Orthogonal learning particle swarm optimization with variable relocation for dynamic optimization

Many real-world optimization problems encounter the presence of uncertainties. Dynamic optimization is a class of problems whose fitness functions vary through time. For these problems, evolutionary algorithm is expected to adapt to the changing environments immediately and find the best solution accurately. Besides, most of the environmental changes may not be too drastic in real-world applications, which indicates the evolutionary information in the past may be helpful for finding the optimum solution in the new environment. As a result, effective reuse of historical evolutionary information is necessary, since it leads a faster convergence after a change has occurred. This paper develops an orthogonal learning particle swarm optimization (OLPSO) with the variable relocation strategy (VRS) to solve the dynamic optimization problem (DOP). The proposed OLPSO-VRS algorithm has two advantages as follows. First and foremost, the orthogonal learning strategy guides particles to fly in better directions by constructing a much promising and efficient exemplar, which can achieve a balance between fast convergence and population diversity. Furthermore, the VRS collects historical information in the stable search stage and then reuse such information to guide the particle variable relocation once the search environment has changed. This operation enables the algorithm to quickly shift to the new promising regions in the changing fitness landscape. We evaluated OLPSO-VRS on several dynamic benchmark problems and compared with several state-of-the-art dynamic algorithms. The results show that OLPSO-VRS obtains very competitive results and enjoys a statistically superior performance on most problems.