A genetic algorithm based augmented Lagrangian method for constrained optimization

Linearly Convergent Evolution Strategies via Augmented Lagrangian Constraint Handling

“…We draw attention, however, to the fact that the observed stability may depend on the chosen parameter setting-in particular the damping factors for the Lagrange factors and the penalty factors-and proper parameter values are necessary to observe stability, especially in larger dimensions and for large numbers of constraints. The conducted analysis gives insight into the behavior of the practical (µ/µw, λ)-ES obtained when optimizing the augmented Lagrangian presented in (9). Indeed, we focus our study on the most difficult case in practice, where all the constraints are active at the optimum.…”

“…The Lagrangian L is combined to a penalty function, which is a function of the constraints gi, to construct the augmented Lagrangian h. Examples of augmented Lagrangians are given in (9) and (10), where…”

“…In [9], the authors present an augmented-Lagrangian-based genetic algorithm for constrained optimization. Their algorithm requires a local search procedure for improving the current best solution in order to converge to the optimal solution and to the associated Lagrange multipliers.…”

Augmented Lagrangian Genetic Algorithm Based Decentralized Control Configuration Design for Fluid Catalytic Cracking Units

“…Also, penalty function approaches often lead to significant distortion of objective function thereby introducing non-linearity and multi-modalities which eventually create a bottleneck to optimization progress in arriving at true constrained optimization solution. In addition, they lack convergence proof but assume optimal solutions to the constrained optimization problem) [20]. In the recent past, augmented Lagrangian technique has received much attention as an efficient method to handle constrained optimization problems [20]- [22].…”

“…In addition, they lack convergence proof but assume optimal solutions to the constrained optimization problem) [20]. In the recent past, augmented Lagrangian technique has received much attention as an efficient method to handle constrained optimization problems [20]- [22]. In augmented Lagrangian technique, a sequence of subproblems which are the outcome of combination of objective function and nonlinear constraint function are minimized while the linear constraints and bounds are not violated.…”