Hybrid methods for constrained parameter optimization problems

Abstract

This dissertation presents three kinds of hybrid methods developed for solving constrained parameter optimization problems: a hybrid method for equality constraints (Hybrid-EQ), a hybrid method with Hessian estimation (Hybrid-HE), and a hybrid method with active set (Hybrid-Active). These hybrid methods enhance the co-evolutionary augmented Lagrangian method to overcome two major disadvantages of the evolutionary algorithm, i.e. poor constraint handling and a low convergence rate. The hybrid methods have two significant features. Parameter and multiplier groups are evolved simultaneously to solve a zero-sum game which is transformed from a constrained parameter optimization problem by augmented Lagrangian method. Gradient individuals of parameter and multiplier groups are propagated by Newton’s method, and they play an important role in accelerating the speed of convergence and improving solution accuracy. Jacobian and Hessian matrices are estimated by weighted least-square method and sequential Hessian update method, respectively. In addition, the hybrid method with active set takes advantage of the active set method which treats inequality constraints effectively. The hybrid methods apply to well-known benchmark optimization problems with constraints. Finding global solution and convergence rate are two major concerns in the numerical simulation.