Constrained optimization problems are very important as they are encountered in many engineering applications. Equality constraints in them are challenging to handle due to tiny feasible region. Additionally, global optimization is required for finding global optimum when the objective function and constraints are nonlinear. Stochastic global optimization methods can handle non-differentiable and multi-modal objective functions. In this paper, a new constraint handling method for use with such methods is proposed for solving equality and/or inequality constrained problems. It incorporates adaptive relaxation of constraints and the feasibility approach for selection. The recent integrated differential evolution (IDE) with the proposed constraint handling technique is tested for solving benchmark problems with constraints, and then applied to many chemical engineering application problems with equality and inequality constraints. The results show that the proposed constraint handling method with IDE (C-IDE) is reliable and efficient for solving constrained optimization problems, even with equality constraints. (C) 2011 Elsevier Ltd. All rights reserved.