A multi-leader Harris hawks optimizer with adaptive mutation and its application for modeling of silicon content in liquid iron of blast furnace

Aiming at the problem that Harris hawks optimizer (HHO) has poor population diversity and is easy to fall into local optimum when solving complex optimization problems, a multi-leader Harris Hawks optimizer with adaptive mutation (MLHHO-AM) is proposed, in which multiple leaders are used to guide the Harris hawks to improve the population diversity. An adaptive mutation is introduced to enhance the ability of the algorithm to jump out of the local optimum. The key feature of the strategy is that Gaussian mutation occurs in some dimensions of the optimal solution, and the number of mutation dimensions is adaptively changed. To verify the numerical optimization performance of MLHHO-AM, the parameter sensitivity, the role of two improved mechanisms, and population diversity are analyzed based on 23 classical test functions. Then, MLHHO-AM is compared with 12 state-of-the-art variants and 11 basic metaheuristic algorithms on IEEE CEC2017 and IEEE CEC2022 benchmark suites. The above test results show that the proposed MLHHO-AM is an effective algorithm with better numerical optimization performance than most competitors. In order to verify ability of MLHHO-AM to handle the practical problem, the parameters of the Elman neural network (ENN) used to build the prediction model of silicon content in liquid iron of blast furnace are optimized by MLHHO-AM. The simulation results based on actual data show that the ENN prediction model based on MLHHO-AM has higher prediction accuracy with R2=0.7563 and RMSE=0.0598. Therefore, the proposed MLHHO-AM has excellent numerical optimization performance and can be used to predict the silicon content in liquid iron of blast furnace.