CUCKOO SEARCH ALGORITHM FOR GLOBAL OPTIMIZATION, MULTIMODAL OPTIMIZATION, AND COMPLETION OF NONLINEAR EQUATIONS SYSTEMS - , SURYANI
Solving systems of nonlinear equations is one of the most difficult numerical computation problems. Newton and Quasi-Newton methods are usually used to solve systems of nonlinear equations, but the convergences of these methods are very sensitive to the initial guess of the solution. To overcome these problems, solving systems of nonlinear equations can be formulated into a global optimization problem. Some of the global optimization methods are gradient-based methods. These methods usually get trapped in local optimum and need the existence of derivative of the objective function. Nowadays, there are many heuristic/metaheuristic methods which do not depend on the derivative of the objective function. These methods do not guarantee to obtain the optimal solution, but produce solutions that nearly optimal. In addition, heuristic/metaheuristic methods are more easily implemented to solve the optimization problems. In this final project, the author solves the problem of finding the roots of systems of nonlinear equations that has been formulated into a global optimization problem by using Cuckoo Search method, which is developed by Yang and Deb (2009) combined with the Grouping Technique, which is developed by Sidarto and Kania (2012). The combination of these methods enables us to find all roots of systems of nonlinear equations both real and complex in one run.