The traditional RAP (Redundancy Allocation Problem) of complex systems has considered only the redundancy of subsystem with homogeneous components. In this paper we extend it as a RAP of complex systems with heterogeneous components which is more flexible than the case of homogeneous components. We model this problem as a nonlinear integer programming problem, find its optimal solution by tabu search, and suggest an example of the efficient reliability design with heterogeneous components. In order to improve the quality of the solution of the tabu search, we suggest a modified tabu search to employ an adaptive procedure (1-opt or 2-opt exchange) to generate the efficient neighborhood solutions. Computational results show that our modified procedure obtains better solutions as the size of problem increases from 30 to 50, even though it requires rather more computing time. With some adjustment of the parameters of the proposed method, it can be applied to the optimal reliability designs of complex systems of ships.