APPROXIMATION ALGORITHMS AND HEURISTICS FOR A 2-DEPOT, HETEROGENOUS HAMILTONIAN PATH PROBLEM A Thesis by RIDDHI

Approximation Algorithms and Heuristics for a 2-Depot, Heterogenous Hamiltonian Path Problem. (August 2010) Riddhi Rajeev Doshi, B.E., North Gujarat University, Patan, India Chair of Advisory Committee: Dr. Sivakumar Rathinam Various civil and military applications of UAVs, or ground robots, require a set of vehicles to monitor a group of targets. Routing problems naturally arise in this setting where the operators of the vehicles have to plan the paths suitably in order to optimize the use of resources available such as sensors, fuel etc. These vehicles may differ either in their structural (design and dynamics) or functional (sensing) capabilities. This thesis addresses an important routing problem involving two heterogeneous vehicles. As the addressed routing problem is NP-Hard, we develop an approximation algorithm and heuristics to solve the problem. Our approach involves dividing the routing problem into two sub-problems: Partitioning and Sequencing. Partitioning the targets involves finding two distinct sets of targets, each corresponding to one of the vehicles. We then find a sequence in which these targets need to be visited in order to optimize the use of resources to the maximum possible extent. The sequencing problem can be solved either by Christofides algorithm or the Lin-Kernighan Heuristic (LKH). The problem of partitioning is tackled by solving a Linear Program (LP) obtained by relaxing some of the constraints of an Integer Programming (IP) model for the problem. We observe the performance of two LP models for the partitioning. The first LP model is obtained by relaxing only the integrality constraints whereas in the second model relaxes both integrality and degree constraints. The algorithms were implemented in a C++ environment with the help of Con-