Abstract
In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO) algorithm which has population diversity with the heuristic global search of differential evolution (DE) algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO) algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.
Highlights
Systems of nonlinear equations arise in many domains of practical importance such as engineering, mechanics, medicine, chemistry, and robotics
Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO) algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations
In order to test the performance of DEIWO for solving nonlinear equation systems, 8 nonlinear equation systems in the literature are used and the testing results are compared with the literature [12]
Summary
Systems of nonlinear equations arise in many domains of practical importance such as engineering, mechanics, medicine, chemistry, and robotics. With the rapid development of computational intelligence, computational intelligence techniques have been used to solve nonlinear equations, such as genetic algorithm [1,2,3], particle swarm optimization algorithm [4], differential evolution algorithm [5], artificial fish-swarm algorithm [6], artificial bee colony algorithm [7] harmony search algorithm [8], and probabilistic-driven search (PDS) algorithm [9] These swarm intelligent algorithm has several advantages when adopted for searching solutions for systems of nonlinear equations: their does not require of a “good” initial point to perform the search, and the search space can be bounded by lower and upper values for each decision variable. This can, be improved either by running the swarm intelligent algorithm for a larger number of iterations ( at a higher computational cost) or by Journal of Applied Mathematics postprocessing the solution produced by the swarm intelligent algorithm with a traditional numerical optimization technique
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