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. INDEX TERMS Uncertainty theory, team orienteering problem with time windows, uncertain programming, iterated local search.

A two-stage approach to the multiple-agent orienteering problem with stochastic weight and capacity constraints

“…They used the convex efficient frontier to handle the two factors. Wang et al (2019) also treated the weight of arcs as an uncertain variable. They proposed the uncertain team OP with time windows and used uncertainty theory to solve it.…”

MOFA/D-URAM for Solving the Air and Missile Defense Problem Based on Uncertainty Theory

“…The prove of Theorem 4.1 is in reference [18] requires that the optimal value j f  of each objective function exists; Additionally, the distance formula with ideal point in (14) can also be replaced by following and theorem 4.1 still holds.…”

“…If a multi-objective optimization problem in ( 13) is decomposed into multiple single-objective models in (14) with different weight vectors, the optimization algorithm can guide each individual to approach different pareto-optimal solution. Generally, the optimal solutions of subproblems with similar weight vectors are small apart in the solution space.…”

“…Liu point out that Uncertainty Theory is a mathematical system that parallel to probability theory, but the results of some problems derived from Uncertainty Theory is superior to that derived from probability theory, especially the problem involving subjective experience [13] . At present, this theory has been widely used in risk analysis, logistics, UAV path planning and other fields [14][15] [16] .…”