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This paper presents the simple approaches to undertake reliability-based design optimization (RBDO) of bridges by integrating the first order reliability approximation and optimal algorithms of Matlab optimization toolbox. The approaches are applied to solve three RBDO problems that represent almost the practical designs of bridges. At every step of the optimal algorithm, reliability index is calculated without increasing the number of constraints to reduce the computational cost. Moreover, these approaches allow users to formulate the real RBDO problems with the separation or combination of component and system failure probabilities as well as equality and inequality probabilistic constraints. Numerical examples indicate the improvement of approaches due to lower design variables and lower cost for comparing to existing results with the same value of target reliability index. The proposed approaches are simple but efficient for solving RBDO problems to produce the better results than existing approaches and the obtained results may be closer to the exact optimization results.