Elephant herding optimization using dynamic topology and biogeography-based optimization based on learning for numerical optimization

With the increasing complexity of optimization problems in the real world, more and more intelligent algorithms are used to solve these problems. Elephant herding optimization (EHO), a recently proposed metaheuristic algorithm, is based on the nomadic habits of elephants on the grassland. The herd is divided into multiple clans, each individual drawing closer to the patriarchs (clan updating operator), and the adult males are separated during puberty (separating operator). Biogeography-based optimization (BBO) is inspired by the principles of biogeography, and finally achieves an equilibrium state by species migration and drifting between geographical regions. To solve the numerical optimization problems, this paper proposes an improved elephant herding optimization using dynamic topology and biogeography-based optimization based on learning, named biogeography-based learning elephant herding optimization (BLEHO). In BLEHO, we change the topological structure of the population by dynamically changing the number of clans of the elephants. For the updating of each individual, we use the update of the operator based on biogeography-based learning or the operator based on EHO. In the separating phase, we set the separation probability according to the number of clans, and adopt a new separation operator to carry out the separation operation. Finally, through elitism strategy, a certain number of individuals are preserved directly to the next generation without being processed, thus ensuring a better evolutionary process for the population. To verify the performance of BLEHO, we used the benchmarks provided by IEEE CEC 2014 for the test. The experimental results were compared with some classical algorithms (ABC, ACO, BBO, DE, EHO, GA, and PSO) and the most advanced algorithms (BBKH, BHCS, CCS, HHO, PPSO, SCA, and VNBA) and analyzed by Friedman rank test. Finally, we also applied BLEHO to the simple traveling salesman problem (TSP). The results show that BLEHO has better performance than other methods.