In cumulative transfer functions, as number of transfer increase, the impact of individual transfer to transfer cost increase linearly or non linearly. This function can effectively explain various passengers's travel behavior who choose their travel routes in integrated transit line networks including bus and railway modes. Using the function, it is possible to simulate general situations such that even though more travel times are expected, less number of transfer routes are preferred. However, because travel cost with cumulative transfer function is known as non additive cost function types in route search algorithms, finding an optimal route in integrated transit networks is confronted by the insolvable enumeration of all routes in many cases. This research proposes a methodology for finding an optimal path considering cumulative transfer function. For this purpose, the reversal phenomenon of optimal path generated in route search process is explained. Also a heuristic methodology for selecting an optimal route among multiple routes predefined by the K path algorithm. The incoming link based entire path deletion method is adopted for finding K ranking path thanks to the merit of security of route optimality condition. Through case studies the proposed methodology is discussed in terms of the applicability of real situations.