Path Planning Algorithms for Multiple Heterogeneous Vehicles

Unmanned aerial vehicles (UAVs) are becoming increasingly popular for surveillance in civil and military applications. Vehicles built for this purpose vary in their sensing capabilities, speed and maneuverability. It is therefore natural to assume that a team of UAVs given the mission of visiting a set of targets would include vehicles with differing capabilities. This paper addresses the problem of assigning each vehicle a sequence of targets to visit such that the mission is completed with the least "cost" possible given that the team of vehicles is heterogeneous. In order to simplify the problem the capabilities of each vehicle are modeled as cost to travel from one target to another. In other words, if a vehicle is particularly suited to visit a certain target, the cost for that vehicle to visit that target is low compared to the other vehicles in the team. After applying this simplification, the problem can be posed as an instance of the combinatorial problem called the Heterogeneous Travelling Salesman Problem (HTSP). This paper presents a transformation of a Heterogenous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast. Additional complications to the sequencing problem come in the form of precedence constraints which prescribe a partial order in which nodes must be visited. In this context the sequencing problem was studied seperately using the Linear Program (LP) relaxation of a Mixed Integer Linear Program (MILP) formulation of the combinatorial problem known as the "Precedence Constrained Asymmetric Travelling Salesman Problem" (PCATSP)

Service scheduling in garden maintenance

Neoturf is a Portuguese company working in the area of project, building and garden’s maintenance. Neoturf would like to have a procedure for scheduling and routing efficiently the clients from garden maintenance services. The company has two teams available during the whole year and an additional team during summer to handle all the maintenance jobs. Each team consists of two or three employees with a vehicle fully equipped with the tools that allow to carry out every kind of maintenance service. In the beginning of each year, the number and frequency of maintenance interventions to conduct during the year, on each client, are accorded. Each client is assigned to the same team and, usually, time windows are established so that visits to the client should occur only within these periods. As the Neoturf costumers’ are geographically spread over a wide region, the total distance on visiting clients is a factor that has a heavy weight on the costs of the company. Neoturf is concerned with reducing these costs, while satisfying the agreements with the clients

The generalized minimum spanning tree polytope and related polytopes

The Generalized Minimum Spanning Tree problem denoted by GMST is a variant of the classical Minimum Spanning Tree problem in which nodes are partitioned into clusters and the problem calls for a minimum cost tree spanning at least one node from each cluster. A different version of the problem, called E-GMST arises when exactly one node from each cluster has to be visited. Both GMST problem and E-GMST problem are NP-hard problems. In this paper, we model GMST problem and E-GMST problem as integer linear programs and study the facial structure of the corresponding polytopes