An enhanced monarch butterfly optimization with self-adaptive crossover operator for unconstrained and constrained optimization problems

Inspired by the phenomenon of migration of monarch butterflies, Wang et al. developed a novel promising swarm intelligence algorithm, called monarch butterfly optimization (MBO), for addressing unconstrained low-dimensional optimization problems. In this paper, we firstly extend the application area of the basic MBO to solve the constrained optimization problems. At the same time, the crossover operator originally used in evolutionary algorithms (EAs) is incorporated into the butterfly adjusting operator in order to strengthen the exploitation of the basic MBO algorithm. Furthermore, the crossover rate is self-adaptively adjusted according to the fitness of the corresponding individual instead of the fixed crossover rate used in EAs. For migration operator, only individuals having better fitness are accepted and passed to the next generation instead of accepting all the individuals in the basic MBO algorithm. After incorporated all the modifications into the basic MBO algorithm, an improved MBO algorithm with self-adaptive crossover namely SACMBO, is proposed for unstrained and constrained optimization problems. Finally, the proposed SACMBO algorithm is further used to solve 22 unstrained optimization problems (with dimension of 100, 300, 500, 1000, and 1500) and 28 constrained real-parameter optimization functions from CEC 2017 competition (with dimension of 50 and 100), respectively. The experimental results indicate that the proposed SACMBO algorithm outperforms the basic MBO and other five state-of-the-art metaheuristic algorithms.