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.
Image thresholding is a challenging task in image processing field. Many efforts have already been made to propose universal, robust methods to handle a wide range of images. Previously by the same authors, an optimization-based thresholding approach was introduced. According to the proposed approach, differential evolution (DE) algorithm, minimizes dissimilarity between the input grey-level image and the bi-level (thresholded) image. In the current paper, micro opposition-based differential evolution (micro-ODE), DE with very small population size and opposition-based population initialization, has been proposed. Then, it is compared with a well-known thresholding method, Kittler algorithm and also with its non-opposition-based version (micro-DE). In overall, the proposed approach outperforms Kittler method over 16 challenging test images. Furthermore, the results confirm that the micro-ODE is faster than micro-DE because of embedding the opposition-based population initialization. The concept of opposition-based learning (OBL) can be categorized into Type-I and Type-II OBL methodologies. The Type-I OBL is based on the opposite points in the variable space while the Type-II OBL considers the opposite of function value on the landscape. In the past few years, many research works have been conducted on development of Type-I OBL-based approaches with application in science and engineering, such as opposition-based differential evolution (ODE). However, compared to Type-I OBL, which cannot address a real sense of opposition in term of objective value, the Type-II OBL is capable to discover more meaningful knowledge about problem’s landscape. Due to natural difficulty of proposing a Type-II-based approach, very limited research has been reported in that direction. In this paper, for the first time, the concept of Type-II OBL has been investigated in detail in optimization; also it is applied on the DE algorithm as a case study. The proposed algorithm is called oppositionbased differential evolution Type-II (ODE-II) algorithm; it is validated on the testbed proposed for the IEEE Congress on Evolutionary Computation 2013 (IEEE CEC-2013) contest with 28 benchmark functions. Simulation results on the benchmark functions demonstrate the effectiveness of the proposed method as the first step for further developments in Type-II OBL-based schemes. Opposition-based learning as a new scheme for machine intelligence is introduced. Estimates and counter-estimates, weights and opposite weights, and actions versus counter-actions are the foundation of this new approach. Examples are provided. Possibilities for extensions of existing learning algorithms are discussed. Preliminary results are provided