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.
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. Abstract The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability scheme is utilized to balance the global exploration and local exploitation. Furthermore, a random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme are merged to avoid stagnation and or premature convergence. Numerical experiments and comparisons on a set of well-known high dimensional benchmark functions indicate that the improved algorithm outperforms and is superior to other existing algorithms in terms of final solution quality, success rate, convergence rate, and robustness. 