Constraint quadratic approximation operator for treating equality constraints with genetic algorithms

This paper presents a new operator for genetic algorithms that enhances their convergence in the case of nonlinear problems with nonlinear equality constraints. The proposed operator, named CQA (Constraint Quadratic Approximation), can be interpreted as both a local search engine (that employs quadratic approximations of both objective and constraint functions for guessing a solution estimate) and a kind of elitism operator that plays the role of "fixing" the best estimate of the feasible set. The proposed operator has the advantage of not requiring any additional function evaluation per algorithm iteration, solely making use of the information that would be already obtained in the course of the usual Genetic Algorithm iterations. The test cases that were performed suggest that the new operator can enhance both the convergence speed (in terms of the number of function evaluations) and the accuracy of the final result.