A Genetic Algorithm Based Augmented Lagrangian Method for Computationally Fast Constrained Optimization

Abstract

Among the penalty based approaches for constrained optimization, Augmented Lagrangian (AL) methods are better in at least three ways: (i) they have theoretical convergence properties, (ii) they distort the original objective function minimally to allow a better search behavior, and (iii) they can find the optimal Lagrange multiplier for each constraint as a by-product of optimization. Instead of keeping a constant penalty parameter throughout the optimization process, these algorithms update the parameters adaptively so that the corresponding penalized function dynamically changes its optimum from the unconstrained minimum point to the constrained minimum point with iterations. However, the flip side of these algorithms is that the overall algorithm is a serial implementation of a number of optimization tasks, a process that is usually time-consuming. In this paper, we devise a genetic algorithm based parameter update strategy to a particular AL method. The strategy is self-adaptive in order to make the overall genetic algorithm based augmented Lagrangian (GAAL) method parameter-free. The GAAL method is applied to a number of constrained test problems taken from the EA literature. The function evaluations required by GAAL in many problems is an order or more lower than existing methods.