Uncertain Team Orienteering Problem with Time Windows Based on Uncertainty Theory

Abstract

Uncertainty theory is a branch of mathematics for modeling indeterminacy, especially belief degrees. This paper considers an application of uncertainty theory in team orienteering problem with time windows. In the problem, travel time is uncertain with known uncertainty distribution, and the impact of uncertainties on visit time and total profit cannot be ignored. Based on the uncertainty theory, a model of uncertain team orienteering problem with time windows (UTOPTW) is established. Since the UTOPTW cannot be solved to optimality within polynomial time, an improved iterated search algorithm is designed considering uncertainties in the insertion step. Finally, several numerical instances are used to verify the effectiveness of the proposed model and algorithm.