On Challenging Techniques for Constrained Global Optimization

Abstract

This chapter aims to address the challenging and demanding issue of solving a continuous nonlinear constrained global optimization problem. We propose four stochastic methods that rely on a population of points to diversify the search for a global solution: genetic algorithm, differential evolution, artificial fish swarm algorithm and electromagnetism-like mechanism. The performance of different variants of these algorithms is analyzed using a benchmark set of problems. Three different strategies to handle the equality and inequality constraints of the problem are addressed. An augmented Lagrangian-based technique, the tournament selection based on feasibility and dominance rules, and a strategy based on ranking objective and constraint violation are presented and tested. Numerical experiments are reported showing the effectiveness of our suggestions. Two well-known engineering design problems are successfully solved by the proposed methods. © Springer-Verlag Berlin Heidelberg 2013.Fundação para a Ciência e a Tecnologia (Foundation for Science and Technology), Portugal for the financial support under fellowship grant: C2007-UMINHO-ALGORITMI-04. The other authors acknowledge FEDER COMPETE, Programa Operacional Fatores de Competitividade (Operational Programme Thematic Factors of Competitiveness) and FCT for the financial support under project grant: FCOMP-01-0124-FEDER-022674info:eu-repo/semantics/publishedVersio