The problem of finding globally optimal constrained stable periodic control processes (globally optimal cycles) arising from the optimization of some chemical, biotechnological, and flight processes is considered. An evolutionary optimization algorithm dealing with a population of cycles evolving by the crossing, and the mutation operations is developed. It incorporates various constraints imposed on the optimized cycles such as the averaged control constraints, the pointwise state constraints, and the stability requirements formulated as the maximal admissible level of the modulus of the Floquet's multipliers. The proposed method is applied to the global periodic optimization of some constrained chemical production processes. (c) 2006 Elsevier Ltd. All rights reserved.