Application of genetic algorithm to the calculation of bound states and local density approximations

A novel method, based on genetic algorithms, has been developed and applied to the solution of differential equations. The new approach is based on the use of real numbers to form the candidate solutions which are improved iteratively by a suitable breeding process. The algorithm was tested in the calculation of the bound states of a double well potential and in the nonlinear density functional calculation. Comparison of the results with those obtained using the direct relaxation method shows excellent agreement.