Minimum cost path problem for Plug-in Hybrid Electric Vehicles

We introduce a practically important and theoretically challenging problem: finding the minimum cost path for PHEVs in a road network with refueling and charging stations. We show that this problem is NP-complete and present a mixed integer quadratically constrained formulation, a discrete approximation dynamic programming heuristic, and a shortest path heuristic as solution methodologies. Practical applications of the problem in transportation and logistics, considering specifically the long-distance trips, are discussed in detail. Through extensive computational experiments, significant insights are provided. In addition to the charging infrastructure availability, a driver's stopping tolerance arises as another critical factor affecting the transportation costs. © 2015 Elsevier Ltd

Solving shortest path problems with a weight constraint and replenishment arcs

This paper tackles a generalization of the weight constrained shortest path problem (WCSPP) in a directed network with replenishment arcs that reset the accumulated weight along the path to zero. Such situations arise, for example, in airline crew pairing applications, where the weight represents duty hours, and replenishment arcs represent crew overnight rests; and also in aircraft routing, where the weight represents time elapsed, or flight time, and replenishment arcs represent maintenance events. In this paper, we review the weight constrained shortest path problem with replenishment (WCSPP-R), develop preprocessing methods, extend existing WCSPP algorithms, and present new algorithms that exploit the inter-replenishment path structure. We present the results of computational experiments investigating the benefits of preprocessing and comparing several variants of each algorithm, on both randomly generated data, and data derived from airline crew scheduling applications

Long-term Informative Path Planning with Autonomous Soaring

The ability of UAVs to cover large areas efficiently is valuable for information gathering missions. For long-term information gathering, a UAV may extend its endurance by accessing energy sources present in the atmosphere. Thermals are a favourable source of wind energy and thermal soaring is adopted in this thesis to enable long-term information gathering. This thesis proposes energy-constrained path planning algorithms for a gliding UAV to maximise information gain given a mission time that greatly exceeds the UAV's endurance. This thesis is motivated by the problem of probabilistic target-search performed by an energy-constrained UAV, which is tasked to simultaneously search for a lost ground target and explore for thermals to regain energy. This problem is termed informative soaring (IFS) and combines informative path planning (IPP) with energy constraints. IFS is shown to be NP-hard by showing that it has a similar problem structure to the weight-constrained shortest path problem with replenishments. While an optimal solution may not exist in polynomial time, this thesis proposes path planning algorithms based on informed tree search to find high quality plans with low computational cost. This thesis addresses complex probabilistic belief maps and three primary contributions are presented: • First, IFS is formulated as a graph search problem by observing that any feasible long-term plan must alternate between 1) information gathering between thermals and 2) replenishing energy within thermals. This is a first step to reducing the large search state space. • The second contribution is observing that a complex belief map can be viewed as a collection of information clusters and using a divide and conquer approach, cluster tree search (CTS), to efficiently find high-quality plans in the large search state space. In CTS, near-greedy tree search is used to find locally optimal plans and two global planning versions are proposed to combine local plans into a full plan. Monte Carlo simulation studies show that CTS produces similar plans to variations of exhaustive search, but runs five to 20 times faster. The more computationally efficient version, CTSDP, uses dynamic programming (DP) to optimally combine local plans. CTSDP is executed in real time on board a UAV to demonstrate computational feasibility. • The third contribution is an extension of CTS to unknown drifting thermals. A thermal exploration map is created to detect new thermals that will eventually intercept clusters, and therefore be valuable to the mission. Time windows are computed for known thermals and an optimal cluster visit schedule is formed. A tree search algorithm called CTSDrift combines CTS and thermal exploration. Using 2400 Monte Carlo simulations, CTSDrift is evaluated against a Full Knowledge method that has full knowledge of the thermal field and a Greedy method. On average, CTSDrift outperforms Greedy in one-third of trials, and achieves similar performance to Full Knowledge when environmental conditions are favourable

Scheduling and Routing of Truck Drivers Considering Regulations on Drivers’ Working Hours

In many countries, truck drivers are obliged by law to take a break or a rest regularly. In the European Union, for example, this is governed by Regulation (EC) No. 561/2006. It states that, after 4.5 hours of driving a truck, it is prohibited to continue driving until a 45-minute break is taken. After accumulating a driving time of 9 hours, a rest of 11 hours is mandatory. These are only two rules of a considerably longer list of break rules set out in this regulation, and it is only one of many regulations there are worldwide. Such breaks and rests have to be planned into the work schedules of the drivers. In general, the task of a dispatcher is to find routes and schedules for the truck drivers such that every customer is served in time. With the regulations on drivers’ working hours, both the routing and the scheduling parts of the task become more challenging. In this thesis, we study several optimization problems that arise in the context of drivers’ working hours. One is known as the truck driver scheduling problem. Here, a sequence of customers is given, and the task is to find a schedule for a driver such that every customer is visited within one of the customer’s time windows and the applicable break rules are complied with. Depending on the regarded break rules, we get different variants of the truck driver scheduling problem. Little is known about the complexity of the individual problem variants. One of the two focal points of this thesis is to present polynomial-time algorithms for different variants of the problem, for which polynomial-time algorithms are not yet known. With this, we can falsify the NP-hardness conjecture of Xu et al. (2003) for an important special case of their considered problem variant. But this thesis is not only about scheduling, it is also about routing. This constitutes the second focal point of this thesis. We present an integrated approach for the vehicle routing and truck driver scheduling problem. Here, a route refers to the order in which the customers are visited. However, the meaning of route is twofold. In another studied problem, the truck driver scheduling and routing problem, it means the sequence of road segments that the driver takes to drive from one customer to the other. In this problem, we take into account that, before taking a break, truck drivers need to head for a rest area or at least a spot where their vehicle can be parked. We even consider the time-dependent scenario in which driving times on road segments vary over the day due to rush hours. Both an exact approach and a heuristic for this problem are presented, and both are evaluated on a recent road network instance of Germany. It turns out that the heuristic is at least two orders of magnitude faster but still hardly worse than the exact approach. Our main motivation is the application in practice. It is our aim – and this is especially true for the second focal point – to provide helpful algorithms that may find their way into software products for dispatchers, like the described approach for the vehicle routing and truck driver scheduling problem is already integrated into the vehicle route planning tools of a commercial provider of logistics optimization software