A parallel heuristic for the travel planning problem

In this paper we propose a parallel heuristic to solve a broad formulation of the travel planning problem. Given a set of destinations and a travel time window, our goal is to find a route that produces a budget travel itinerary, involving plane flights, hotels, stays in each destination and departure/arrival times. When the sequence of cities is fixed, the problem is commonly modeled in literature as a time-dependent network and the best itinerary is computed using shortest path algorithms. However, in our formulation, finding the order of cities that minimizes the total cost is also a goal. Therefore, our formulations stand for a Time Dependent Shortest Path Problem (TDSPP) embedded in the NP-Hard Travel Salesman Problem (TSP). Since an exact approach for our problem would be very time consuming depending on the number of cities, we use a parallel Iterated Local Search (ILS) heuristic to search for promising candidate routes in a realistic travel network. We present experimental results on 285 instances and show that our approach takes in average up to 3 minutes to reach solutions in average less than 3% divergent from an exact implementation. Additionally, our method reaches the optimal solution in about 30% of the test cases.