-adaptation and cooperative co-evolution