On Challenging Techniques for Constrained Global Optimization Isabel A. C. P. Esp´ ırito Santo, Lino Costa, Ana Maria A. C. Rocha, M. A. K. Azad and Edite M. G. P. Fernandes Abstract This chapter aims to address the challenging and demanding issue of solving a continuous nonlinear constrained global optimization problem. We pro- pose 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 dif- ferent 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 engi- neering design problems are successfully solved by the proposed methods. 1 Introduction The problem that is addressed in this chapter is a continuous nonlinear constrained global optimization problem with the general form min x∈Ω f (x), subject to h(x)= 0 , g(x) ≤ 0 , (1) where some of the functions f : R n → R, h : R n → R m and g : R n → R p are nonlinear and Ω = {x ∈ R n : l ≤ x ≤ u}. The function f (x) is the objective function, the equa- Isabel A. C. P. Esp´ ırito Santo, Lino Costa and Ana Maria A. C. Rocha Department of Production and Systems, University of Minho, 4710-057 Braga, Portugal, e-mail: {iapinho,lac,arocha}@dps.uminho.pt M. A. K. Azad and Edite M. G. P. Fernandes Algoritmi R&D Centre, University of Minho, 4710-057 Braga, Portugal, e-mail: {akazad,emgpf}@dps.uminho.pt 1