Pyramidal tours and multiple objectives

Abstract

In this study, we work on the traveling salesperson problems and bottleneck traveling salesperson problems that have special matrix structures and lead to polynomially solvable cases. We extend the problems to multiple objectives and investigate the properties of the nondominated points. We develop a pseudo-polynomial time algorithm to find a nondominated point for any number of objectives. Finally, we propose an approach to generate all nondominated points for the biobjective case.