Projection-based local search operator for multiple equality constraints within genetic algorithms

Abstract

This paper presents a new operator for genetic algorithms that enhances convergence in the case of multiple nonlinear equality constraints. The proposed operator, named CQA-MEC (Constraint Quadratic Approximation for Multiple Equality Constraints), performs the steps: (i) the approximation of the non-linear constraints via quadratic functions; (ii) the determination of exact equality-constrained projections of some points onto the approximated constraint surface, via an iterative projection algorithm; and (iii) the re-insertion of the constraint- satisfying points in the genetic algorithm population. This operator can be interpreted both as a local search engine (that employs local approximations of constraint functions for correcting the feasibility) and a kind of elitism operator for equality constrained problems that plays the role of "fixing" the best estimates of the feasible set. The proposed operator has the advantage of not requiring any additional function evaluation per algorithm iteration, solely making usage of the information that is 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.