MODELING RICH AND DYNAMIC VEHICLE ROUTING PROBLEMS IN HEURISTICLAB Stefan Vonolfen(a), Michael Affenzeller(b), Stefan Wagner(c) (a) (b) (c) Upper Austria University of Applied Sciences, Campus Hagenberg School of Informatics, Communication and Media Heuristic and Evolutionary Algorithms Laboratory Softwarepark 11, A-4232 Hagenberg, Austria (a)[email protected], (b)[email protected], (c)[email protected] ABSTRACT to Eksioglu et al. (2009). A survey on recent advances Transport is one of the largest emission driving forces and challenges in the field of vehicle routing is given by and has many economic and social impacts. Thus it is Golden and his colleagues (2008). crucial to model and optimize practical transportation Challenges in contemporary vehicle routing problems. In this paper we present a flexible modeling research are on the one hand rich models that include and optimization framework integrated in the open many practical side constraints (Hartl et al. 2006) and source environment HeuristicLab. We show, how rich on the other hand dynamic and stochastic formulations and dynamic vehicle routing problem variants can be (Zeimpekis et al. 2007, Pillac et al. 2011). integrated in our framework. Using this model, we Thus it is crucial to have a flexible software perform an algorithmic study where we compare several platform that can be applied to various variants of heuristic and metaheuristic algorithms for the dynamic dynamic vehicle routing problems. In this work, we pickup and delivery problem with time windows. present how rich, dynamic vehicle routing problems are modeled in the open-source platform HeuristicLab Keywords: dynamic vehicle routing problem, (Wagner, 2009). simulation, optimization 2. METHODOLOGY 1. INTRODUCTION To model dynamic VRPs, a simulation component is According to a recent report by the European required that replaces the real practical environment. It Commission and Eurostat (2011), transport caused can be used both for algorithm development and 19.5% of all greenhouse gas emissions in 2008. The scenario evaluation. Thus, the combination of emissions generated by transport grew by 5% between simulation and optimization is a powerful technique in 1999 and 2008 and thus transport is one of the largest that context. emission driving forces. This is explained by increasing The overall model is illustrated in Figure 1. The transport volumes and a lack of cleaner fuels and simulation component contains a problem environment modes. As a result, an energy-efficient transport is an that specifies the constraints such as number of important contribution to a sustainable development. vehicles, capacities or the underlying transport network. The vehicle routing problem (VRP) is an important The simulation model is based on Vonolfen et al. problem class in operations research (OR) since it can (2010) and has been adapted to dynamic problems. be used to model many different types of transportation The problem environment generates orders problems. Since its original formulation by Dantzig and dynamically which are transportation requests that have Ramser (1959), many variants have emerged and have to be served by a fleet of vehicles. The vehicles act been successfully applied in practice. For a taxonomic inside the problem environment and deliver the orders overview of different VRP variants the reader is referred given the constraints. Proceedings of the International Conference on Harbor Maritime and Multimodal Logistics M&S, 2012 ISBN 978-88-97999-11-9; Bruzzone, Gronalt, Merkuryev,Figure Piera,1: Simulation Talley Eds. and Optimization 96 Figure 2: Problem and Algorithm Model Whenever a dynamic event happens in the problem period (i.e. a day of operation). Each request is environment (e.g. an order is delivered, a new order characterized by a pickup and a delivery location and appears or a vehicle breaks down), a change event is the size of the load to be transported. For each location, triggered and the optimization component is notified. a time window is given in which the service has to The optimization component reacts to changes and occur. A request has to be fulfilled by exactly one triggers actions that are performed by the vehicles. service of a single vehicle; this means that split Different routing algorithms implemented in deliveries are not allowed. In the dynamic formulation, HeuristicLab are integrated by the optimization not all requests are known in advance but are revealed interface. The optimization interface transforms the during the planning period. current situation (including the recent changes) to a Dynamic vehicle routing problems are problem model and calls the underlying algorithm. The characterized by changing information and the routes algorithm returns a route plan which is mapped to evolve regarding to those inputs in real-time (Psaraftis actions that are performed by the vehicles. 1988). The focus will be on the arrival of new requests The grey components in the picture (problem and during the planning process. At a certain time instant t algorithm) have to be adapted to the problem the route plan is divided into three parts (Ichoua et al. environment and are highly dependent on the side 2007): the completed movements, the current constraints. Thus, a flexible problem and algorithm movement and the planned movements. model is required in HeuristicLab to be able to model Early research on dynamic PDP includes Shen et al. diverse rich variants of practical VRPs. (1995) and Potvin et al. (1995) where they apply neural The model is illustrated in Figure 2. Each problem networks with learning capabilities. model requires certain side constraints that have to be In terms of neighborhood based metaheuristics, a considered by the algorithm solving it. For instance, tabu search algorithm with a neighborhood elimination practical problems may consist of multiple depots, a matrix was applied by Malca and Semet (2004). heterogeneous fleet or incorporate pickup and delivery Gendreau and Potvin (1998) apply a tabu-search operations. heuristic based on a neighborhood of ejection chains. A The algorithm is composed of building blocks two-phase solution approach where a tabu search is called operators. The operators offer certain features combined with different waiting strategies is examined that can be considered. The algorithm can be modeled by Mitrovic-Minic and Laporte (2004). in a flexible way. For a certain problem environment, But also population-based metaheuristcs have been suitable operators can be chosen that can consider the applied successfully. A grouping-based genetic required side constraints. Operators developed for other algorithm is applied to a set of benchmark instances by rich practical VRP variants can be reused in other Pankratz (2005). A genetic algorithm hybridized with problem environments. fuzzy clustering for predictive control is presented by Saez et al. (2009). 3. PROBLEM FORMULATION To illustrate our model, we implemented an example 4. ALGORITHMS practical VRP variant and tested different algorithms for In this work, two different strategies for optimizing that problem environment. dynamic pickup and delivery problems are examined, In particular, we consider the dynamic pickup and namely updating of the current plan and complete delivery problem with time windows (PDPTW) which reoptimization. The first approach corresponds to can be considered as a rich transportation problem. integrating the new requests in the planned movement Practical applications of the dynamic PDPTW are while the second approach relies on a complete manifold and include full-truckload problems, less-than- reoptimization whenever new information is revealed. truckload problems and passenger transportation. Both commonly used heuristics as well as Its formulation is based on the static PDPTW metaheuristics are analyzed. The algorithms are detailed model (Savelsbergh 1995). A fleet of vehicles has to in the following. serve a set transportation requests during a planning Proceedings of the International Conference on Harbor Maritime and Multimodal Logistics M&S, 2012 ISBN 978-88-97999-11-9; Bruzzone, Gronalt, Merkuryev, Piera, Talley Eds. 97 4.1. Heuristics for improving moves. The soft aspiration criterion A straightforward approach of updating the current accepts both new best solutions and moves that are route plan according to newly arriving requests is to better than the individual where the move has been set insert them at the best possible position of the planned tabu. A fixed tabu tenure has been used because all routes. This is often referred to as the best insertion tested instances consist of the same number of heuristic. A major drawback is that decisions made in customers. At the arrival of a new request, 100 the past that correspond to planned movements cannot iterations are performed. be changed at a later time during the planning process. Whenever a new request arrives, there are two This issue can be overcome by a complete approaches in integrating it in the current route plan reoptimization of the planned routes at each time step t (Ichoua et al. 2007). The first approach is a complete given the current situation. This can be done for reoptimization, the second approach is a local update instance by means of a construction heuristics. A push whenever new information is revealed. In the local forward insertion heuristic is examined which has been update approach, the route plan is not computed from originally proposed by Solomon (1987) for the vehicle scratch but information about previous time steps is routing problem with time windows (VRPTW). It has used. In the case of the genetic algorithm, whenever a been adapted to the PDPTW by Li and Lim (2001). It new request arrives it is inserted into each individual of basically inserts pairs of locations into routes. A pair of the population using the best insertion heuristic. For the locations consists of a pickup and a delivery location. local update tabu search algorithm, the current solution First a route is initialized with a pair based on the and the tabu list are updated. distance to depot and time windows.