Sparsely populated areas tend to be poorly served by Fixed Line and Schedule (FLS) public transport systems as the operation of a regular bus line is not economically viable for such areas. Therefore, introducing a Demand Responsive Transport (DRT) to partially replace FLS can result in increasing mobility service accessibility and inclusion. In this paper, a mixed-integer linear problem (MILP) is proposed to design an integrated FLS and DRT network for a transport operator. Passengers behavior is implicitly incorporated in our proposed approach via a discrete choice model. In addition, a tailored Adaptive Large Neighborhood Search (ALNS) coupled with tabu search and simulated annealing are introduced. We test our algorithm on real instances from a public transport operator in the Netherlands. The proposed algorithm can solve the problem up to 170 times faster than the MILP within 4% to 10% gap. Our proposed resolution approach investigates the temporal and spatial feasibility of deploying these integrated mobility systems based on the service level and provides recommendations to public transport operators.