In the RBDO applications which include a reliability analysis and an optimization algorithm, Sequential Quadratic Programming (SQP) is frequently used for the optimization. In this work, in addition to SQP, some heuristic algorithms such as Simulating Annealing (SA), Genetic Algorithms (GA) and Harmony Search (HS) are employed as optimization methods to demonstrate the performance, accuracy and efficiency of the corresponding methods in the RBDO process. The probabilistic constraints are evaluated by using Reliability Index Approach (RIA). The optimum design of a monopod offshore tower is presented as a numerical example to show the applicability of the proposed algorithm. Graphical and tabular forms are proposed to compare the efficiency of the optimization methods used in the Reliability Based Design Optimization (RBDO) process. As a result, heuristic algorithms exhibit good performance although they call many function evaluations including constraints and objective functions.