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{"}The simplified model is characterized not only by its structure (to be found by the GP) but also by a set of tuning parameters a to be found by model tuning, i.e. the least squares fitting of the model into the set of values of the original response function:{"} {"}The allocation of tuning parameters a to an individual tree follows the basic algebraic rules. To identify the parameters of the expression by the nonlinear least-squares fitting, i.e. to solve the optimization problem in (1), a combination of a GA and a nonlinear mathematical programming method [9] is used. The output of the GA is the initial guess for the subsequent derivative-based optimization method which amounts to a variation of the Newton's method in which the Hessian matrix is approximated by the secant (quasi-Newton) updating method. Once the technique comes sufficiently close to a local solution, it normally converges quite rapidly. To promote convergence from poor starting guesses the algorithm uses the adaptive update of the Hessian and, consequently, the algorithm is reduced to either a Gauss-Newton or Levenberg-Marquardt method. {"}
{"}Three-bar truss optimization problem{"}
{"}The output of the algorithm still needs some manual post-processing in order to get rid of those terms in the expression that give a null or tiny contribution, for example when the same value is added and subtracted. It is then suggested to run the problem several times in order to identify, by comparison, the most likely components.{"}",
Genetic Programming entries for Vassili V Toropov Luis F Alvarez