Related papers: Aircraft routing: periodicity and complexity
The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on…
We consider a coordinated complexity-aware 4D trajectory planning problem in this paper. A case study of multiple aircraft traversing through a sector that contains a network of airways and waypoints is utilized to illustrate the model and…
Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. UAVs can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in…
We consider a Persistent Intelligence, Surveillance and Reconnaissance (PISR) routing problem, which includes collecting data from a set of specified task locations and delivering that data to a control station. Each task is assigned a…
Evaluating conjunctive queries and solving constraint satisfaction problems are fundamental problems in database theory and artificial intelligence, respectively. These problems are NP-hard, so that several research efforts have been made…
A hybrid network is a static (electronic) network that is augmented with optical switches. The Reconfigurable Routing Problem (RRP) in hybrid networks is the problem of finding settings for the optical switches augmenting a static network…
Due to complex sets of interrelated activities in aircraft heavy maintenance (AHM), many airlines have to deal with substantial aircraft maintenance downtime. The scheduling problem in AHM is regarded as an NP-hard problem. Using exact…
This paper deals with the Pollution-Routing Problem (PRP), a Vehicle Routing Problem (VRP) with environmental considerations, recently introduced in the literature by [Bektas and Laporte (2011), Transport. Res. B-Meth. 45 (8), 1232-1250].…
In train routing, the headway is the minimum distance that must be maintained between successive trains for safety and robustness. We introduce a model for train routing that requires a fixed headway to be maintained between trains, and…
Temporal dependencies between customer visits, such as synchronization constraints, pose a fundamental challenge in vehicle routing. These dependencies, which arise in applications such as home healthcare routing, aircraft scheduling, and…
Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Some human-machine systems are designed so that machines (robots) gather and deliver data to remotely located operators (humans) through an interface in order to aid them in classification. The performance of a human as a (binary)…
We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the…
We study the practical setting in which regular- and reserve-crew schedules are dynamically maintained up to the day of executing the schedule. At each day preceding the execution of the schedule, disruptions occur due to sudden…
This paper studies the problem of scheduling urban air mobility trips when travel times are uncertain and capacity at destinations is limited. Urban air mobility, in which air transportation is used for relatively short trips within a city…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of…