Hybridizing artificial bee colony with monarch butterfly optimization for numerical optimization problems

The aim of the study was to propose a new metaheuristic algorithm that combines parts of the well-known artificial bee colony (ABC) optimization with elements from the recent monarch butterfly optimization (MBO) algorithm. The idea is to improve the balance between the characteristics of exploration and exploitation in those algorithms in order to address the issues of trapping in local optimal solution, slow convergence, and low accuracy in numerical optimization problems. This article introduces a new hybrid approach by modifying the butterfly adjusting operator in MBO algorithm and uses that as a mutation operator to replace employee phase of the ABC algorithm. The new algorithm is called Hybrid ABC/MBO (HAM). The HAM algorithm is basically employed to boost the exploration versus exploitation balance of the original algorithms, by increasing the diversity of the ABC search process using a modified operator from MBO algorithm. The resultant design contains three components: The first and third component implements global search, while the second one performs local search. The proposed algorithm was evaluated using 13 benchmark functions and compared with the performance of nine metaheuristic methods from swarm intelligence and evolutionary computing: ABC, MBO, ACO, PSO, GA, DE, ES, PBIL, and STUDGA. The experimental results show that the HAM algorithm is clearly superior to the standard ABC and MBO algorithms, as well as to other well-known algorithms, in terms of achieving the best optimal value and convergence speed. The proposed HAM algorithm is a promising metaheuristic technique to be added to the repertory of optimization techniques at the disposal of researchers. The next step is to look into application fields for HAM.