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Application of Powell fruit fly optimization algorithm to solutions of nonlinear equations

Solution to nonlinear equations is with extensive practical meanings in engineering. The convergence of classic numerical solutions is dependent on the initial value which is actually hard to be determined in actual computation. Thus, a new solution to nonlinear equations called PFOA is put forward to turn the complicated solution to nonlinear equations to function optimization. Group search and global convergence of the fruit fly optimization algorithm (FOA) can be fully utilized via PFOA, thereby effectively overcoming the initial point sensitivity of Powell. However, positive local optimal solution can be realized by Powell, so the two algorithms are improved effectively along with integration and complementation in this paper. Five typical nonlinear equations are selected, and the calculation results show the designed PFOA is superior to the basic FOA and is considered a successful solution to nonlinear equations.