Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

Recent advances in differential evolution – An updated survey

Differential Evolution: A review of more than two decades of research

https://repository.up.ac.za/bitstream/handle/2263/8794/Omran_Bare%282008%29.pdf?sequence=1

Bare bones differential evolution

Population size of Differential Evolution (DE) algorithms is often specified by user and remains fixed during run. During the first decade since the introduction of DE the opinion that its population size should be related to the problem dimensionality prevailed, later the approaches to DE population size setting diversified. In large number of recently introduced DE algorithms the population size is considered to be problem-independent and often fixed to 100 or 50 individuals, but alongside a number of DE variants with flexible population size have been proposed. The present paper briefly reviews the opinions regarding DE population size setting and verifies the impact of the population size on the performance of DE algorithms. Ten DE algorithms with fixed population size, each with at least five different population size settings, and four DE algorithms with flexible population size are tested on CEC2005 benchmarks and CEC2011 real-world problems. It is found that the inappropriate choice of the population size may severely hamper the performance of each DE algorithm. Although the best choice of the population size depends on the specific algorithm, number of allowed function calls and problem to be solved, some rough guidelines may be sketched. When the maximum number of function calls is set to classical values, i.e. those specified for CEC2005 and CEC2011 competitions, for low-dimensional problems (with dimensionality below 30) the population size equal to 100 individuals is suggested; population sizes smaller than 50 are rarely advised. For higher-dimensional artificial problems the population size should often depend on the problem dimensionality d and be set to 3d–5d. Unfortunately, setting proper population size for higher-dimensional real-world problems (d>40) turns out too problem and algorithm-dependent to give any general guide; 200 individuals may be a first guess, but many DE approaches would need a much different choice, ranging from 50 to 10d. However, quite clear relation between the population size and the convergence speed has been found, showing that the fewer function calls are available, the lower population sizes perform better. Based on the extensive experimental results the use of adaptive population size is highly recommended, especially for higher-dimensional and real-world problems. However, which specific algorithms with population size adaptation perform better depends on the number of function calls allowed.

Review of Differential Evolution population size

This paper introduces a Genetic Algorithm (GA) based optimization for rule base and scaling factors adjustment to enhance the performance of fuzzy logic controllers. First a recursive rule base adjustment algorithm is developed, which has the benefit that it is computationally more efficient for the generation of a decision table. Then utilizing the advantage of GA optimization, a novel approach that each random combination of the optimized parameters (including the membership function selection for the rule base and controller scaling factors) is coded into a Real Coded string and treated as a chromosome in genetic algorithms is given. The optimization for rule base with the correspondent membership function and scaling factors using GA is easy to be realization in engineering. Simulation results are presented to support this thesis.

Computational Intelligence

Using competitive population evaluation in a differential evolution algorithm for dynamic environments

This paper investigates optimization in dynamic environments where the numbers of optima are unknown or fluctuating. The authors present a novel algorithm, Dynamic Population Differential Evolution (DynPopDE), which is specifically designed for these problems. DynPopDE is a Differential Evolution based multi-population algorithm that dynamically spawns and removes populations as required. The new algorithm is evaluated on an extension of the Moving Peaks Benchmark. Comparisons with other state-of-the-art algorithms indicate that DynPopDE is an effective approach to use when the number of optima in a dynamic problem space is unknown or changing over time.

/pdf/differential-evolution-for-dynamic-environments-with-unknown-3zwzogvi4q.pdf

Differential evolution for dynamic environments with unknown numbers of optima

World Congress on Nature and Biologically Inspired Computing (NaBIC) is organized to discuss the state-of-the-art as well as to address various issues with respect to Nurturing Intelligent Computing Towards Advancement of Machine Intelligence. This Volume contains the papers presented in the Seventh World Congress (NaBIC15) held in Pietermaritzburg, South Africa during December 01-03, 2015. The 39 papers presented in this Volume were carefully reviewed and selected. The Volume would be a valuable reference to researchers, students and practitioners in the computational intelligence field.

Advances in Nature and Biologically Inspired Computing: Proceedings of the 7th World Congress on Nature and Biologically Inspired Computing

Concurrent controller and Simulator Neural Network development for a differentially-steered robot in Evolutionary Robotics

Robotic simulators are used extensively in Evolutionary Robotics (ER). Such simulators are typically constructed by considering the governing physics of the robotic system under investigation. Even though such physics-based simulators have seen wide usage in ER, there are some potential challenges involved in their construction and usage. An alternative approach to developing robotic simulators for use in ER, is to sample data directly from the robotic system and construct simulators based solely on this data. The authors have previously shown the viability of this approach by training Artificial Neural Networks (ANNs) to act as simulators in the ER process. It is, however, not known how this approach to simulator construction will compare to physics-based approaches, since a comparative study between ANN-based and physics-based robotic simulators in ER has not yet been conducted. This paper describes such a comparative study. Robotic simulators for the motion of a differentially-steered mobile robot were constructed using both ANN-based and physics-based approaches. These two approaches were then compared by employing each of the developed simulators in the ER process to evolve simple navigation controllers for the experimental robot in simulation. Results obtained indicated that, for the robotic system investigated in this study, ANN-based robotic simulators offer a promising alternative to physics-based simulators.

Mathys C. du Plessis

Papers

Using competitive population evaluation in a differential evolution algorithm for dynamic environments

Differential evolution for dynamic environments with unknown numbers of optima

Advances in Nature and Biologically Inspired Computing: Proceedings of the 7th World Congress on Nature and Biologically Inspired Computing

Concurrent controller and Simulator Neural Network development for a differentially-steered robot in Evolutionary Robotics

A comparison of neural networks and physics models as motion simulators for simple robotic evolution