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In the face of these diverse forms of opposition existed widely in real-world contexts, as a novel concept in computational intelligence, opposition-based learning (OBL) was originally introduced to accelerate the population-based algorithm. In addition, its superiority has been proved mathematically and experimentally. Two key elements (function prototype and algorithm design) that influence the algorithm performance, however, has not yet fully discussed in the past decade. In this paper, two OBL strategies are reexamined in respect of function prototype and algorithm design. In the first part of this paper, considering the position relationship between the optimal solution and the center point, some well-known benchmark functions are divided into three categories. Then, quasi-opposition-based differential evolution (QODE) is investigated by two approaches: solving several benchmark functions of various function types and solving the same functions with a different optimal solution. The numerical experiments reveal that “smart” matching between the benchmark functions and the QOBL is an important factor to the good performance of QODE. In the second part of this paper, a novel individual-based embedding method is proposed to coincide with the classical definition of opposition-based optimization. Then, two opposition-based differential evolution algorithms are compared to discuss the differences between the two embedding methods. The experimental results confirm that the convergence differences stem from the embedding method chosen in the OBL scheme rather than the utilization rate of opposite points. Furthermore, the impacts caused by various function types and jumping rate are also discussed.

Abstract: Diverse forms of opposition are already existent virtually everywhere around us, and utilizing opposite numbers to accelerate an optimization method is a new idea. Since 2005, opposition-based learning is a fast growing research field in which a variety of new theoretical models and technical methods have been studied for dealing with complex and significant problems. As a result, an increasing number of works have thus proposed. This paper provides a survey on the state-of-the-art of research, reported in the specialized literature to date, related to this framework. This overview covers basic concepts, theoretical foundation, combinations with intelligent algorithms, and typical application fields. A number of challenges that can be undertaken to help move the field forward are discussed according to the current state of the opposition-based learning. [Copyright &y& Elsevier]