Path-Based Approaches to Robust Network Design Problems Considering Boundedly Rational Network Users

Network users may choose non-shortest paths, when (1) they satisfice with sub-optimal routes, or (2) they have perception errors of the decision environment. The notion of generalized bounded rationality has been recently proposed to create a unified framework for these two sources of behavioral uncertainty in route choices. When the notion of generalized bounded rationality is used in robust network design problems, we obtain a bi-level optimization problem with the min–max objective function at the upper level, with three layers of optimization in total. In this paper, we derive equivalent single-level path-based formulations that are readily solvable by available optimization libraries. We show how to incorporate them into robust multi-commodity network design problems in hazardous materials transportation.