Computational Optimization and Applications
Genetic Algorithms Plus Data Structures Equals Evolution Programs
Genetic Algorithms Plus Data Structures Equals Evolution Programs
Advances in Engineering Software - Special issue on evolutionary optimization of engineering problems
Evolutionary algorithms for constrained parameter optimization problems
Evolutionary Computation
An adaptive penalty formulation for constrained evolutionary optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
A truncated Newton method in an augmented Lagrangian framework for nonlinear programming
Computational Optimization and Applications
Journal of Global Optimization
Investigating EA solutions for approximate KKT conditions in smooth problems
Proceedings of the 12th annual conference on Genetic and evolutionary computation
A hybrid cooperative search algorithm for constrained optimization
Structural and Multidisciplinary Optimization
Augmented Lagrangian for cone constrained topology optimization
Computational Optimization and Applications
An augmented Lagrangian fish swarm based method for global optimization
Journal of Computational and Applied Mathematics
Augmented Lagrangian functions for constrained optimization problems
Journal of Global Optimization
Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization
Computational Optimization and Applications
Evolutionary programming techniques for constrained optimizationproblems
IEEE Transactions on Evolutionary Computation
Coevolutionary augmented Lagrangian methods for constrainedoptimization
IEEE Transactions on Evolutionary Computation
Sensitivity analysis of hyperbolic optimal control problems
Computational Optimization and Applications
An artificial fish swarm algorithm based hyperbolic augmented Lagrangian method
Journal of Computational and Applied Mathematics
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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, thereby providing a better function landscape for search, and (iii) they can result in computing optimal Lagrange multiplier for each constraint as a by-product. Instead of keeping a constant penalty parameter throughout the optimization process, these algorithms update the parameters (called multipliers) 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 requires a serial application of a number of unconstrained optimization tasks, a process that is usually time-consuming and tend to be computationally expensive. In this paper, we devise a genetic algorithm based parameter update strategy to a particular AL method. The proposed strategy updates critical parameters in an adaptive manner based on population statistics. Occasionally, a classical optimization method is used to improve the GA-obtained solution, thereby providing the resulting hybrid procedure its theoretical convergence property. The GAAL method is applied to a number of constrained test problems taken from the evolutionary algorithms (EAs) literature. The number of function evaluations required by GAAL in most problems is found to be smaller than that needed by a number of existing evolutionary based constraint handling methods. GAAL method is found to be accurate, computationally fast, and reliable over multiple runs. Besides solving the problems, the proposed GAAL method is also able to find the optimal Lagrange multiplier associated with each constraint for the test problems as an added benefit--a matter that is important for a sensitivity analysis of the obtained optimized solution, but has not yet been paid adequate attention in the past evolutionary constrained optimization studies.