Abstarct: Although most of the design and optimization of structures, Effective parameters in their assumed to be Certain but Indeed the parameters such as load, yield strength, modulus of elasticity, cross-sectional area , length of element and etc. is not conclusive. so in the new methods for optimization of structures for More rational consideration of Parameters of non-deterministic instead of using safety factors some or all of the parameters rather than the absolute quantity are defined the random variables and until used design and optimization methods. In this thesis assess the reliability of two-dimensional and three-dimensional frxame structures, is performed with matrix formulation baxsed on stiffness method and to determine the failure paths used from branch and bound method until prevent estimate the probability of failure of structural systems derived from probability of failure of elements that has unacceptable results. Area selection optimization of steel moment frxame structures is done without using of designed regulations and by considering the performance of structural systems and type of distribution of probability of random variables. Target of this optimization of this structure, is minimize structure weight with element reliability and system reliability constraints. Optimization is done by using island genetic algorithm with parallel processing and also the proposed developed operators hybrid genetic algorithm methods. For this purpose, writed the programs by matlab programming language.