A Granular Tabu Search algorithm for the Dial-a-Ride Problem

The Simulation of Dynamic Shared Taxi Routing Problem

“…Diana et al presented a parallel regret insertion heuristic for the solution to large-scale DARP with the constraint of time windows [4]. Kirchler et al proposed a granular tabu search algorithm for the static DARP modeled by a mixed integer linear programming formulation, with the objective of generating good solutions in a short amount of time [5].Sophie N. Parragh et al brought forward a variable neighborhood search-based heuristic for the static multi-vehicle DARP using three classes of neighborhoods [6]. In Parragh and Schmid, a hybrid column generation and large neighborhood search approach to the static DARP was presented and more than two-thirds computation time was saved meanwhile the solution quality was guaranteed [7].…”

A memetic algorithm for the patient transportation problem

“…This eight-step scheme was often employed in subsequent studies. Recently, Kirchler and Wolfler Calvo [24] proposed a granular tabu search in which the assignment problem is solved to define the closeness of two customers. The variable neighborhood search (VNS) was addressed by Parragh et al [38], who designed several novel neighborhood structures.…”

“…For any route, the number of assistants onboard remains the same throughout the entire trip, which is reflected by Constraint (23), where o max refers to the maximum number of assistants required by clients. Constraint (24) guarantees that the end time of a route is not earlier than its start time. This constraint is needed in case some routes are empty.…”

“…Thus, to solve the ride time constraint, we adapt the eight-step evaluation scheme proposed by Cordeau and Laporte [13], which uses the forward time slack introduced by Savelsbergh [49]. The forward time slack defines the maximum amount of time by which the start time can be delayed at one node without causing the other nodes to violate the time windows and ride time constraints [24]. For node n i in the route ðn 0 ; n 1 ; …; n q Þ, where n 0 and n q represent the depot, the calculation is as follows:…”

A branch-and-cut algorithm for a realistic dial-a-ride problem

“…They can provide an initial solution (Toth and Vigo, 1997;Aldaihani and Dessouky, 2003) for the improvement heuristics, or applied in the instances when hundreds of requests are involved and a solution is needed in seconds (Jaw et al, 1986;Diana and Dessouky, 2004;Luo and Schonfeld, 2007). Improvement heuristics, on the other hand, usually attempt to improve the quality of a solution by a local search procedure involving relocation or exchange of vertices or clients (Toth and Vigo, 1997;Cordeau and Laporte, 2003b;Xiang et al, 2006;Kirchler and Wolfler Calvo, 2013;Paquette et al, 2013). To date, the deterministic annealing algorithm proposed by Braekers et al (2014) has been the best heuristic for the homogeneous and heterogeneous DARP, both in terms of solution quality and computation time.…”