Lagrangian-Based Evolutionary Programming for Constrained Optimization

Abstract

In this paper, Lagrangian-based evolutionary programming, Evolian is proposed for the general constrained optimization problem, which incorporates the concept of (1) multi-phase optimization process and (2) constraint scaling techniques to resolve the ill-conditioning problem. In each phase of Evolian, the typical EP is performed using augmented Lagrangian objective function with a penalty parameter fixed. If there is no improvement in the best objective function in one phase, another phase is performed after scaling the constraints, and updating the Lagrange multipliers and penalty parameter. Simulation results indicate that Evolian gives outperforming or at least reasonable solutions for multivariable heavily constrained optimization problem compared to other several evolutionary computation based methods.