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Route planning is a complex task which has many applications in the civilian and military worlds. This project seeks to develop planning tools to aid in planning search and rescue operations while taking into account uncertain factors such as weather, type of terrain, physical feasibility of search pattern, threat levels, desired coverage, risk and survivability considerations. The team will study the process of selecting a path for a vehicle to follow through friendly or unfriendly terrain based on multiple constraints and criteria.

Reactive Systems are formal systems that cause events in the physical world, in reaction to a set of monitored inputs. Examples include control systems for aircraft, medical devices, industrial processes, and consumer appliances. In many of these examples, safety (and often security) of the system is of paramount importance. To say anything at all about whether such a system is safe or secure, one has to be able to predict its behavior under the conditions that the system may encounter in use.

To create a flight plan is to determine the path, altitude, and speed an airplane will use during its flight. This plan must be submitted to regulatory authorities before takeoff and updated throughout the flight. Increasing fuel costs give an added importance to these decisions. New policies offering an increased flexibility in choosing paths and new information systems giving access to more complete and up-to-date weather information pave the way for productivity gains for air carriers.

Efficiency in modern industrial operations requires that available resources are deployed in an optimal manner. The study of facility location is concerned with the placement of one of more facilities in a way that meets a particular objective, such as minimizing transportation costs, providing a high level of service to customer or capturing market share. This project, by exploiting the mathematics of computational geometry and algorithmic graph theory, develops new tools to aid in the location of facilities to optimally serve the demands of customers.