Hybrid Artificial Fish School Algorithm Based on Mutation Operator for Solving Nonlinear Equations

To overcome the problems of the classical algorithms for solving nonlinear equations, such as high sensitivity to the initial guess of the solution, poor convergence reliability and can´t get all solutions, etc. A hybrid artificial fish swarm algorithm based on mutation operator (HAFSA) is proposed, which combined the advantages of artificial fish school algorithm (AFSA) and the Hooke-Jeeves method. The HAFSA sufficiently exerted the advantages of AFSA such as group search and global convergence, can efficiently overcome the problem of high sensitivity to initial guess, and it also had a high convergence rate and solution precision just because it used the Hooke-Jeeves method which has high local convergence for local search. Besides, mutation operator is embedded to avoid the common defect of premature convergence of the hybrid algorithm. The experimental results show that the proposed hybrid algorithm outperforms the classical numerical methods and the standard artificial fish swarm algorithm significantly in terms of effectiveness and efficiency.