Advances in Industrial Engineering

Advances in Industrial Engineering

A learning-based co-evolutionary approach with semi-bandit feedback for the vehicle routing problem

Authors
1 Industrial Engineering Group, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan, 87717-67498, Iran.
2 Department of Industrial Engineering, Faculty of Engineering, College of Farabi, University of Tehran, Qom, Iran.
Abstract
he Network-Interdicted Vehicle Routing Problem (NIVRP) extends classical VRP settings by incorporating network interdiction, where selected arcs or nodes may be disrupted or rendered inaccessible. Consequently, routing decisions must account for potential interdictions. This setting induces a strategic conflict between Logistics Service Providers (LSPs) and an adversarial interdictor seeking to disrupt routes by targeting specific arcs. Typically, the interdictor lacks complete prior information regarding depot locations and customer demands, and acquiring such information is costly. Through repeated interactions, however, the interdictor can observe selected routes and seized cargo on interdicted arcs, gradually refining demand estimates and reducing uncertainty. Over time, this process enables increasingly accurate predictions of illicit cargo flows. The interaction is modeled as a repeated game, in which the interdictor engages in an online learning process to adapt to dynamically changing checkpoint configurations. This study analyzes this conflict within a repeated game framework using an online learning approach. A bi-level metaheuristic algorithm, leveraging semi-bandit feedback, is proposed. Computational experiments on randomly generated instances demonstrate that the proposed learning-based method significantly outperforms benchmark approaches and exhibits satisfactory convergence behavior.
Keywords
Subjects


Articles in Press, Accepted Manuscript
Available Online from 08 July 2026