In this dissertation, we examine three important routing problems. In the second chapter we investigate the Close-Enough Traveling Salesman Problem (CETSP) in which a salesman must get within a specified radius of each node to visit it. The third chapter studies the multi-vehicle extension of the CETSP, the Close-Enough Vehicle Routing Problem (CEVRP). In the fourth chapter, we develop a post-processor to improve the accuracy of our heuristics for solving the CETSP and CEVRP. In the fifth chapter, we solve the Sequence-Dependent Team Orienteering Problem (SDTOP) in which the profit received for each node visited is dependent on the sequence in which all the nodes are visited. We summarize the dissertation in the final chapter.

The CETSP, CEVRP, and SDTOP have application in aerial reconnaissance route planning. We formulate each problem as a mathematical program and apply heuristic and combinatorial optimization techniques to solve them. We present the results of extensive computational experiments that show that our methods produce high-quality solutions quickly.