A tabu-embedded simulated annealing algorithm for a selective pickup and delivery problem

Several actors are involved in the transport of goods. To model freight transport, the di erent actors who take part in the decision making process have to be represented. In Maes et al. (2012) a conceptual framework is presented to model freight transport. The key actors in this framework are rms, carriers, and forwarders. This allows the model to work on an activity-based level, focusing on the di erent activities of each actor. The decision making process of carriers is one of the key aspects in modelling logistic decisions in a behaviour based transportation model. When modelling at an activity-based level, the behaviour of carriers has to be taken into account. The framework of Maes et al. (2012) formulates decisions of the carrier as a selective pickup and delivery problem (PDSP). This is a novel approach to model logistic decisions in models with the objective to explain and predict freight ows. One of the important decisions a carrier has to make is whether or not to accept a transport request in order to maximize his pro t. The selection of requests in a paired pickup and delivery problem is not often studied in literature. Next to this decision, he also needs to schedule the transport orders that are accepted into the di erent vehicles and construct a routing plan, given time and capacity limitations. The PDSP is NP-hard as it is a generalization of the travelling salesman problem. To be able to generate good results a Tabu-embedded Simulated Annealing (TSA) algorithm is proposed. This algorithm is initiated with a parallel insertion heuristic. Four local search operators are de ned to improve the initial solution. A distinction may be made between classical PDP search operators and search operators speci cally developed for the PDSP. Two new local search operators are de ned to deal with the selection of transport requests consisting of paired pickup and delivery locations. The TSA algorithm starts with the insertion heuristic to create a rst feasible solution. This solution is further improved by use of the improvement heuristic. Instead of repeating the tabu search until the procedure terminates, it is restarted from the current best solution after several iterations without any improvement. At the same time the global annealing temperature is reset. The generation of new best solutions is done using simulated annealing. To avoid cycling, the visited solutions are recorded into a tabu set, which contains the total pro t of a solution. Since the probability of two di erent solutions ha-