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
2046737544 2007220325 2018188932
A new adaptive Differential Evolution algorithm called EWMA-DE is proposed. In original Differential Evolution algorithm three different control parameter values must be pre-specified by the user a priori; Population size, crossover constant and mutation scale factor. Choosing good parameters can be very difficult for the user, especially for the practitioners. In the proposed algorithm the mutation scale factor is adapted using a novel exponential moving average based mechanism, while the other control parameters are kept fixed as in standard Differential Evolution. The algorithm was initially evaluated by using the set of 25 benchmark functions provided by CEC2005 special session on real-parameter optimization and compared with the results of standard DE rand 1 bin version. Results turned out to be rather promising; EWMA-DE outperformed the original Differential Evolution in majority of tested cases, which is demonstrating the potential of the proposed adaptation approach. 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 studies the efficiency of a recently defined population-based direct global optimization method called Differential Evolution with self-adaptive control parameters. The original version uses fixed population size but a method for gradually reducing population size is proposed in this paper. It improves the efficiency and robustness of the algorithm and can be applied to any variant of a Differential Evolution algorithm. The proposed modification is tested on commonly used benchmark problems for unconstrained optimization and compared with other optimization methods such as Evolutionary Algorithms and Evolution Strategies.