The first/last mile problem in urban transportation services refers to limited connectivity and accessibility to high capacity commuter lines. This is often encountered in low-density residential areas, where low flexibility and resources of traditional public transportation systems lead to reduced service coverage. Demand-responsive transit (DRT) offers an alternative for providing first/last mile feeder services to low density areas, because of its flexibility in adjusting to different demand patterns. This paper presents a mathematical model and a genetic algorithm for efficiently designing DRT type first/last mile routes. The model is applied for the case of a residential area in Athens, Greece and results are discussed.