A quadratic approximation-based local search operator for handling two equality constraints in continuous optimization problems

This work presents extensions of the general methodology of employing quadratic approximations of the objective function and constraints for handling non-linear equality constraints in single-objective optimization problems. The methodology does not require any extra function evaluation since the quadratic approximations are constructed using only information that would be already obtained in the course of the optimization algorithms. The methodology is coupled with the Real Biased Genetic Algorithm to tackle non-linear single-objective optimization problems with two equality constraints. The modified algorithm is tested with a set of analytical problems. The results show the modified algorithm finds the constrained optima with enhanced precision and faster convergence. Considering that the new technique does not impose any additional cost to the algorithms, it can be stated that the technique is also suitable for costly black-box problems.