One of the most famous and most studied problems of operations research is the traveling salesman problem. Despite its simple formulation, it has found application in many different fields and to this day is the subject of active research, both related to the development of new methods and approaches to its solution and the creation of generalized problem statements and new mathematical models for their formalization. This paper is devoted to the study of the influence of two types of additional constraints on the speed of the Gurobi and CPLEX programs when solving a special class of routing problems. Formulations of problems of finding the shortest cycle and path that visits a given number of vertices from the graph clusters are presented. Mathematical models of mixed integer linear programming for their solution based on Miller, Tucker and Zemlin constraints and on Gavish and Graves constraints are described. The results of computational experiments are presented, which demonstrate the impact of additional constraints on the speed of solving problems using these models.
Korablov et al. (2025) studied this question.