Differential evolution (DE) algorithm with a small population size is called Micro-DE (MDE). A small population size decreases the computational complexity but also reduces the exploration ability of DE by limiting the population diversity. In this paper, we propose the idea of combining ensemble mutation scheme selection and opposition-based learning concepts to enhance the diversity of population in MDE at mutation and selection stages. The proposed algorithm enhances the diversity of population by generating a random mutation scale factor per individual and per dimension, randomly assigning a mutation scheme to each individual in each generation, and diversifying individuals selection using opposition-based learning. This approach is easy to implement and does not require the setting of mutation scheme selection and mutation scale factor. Experimental results are conducted for a variety of objective functions with low and high dimensionality on the CEC Black- Box Optimization Benchmarking 2015 (CEC-BBOB 2015). The results show superior performance of the proposed algorithm compared to the other micro-DE algorithms.
A population size adaptation method is proposed in @cite_16 which measures the Euclidean distance between individuals and finds out if the population diversity is poor and or it moves toward stagnation. Depending on the search situation, it generates new individuals. A population size reduction method for cDE is proposed in @cite_31 , where the population size gradually reduces during the evolution. Cumu-DE is an adaptive DE and the effective population size is adapted automatically using mechanism based on a probabilistic model @cite_19 . The term effective refers to the effective part of the population where its size shrinks as the algorithm has more successful trials. Gradual reduction of the population size is another approach that has demonstrated higher robustness and efficiency compared to generic DE @cite_25 .
@cite_19 @cite_31 @cite_16 @cite_25
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In differential evolution (DE), there are many adaptive algorithms proposed for parameters adaptation. However, they mainly aim at tuning the amplification factor F and crossover probability CR. When the population diversity is at a low level or the population becomes stagnant, the population is not able to improve any more. To enhance the performance of DE algorithms, in this paper, we propose a method of population adaptation. The proposed method can identify the moment when the population diversity is poor or the population stagnates by measuring the Euclidean distances between individuals of a population. When the moment is identified, the population will be regenerated to increase diversity or to eliminate the stagnation issue. The population adaptation is incorporated into the jDE algorithm and is tested on a set of 25 scalable CEC05 benchmark functions. The results show that the population adaptation can significantly improve the performance of the jDE algorithm. Even if the population size of jDE is small, the jDE algorithm with population adaptation also has a superior performance in comparisons with several other peer algorithms for high-dimension function optimization. This paper presents a novel evolutionary optimization strategy based on the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). This new approach is intended to reduce the number of generations required for convergence to the optimum. Reducing the number of generations, i.e., the time complexity of the algorithm, is important if a large population size is desired: (1) to reduce the effect of noise; (2) to improve global search properties; and (3) to implement the algorithm on (highly) parallel machines. Our method results in a highly parallel algorithm which scales favorably with large numbers of processors. This is accomplished by efficiently incorporating the available information from a large population, thus significantly reducing the number of generations needed to adapt the covariance matrix. The original version of the CMA-ES was designed to reliably adapt the covariance matrix in small populations but it cannot exploit large populations efficiently. Our modifications scale up the efficiency to population sizes of up to 10n, where n is the problem dimension. This method has been applied to a large number of test problems, demonstrating that in many cases the CMA-ES can be advanced from quadratic to linear time complexity. As one of the popular evolutionary algorithms, differential evolution (DE) shows outstanding convergence rate on continuous optimization problems. But prematurity probably still occurs in classical DE when using relatively small population, which is discussed in this paper. Considering that large population may significantly raise the computational effort, we propose a modified DE using smaller population (DESP) by introducing extra disturbance to its mutation operation. In addition, an adaptive adjustment scheme is designed to control the disturbance intensity according to the improvement during the evolution. To test the performance of DESP, two groups of experiments are conducted. The results show that DESP outperforms DE in terms of convergence rate and accuracy. In this paper differential evolution is extended by using the notion of speciation for solving multimodal optimization problems. The proposed species-based DE (SDE) is able to locate multiple global optima simultaneously through adaptive formation of multiple species (or subpopulations) in an DE population at each iteration step. Each species functions as an DE by itself. Successive local improvements through species formation can eventually transform into global improvements in identifying multiple global optima. In this study the performance of SDE is compared with another recently proposed DE variant CrowdingDE. The computational complexity of SDE, the effect of population size and species radius on SDE are investigated. SDE is found to be more computationally efficient than CrowdingDE over a number of benchmark multimodal test functions.