Coevolutionary augmented Lagrangian methods for constrained optimization

Abstract

This paper introduces a coevolutionary method developed for solving constrained optimization problems, This algorithm is based on the evolution of two populations with opposite objectives to solve saddle-point problems, The augmented Lagrangian approach is taken to transform a constrained optimization problem to a zero-sum game with the saddle-point solution. The populations of the parameter vector and the multiplier vector approximate the zero-sum game by a static matrix game, in which the fitness of individuals is determined according to the security strategy of each population group. Selection, recombination, and mutation are done by using the evolutionary mechanism of conventional evolutionary algorithms such as evolution strategies, evolutionary programming, and genetic algorithms. Four benchmark problems are solved to demonstrate that the proposed coevolutionary method provides consistent solutions with better numerical accuracy than other evolutionary methods.