Industrial Applications of Genetic Algorithms:Gauss-Legendre Integration Using Genetic Algorithms

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SUMMARY

A hybrid scheme for solving the systems of nonlinear equations resulting from the application of Gauss-Legendre quadrature has been described and tested. Gauss-Legendre quadrature is an effective numerical integration technique because it simultaneously selects the best values of both the quadrature nodes and the weights, whereas most quadrature methods focus solely on the value of the weights. However, solving the systems of nonlinear equations resulting from the implementation of this quadrature method is difficult. Thus, a hybrid scheme capturing the strengths of both a traditional Newton method and a GA was developed. The hybrid scheme combines the rapid convergence characteristics of the derivative-based Newton-Raphson method (once a quality initial guess is determined) and the global search capabilities of GAs. The result is a method that dramatically reduces the computational time and effort required to implement Gauss-Legendre quadrature.

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