This dissertation introduces a new class of selective traveling salesman problem (TSP) and vehicle routing problem (VRP) in which the goal is to maximize the served demand. Using solution frameworks developed for these selective TSPs and VRPs, the decision-maker has the opportunity to implement efficient planning tools to schedule vehicle tours with respect to the budget and time constraints. In this dissertation, mixed-integer linear mathematical models are developed and solved for each problem, where the goal is maximization of served demand. The problems considered in this dissertation are the following: traveling salesman problem with partial coverage (TSPWPC), capacitated vehicle routing problem with partial coverage (CVRPWPC), multiple traveling salesman problem with partial coverage (MTSPWPC), and multiple depot capacitated vehicle routing problem with partial coverage (MDCVRPWPC). The proposed models were solved using exact solution methods and metaheuristic methods such as hybrid genetic algorithms. The proposed hybrid genetic algorithms (HGAs) consider the polar angle of the nodes and incorporate clustering algorithms to determine and improve the solutions, which can be obtained by regular genetic algorithms (GAs). In the proposed selective multiple vehicle mathematical models, we also utilize sweep and assignment methods to generate structured solutions. This dissertation also presents detailed numerical experimentation, as well as computational results to assess the performance of the proposed algorithms.