Heterogeneous Differential Evolution with Memory Enhanced Brownian and Quantum Individuals for Dynamic Optimization Problems

Abstract

In order to solve the dynamic optimization problem (DOP), this paper proposes to use a heterogeneous differential evolution (HDE) algorithm framework with memory enhanced Brownian and quantum (MEBQ) individual scheme. The proposed HDE/MEBQ algorithm has the following two advantages when solving DOP. First and foremost, the HDE optimization framework can satisfy the problem requirement of different characteristics. DOP is actually a continuous process to solve different kinds of optimization problems to meet new requirements when the search environmental change occurs. Therefore, HDE/MEBQ is able to fastly respond to the environmental changes of DOP as the HDE framework uses multiple populations with heterogeneous parameters and operators to meet different search requirements in various search environments. Secondly, according to the phenomenon that most of the environmental changes may not be too drastic in real-world applications, historical information in the past may be useful for finding the optimum solution in the new environment. Thus, the MEBQ scheme used in HDE/MEBQ provides helpful historical evolutionary information from the elite ancestors for guiding individuals to evolve in a new environment strongly and to obtain faster convergence and a more precise solution. We evaluated HDE/MEBQ on several DOPs from CEC 2009 and compared with several state-of-the-art dynamic evolutionary algorithms. The results show that HDE/MEBQ performs superior in statistics and gets very competitive results in most of the test conditions, especially in complex DOPs.