Hybrid constrained simulated annealing and genetic algorithms for nonlinear constrained optimization

The paper presents a framework that unifies various search mechanisms for solving constrained nonlinear programming (NLP) problems. These problems are characterized by functions that are not necessarily differentiable and continuous. Our proposed framework is based on the first-order necessary and sufficient condition for constrained local minimization in discrete space that shows the equivalence between discrete-neighborhood saddle points and constrained local minima. To look for discrete-neighborhood saddle points, we formulate a discrete constrained NLP in an augmented Lagrangian function and study various mechanisms for performing ascents of the augmented function in the original-variable subspace and descents in the Lagrange-multiplier subspace. Our results show that CSAGA, a combined constrained simulated annealing (SA) and genetic algorithm (GA), performs well. Finally, we apply iterative deepening to determine the optimal number of generations in CSAGA and show that performance is robust with respect to changes in population size.