New mathematical formulations for the generalized selective travelling salesman problems

The Orienteering Problem (OP), in other words the Selective Traveling Salesman Problem (STSP) is an optimization problem which salesman starts from a starting node (center, warehouse) under the cost (time or distance) constraint and aims to find a tour by visiting the nodes (customers) that supply the maksimum profit. The STSP is a type of Traveling Salesman Problem (TSP) which aims to maximize the profit from the visited customers rather than minimizing the cost. There is no obligation to visit all customers as in TSP. Customers can be single, or they can be groups (clusters) that containing many customers. It is called clusters formed by more than one customer. The problems that the salesman visits to customers who are divided into clusters are the generalized aspects of the STSP.This thesis deals with two different generalized extensions of STSP that have not been studied previously. The problem that the salesman visits only one of the customers in the cluster is the Selective Generalized Traveling Salesman Problem (SGTSP), another type of problem in which all customers in the cluster are being visited is called the Selective Clustered Travelling Salesman Problem (SCTSP). Two node-based and two edge-based mathematical models are proposed for two new problems described in the scope of this thesis. The performances of the proposed mathematical models on test problems are analyzed. As a result of the numerical analyzes, the superiority of the edge-based mathematical model for both problems is seen.