Evolian: Evolutionary Optimization Based on Lagrangian with Constraint Scaling

Abstract

In this paper, an evolutionary optimization method, Evolian, is proposed

for the general constrained optimization problem, which incorporates the

concept of (1) a multi-phase optimization process and (2) constraint scaling techniques

to resolve problem of ill-conditioning. In each phase of Evolian, the typical

evolutionary programming (EP) is performed using an augmented Lagrangian objective

function with a penalty parameter fixed. If there is no improvement in the

best objective function in one phase, another phase of Evolian is performed after

scaling the constraints and then updating the Lagrange multipliers and penalty

parameter. This procedure is repeated until a satisfactory solution is obtained.

Computer simulation results indicate that Evolian gives outperforming or at least

reasonable results for multivariable heavily constrained function optimization as

compared to other evolutionary computation-based methods.