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.
Differential evolution (DE) is one of the highest performance, easy to implement, and low complexity population-based optimization algorithms. Population initialization plays an important role in finding better candidate solution and faster convergence of the population to a global optimum. It has been shown in the literature that large population sizes for large-scale problems necessarily does not show a statistically significant performance improvement over medium size population. In this paper, we emphasise on importance of population initialization and discuss effects of using centroid-based population initialization in DE, with focus on micro-DE (i.e. DE with small population size). Experimental results for high and low dimensional problems with small and standard population sizes on CEC Black-Box Optimization Benchmark problems 2015 (CEC-BBOB 2015) show centroid initialization can increase performance of DE algorithm, compared to the conventional initialization method. The study and research of evolutionary algorithms (EAs) is getting great attention in recent years. Although EAs have earned extensive acceptance through numerous successful applications in many fields, the problem of finding the best combination of evolutionary parameters especially for population size that need the manual settings by the user is still unresolved. In this paper, our system is focusing on differential evolution (DE) and its control parameters. To overcome the problem, two new systems were carried out for the self-adaptive population size to test two different methodologies (absolute encoding and relative encoding) in DE and compared their performances against the original DE. Fifty runs are conducted for every 20 well-known benchmark problems to test on every proposed algorithm in this paper to achieve the function optimization without explicit parameter tuning in DE. The empirical testing results showed that DE with self-adaptive population size using relative encoding performed well in terms of the average performance as well as stability compared to absolute encoding version as well as the original DE. The development of low-level heuristics for solving instances of a problem is related to the knowledge of an expert. He needs to analyze several components from the problem instance and to think out an specialized heuristic for solving the instance. However if any inherent component to the instance gets changes, then the designed heuristic may not work as it used to do it. In this paper it is presented a novel approach to generated low-level heuristics; the proposed approach implements micro-Differential Evolution for evolving an indirect representation of the Bin Packing Problem. It was used the Hard28 instance, which is a well-known and referenced Bin Packing Problem instance. The heuristics obtained by the proposed approach were compared against the well know First-Fit heuristic, the results of packing that were gotten for each heuristic were analized by the statistic non-parametric test known as Wilcoxon Signed Rank test.