Reliability problems are an important type of optimization problems that are motivated by different needs of real world applications such as telecommunication systems, transformation systems, and electrical systems, so on. This paper studies a special type of these problems which is called redundancy allocationproblem (RAP) and develops a bi-objective RAP (BORAP).Reliability is an important feature in the mechanical and electrical systems, which is discussed in thcommunications industries, internet networks, telecommunication systems, power generation systems manufacturing facilities and etc. Finding the optimal level of reliability based on system constraints, is called a "reliability optimization problem". The variety of system structures and resource constraints for improving the reliability has led to design and analyze several optimization models. One of the methods to improve system reliability is using the redundant components in the system. it has proven that Redundancy Allocation Problem (RAP) is a kind of NP-hard problems and the computation grows exponentially by increasing problem size and constraints. Hence, finding the appropriate solution is important for these problems In this thesis, the redundancy allocation problem is studied for improving the reliability of series - parallel systems and minimizing the cost of the system based on the multiple component choices, and Non-dominated sorting genetic algorithm has been applied for the purpose of solving. Sine in the estimation of reliability in each component has uncertainty and are not exact. So for removing tambiguity from the numbers, there are many ways. One of this way is that we use fuzzy numbers. In this research triangu fuzzy number were used. For solving the multi objective model, we shoud use the exact model. In this study the expected value method used for de-fuzzy model.algorithm has been introduced to construct the membership function an non-. Functions of intuitionistic fuzzy numbers are calculated to construct the membership functionand non-membership function of fuzzy reliability via non-linear programming techniques. Using proposed algorithm, membership functions and non-membership functions of fuzzy reliability of a series system and a parallel systems are constructed. The present study investigates reliability optimization, minimizing system’s cost and system requirements in terms of electrical and system and suggests pareto solutions based on Non-dominated sorting genetic algorithm. In order to illustrate the application of the redundancy allocation problem and performance of the proposed Non-dominated sorting genetic algorithm, an electrical system was evaluated. Considered system is an electronic board which is used in medical equipments and now it is produced by the Isfahan Optics-Sa Iran Company. In this equipment, in addition to volume and weight constraints, it is necessary that using Non-linear constraint to solving problem because in reality constraints are not linear. The present study has suggested an appropriate algorithm and pareto solution for solving reliability optimization problems in series - parallel systems based on redundancy allocation. Pareto solutions help the decision maker to select the best strategy for structure of the electronic bord