Metaheuristics for solving the Dial-a-Ride problem

Abstract

Many transit agencies face the problem of generating routes and schedules to meet customer requests consisting of either pickup or dropoff requests using an available fleet of vehicles. The Dial-a-Ride Problem (DARP) is a mathematical model that closely approximates the problem faced by these agencies. The problem is a generalization of the well-known Pickup and Delivery Vehicle Routing Problem or Vehicle Routing Problem with Time Window. However, due to the high level of service required by this type of transportation service, additional operational constraints must be considered. While the DARP can be solved exactly by various techniques, exact approaches for the solution to real-world problems (typically consisting of hundreds of requests) are not practical. The time required is often excessive as the problem is NP-hard. In this thesis, we develop heuristics that find high quality solutions in a reasonable amount of computer time for the many-to-many, advanced reservation, multi-vehicle, single-depot, static DARP. The objectives considered include the minimization of total travel time and excess ride time, and the problem is subjected to maximum ride time, route duration, vehicle capacity, and wait time constraints. The cluster-first route-second approach is adopted. Clustering is performed using either Tabu Search (TS) or Scatter Search (SS) while routing is performed via insertion. The class of insertion heuristics has been extensively applied to the DARP. Earlier algorithms focused on feasible insertions but recently, heuristics that allow infeasible insertions to be considered during searches have been introduced. In this research, two insertion heuristics are considered: IRAU, which assigns requests only when they are feasible, and IRDU, which assigns all requests even if they result in infeasibilities. Comparison studies show that the benefit of using a particular algorithm depends on the statistical properties of the data sets used. Overall, the algorithms generated better solutions than a previously published real-world (322-request) problem and found the optimal solutions for constructed (32-request and 80-request) problems with known optimal solutions.