Current Topics


A heuristic algorithm for scheduling driving time and working time breaks in vehicle tours

Based on an ongoing industry project in collaboration with Deutsche Post DHL, your task is to develop and implement a heuristic algorithm for scheduling driving time and working time breaks (which are prescribed by law) in existing vehicle tours. We define a vehicle tour as a sequence of single trips. Each of these trips is characterized by (i) a vehicle type, (ii) a facility where the trip starts, (iii) a facility where the trip ends, and (iv) the starting time at which the vehicle departs for the trip. Required driving time and working time breaks can be scheduled before departing a facility, after arriving at a facility, or during a trip.

In this thesis, a heuristic algorithm to schedule driving time and working time breaks
in vehicle tours will be developed and implemented. The implemented heuristic algorithm is evaluated on test instances that are inspired by the application context of Deutsche Post DHL.
Algorithms from literature on similar optimization problems that consider driving time and working time breaks will be described and categorized.

If you are interested, please send an e-mail including your CV and transcript of records to .


Reinforcement Learning a Stochastic Dynamic Vehicle Routing Problem with Incomplete Information

Vehicle Routing Problems (VRPs) concern the decision of determining a set of routes for a fleet of vehicles that travel from (possibly more than) one central depot to provide service to (or collect items from) a set of customers, often in an urban environment. VRPs have a colorful range of applications in logistics and mobility services, such as transporting goods or passengers, or conducting services at customer homes. In many cases of VRPs, the decision maker (DM) is uncertain about the problem data. In such situations, the DM learns about such information sequentially, over multiple periods, in a dynamic manner. For example, additional customer requests might arrive during the routing mission, the travel time might increase due to road congestions, and the size of the available fleet might change due to accidents and malfunction of vehicles. In such situations, the dynamic nature of how the stochastic information unfolds gives rise to a class of VRPs known as Stochastic Dynamic Vehicle Routing Problem (SDVRP).

The goal of this thesis is to study an SDVRP in which a single vehicle is available to serve customer requests in a given time horizon defined by the vehicle driver’s shift. In this problem, some customer requests are known in advance, but others are received during the day. When a new request occurs, the DM needs to decide whether the new request is accepted or rejected. If the new request is accepted, the DM has to decide on how to update the route to include the location of the newly accepted request. Otherwise, the rejected requests are lost forever. The goal of the DM is to maximize the number of fulfilled requests.

A common approach to proceed with solving an SDVRP is to (1) assume that the underlying stochastic process can be analyzed and transferred into a predictive model (e.g., nominal probability distribution), (2) use the predictive model to anticipate future scenarios (e.g., the likelihood of a customer request occurring at a given location), and (3) incorporate the predicted scenarios into the framework of optimizing the routing decision. Nevertheless, constructing the predictive model requires sufficient past observations (e.g., previous customer requests), which might not always be available. This can be circumvented by leveraging a reinforcement learning framework that allows the DM to use an adaptive prediction model. In this case, initially, the DM is unsure how the predictive model should reflect the uncertainty. However, as time progresses, the DM observes new realizations of the stochastic process (e.g., new demand requests) and updates their belief about how the predictive model should anticipate the uncertainty. For instance, this could be a situation in which the DM does not know in advance the demand distribution at different locations. However, as more demand requests arrive, the DM revises the predictive model to reflect the different levels of demand requests at different locations.

If you are interested, please feel free to write an email with your CV and your transcript of records to .


A framework for the vehicle routing problem with dynamically inserted intermediate stops and its application to the skip loader problem

The thesis will be supervised by an employee of PTV AG in Karlsruhe. The thesis will ideally be worked on directly in Karlsruhe. There, the work can be based on an existing code base can be used.

In the context of this thesis, a theoretical framework for VRP variants shall be developed which have the following in common: along a tour, in addition to order stops (e.g., pickup or delivery stops) have to be scheduled in order for the tour to be valid. In rare cases, more than one intermediate stop is made.

A problem with this feature is the skip loader problem. The skip loader is used to transport empty skips to customers. As a rule, full skips are taken away and immediately driven to a disposal site. The empty skip can then be dropped off at the next customer. The problem becomes more difficult due to the fact that there are skips in two sizes (different DIN), whereby each vehicle can transport both types of skips (homogeneous fleet). It is possible that an empty skip is first driven to a loading point, where another skip has to be loaded, in case the next customer requires a different type of skip. In this simple case, there is only one loading point (here, called a depot) and the vehicle has to drive there if the next customer requires a different type of skip than the one that is loaded.

In this thesis, a theoretical framework will be developed to solve such problems. After implementing a solution procedure for the skip loader problem, the effectiveness will be investigated by means of generated test instances. Different problems with the above property should be solvable with the framework and discussed in the thesis (i.e., a simple variant of the EVRP and a simple variant of the truck-and-trailer problem).

If you are interested, please send an e-mail including your CV and transcript of records to .


The Lin-Kernighan Neighborhood operator for the Vehicle Routing Problem with Time Windows

The Capacitated Vehicle Routing Problem (CVRP) deals with the task of meeting the demands of a set of customers with a fleet of vehicles at minimum cost. Each customer must be visited exactly once, vehicle routes start and end at the depot, and vehicle capacities must be respected. The VRP with Time Windows (VRPTW) is an extension of the CVRP which additionally requires that service at the customers is started within given time windows. Heuristic solution methods for the VRPTW are often based on local search: a starting solution generated by a construction heuristic is iteratively improved by the use of so-called neighborhood operators. The Lin-Kernighan neighborhood operator deletes and creates edges in a stepwise fashion such that the sum of the partial improvements remains positive.

In this master thesis, the Lin-Kernighan operator shall be integrated into a local search for the VRPTW. A generalized objective function is used, which allows constraint violations and handles them by means of penalty costs, thus enabling the search to consider infeasible solutions. The search with the LK operator is strongly accelerated by evaluating only those partial moves that have a positive effect on the cost function. The central question of the work is how potentially infeasible partial moves can be evaluated in the course of the search. Programming skills are beneficial for working on this topic.

If you are interested, please feel free to write an email to .


Learning good starting solutions for local search algorithms

Local-search-based algorithms are widely used to solve vehicle routing problems (VRPs). Starting with an initial solution, the iterative application of so-called neighborhood operators modifies the solution until a local optimum is reached. To escape from these, metaheuristics that rely on local search often use some sort of diversification mechanism. Over the last decades, many different diversification methods have been developed, which, e.g., rely on randomized multi-starts or perturbation steps. Boyan and Moore (2000) introduced the idea of trying to learn good starting solutions by generating an evaluation function that predicts the outcome of a local search given a specific starting solution. They developed the so-called STAGE algorithm that alternates local search and learning steps. Features are thereby used to represent solutions in a compact fashion and serve as input to the evaluation function. Even though the STAGE algorithm has already been successfully applied to combinatorial optimization problems like the bin-packing problem, there is no application to VRPs yet.

The goal of this master thesis is to continue on previous work at the chair and to improve the performance of our version of the STAGE algorithm to solve multi-depot VRPs. Precisely, the following questions shall be addressed:

  • Are there additional features beyond those we have investigated to characterize VRP solutions and how do they perform?
  • Which neighborhood operators should be used to perform the local search? Which should be used to obtain good neighboring solutions according to the evaluation function?
  • Which machine learning model should be used to realize the evaluation function (linear, polynomial regression, …)?

Programming skills are beneficial for working on this topic. If you are interested, please feel free to write an email to