A Hyperheuristic for the Dial-a-Ride Problem with Time Windows

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 707056, 12 pages http://dx.doi.org/10.1155/2015/707056 Research Article A Hyperheuristic for the Dial-a-Ride Problem with Time Windows Enrique Urra,1 Claudio Cubillos,1 and Daniel Cabrera-Paniagua2 1 Escuela de Ingenierı́a Informática, Pontificia Universidad Católica de Valparaı́so, Avenida Brasil 2950, 2340025 Valparaı́so, Chile Escuela de Ingenierı́a Comercial, Universidad de Valparaı́so, Pasaje La Paz 1301, 2531075 Viña del Mar, Chile 2 Correspondence should be addressed to Enrique Urra; Received 25 September 2014; Accepted 15 December 2014 Academic Editor: Haipeng Peng Copyright © 2015 Enrique Urra et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The dial-a-ride problem with time windows (DARPTW) is a combinatorial optimization problem related to transportation, in which a set of customers must be picked up from an origin location and they have to be delivered to a destination location. A transportation schedule must be constructed for a set of available vehicles, and several constraints have to be considered, particularly time windows, which define an upper and lower time bound for each customer request in which a vehicle must arrive to perform the service. Because of the complexity of DARPTW, a number of algorithms have been proposed for solving the problem, mainly based on metaheuristics such as Genetic Algorithms and Simulated Annealing. In this work, a different approach for solving DARPTW is proposed, designed, and evaluated: hyperheuristics, which are alternative heuristic methods that operate at a higher abstraction level than metaheuristics, because rather than searching in the problem space directly, they search in a space of low-level heuristics to find the best strategy through which good solutions can be found. Although the proposed hyperheuristic uses simple and easy-toimplement operators, the experimental results demonstrate efficient and competitive performance on DARPTW when compared to other metaheuristics from the literature. 1. Introduction The dial-a-ride problem with time windows (DARPTW) [1] is known in the literature as a complex combinatorial optimization problem related to transportation, in which a set of customers must be picked up from an origin location and they must be delivered to a destination location. For achieving this, a set of vehicles are available, and a transportation schedule must be constructed for each one, which should be subject to several constraints. In the time-window-free version of the problem (DARP), the vehicles have freedom for defining the time at which customers are picked up/delivered, but under the time-window version (DARPTW, the one considered in this research) a vehicle schedule must assure that the customer is served in a restricted time range: the time windows (TW) itself. That constraint adds an important complexity degree to the problem, which can be proven to be 𝑁𝑃-hard [2]. DARPTW comes from a family of pickup-anddelivery problems that originates from the travel salesman problem (TSP) [3]. While most of them must deal with objects, in DARPTW people must be transported; therefore, the problem evaluation is closely related with quality of service issues; for example, the total time a customer remains onboard a vehicle should not be excessive. The solution space of the DARPTW problem is particularly challenging for any automated solving mechanism, because small changes in the solution structure could lead to completely infeasible solutions. For example, if a client is moved to a different vehicle schedule, a complete restructure of the latter is required, and it is highly probable that previous constraints that were fulfilled are now violated. Because of this and considering the high number of involved variables, common solutions in the literature for the DARPTW are based on heuristic methods. For example, Genetic Algorithms (GA) is a metaheuristic approach used in several works. In [4], a first bit-solution based variant was evaluated, and considering several feasibility problems involved in this implementation, an improved integer-based representation and more specialized operators were tested, which allowed converging towards feasible and better solutions. 2 In [2], a classical cluster-first, route-second approach was implemented, in which clustering is the process of assigning customers to vehicles and routing is the process of defining the order of the pickup and delivery of customers. The GA was used exclusively for the clustering process. In a previous work [5], a GA that uses preprocessing mechanisms for reducing the search space complexity was implemented, allowing executing more efficiently specialized solution-modification operators alongside the genetic operators. Another novel contribution of the latter research was implementing the GA for solving both scheduling components of the solutions: the routing and the clustering. A different metaheuristic used for solving DARPTW is Simulated Annealing (SA); for example, in [6] this technique was mixed with other specialized smaller heuristics, generating an efficient and stable approach that particularly improved quality of service issues. In [7], a multiobjective SA algorithm was implemented and embedded into a multiagent system to solve the dynamic version of the problem. Among heuristic methods, metaheuristics algorithms are the most used techniques through which problems as DARPTW are solved. The prefix “meta” is because they define an abstract framework whose components must be adapted to the solved problem by including extensive problem knowledge within the operations of the algorithm [8]. This adaptation process allows a metaheuristic algorithm to perform efficiently for the target problem, but the main trade-off is a costly implementation process that can be eventually infeasible for real production environments. Under this scenario, a new type of heuristic method named hyperheuristics [9–11] appears in the optimization research field as a more balanced alternative in which, rather than adapting the main search mechanisms, these ones are encapsulated in a high-level layer that can be reused among different problems or families of problems. For achieving this idea at the design level, a hyperheuristic requires several low-level heuristics provided by the problem domain, that is, very simple and specialized operators. A hyperheuristic uses these low-level heuristics for searching an efficient search strategy by leveraging their combined behavior in different manners. Many applications of hyperheuristic solvers were developed during the last decade [12]; however, no implementations for the DARPTW are currently provided to our knowledge. Only the work in [13] addresses (...truncated)