An algorithm called genetic shortest-path algorithm is presented to solve capacitated minimal Steiner tree problems in graphs with complex flows and arbitrary arc cost functions, but without negative cycles. Voltage constraint can also been taken into consideration by the algorithm. Hence, it can solve various power distribution system optimization problems with detailed mathematical models. In the proposed algorithm, a local optimization method based on shortest path algorithm and heuristics is used to find the local optimums, in which the minimum cost objective and all constraints are considered and the specialties of the problems are made good use of. Genetic operations are only used to search the global optimum from the local optimums. Therefore, this algorithm overcomes the disadvantage of general genetic algorithm in local searching. An example for distribution system planning problem with large scale is given to demonstrate the power of the algorithm.