REA Press Null REA Press3042-22643042-2264 REA Press https://doi.org/10.22105/raise.v2i1.37 Research Article Hub location problem, Lagrangian relaxation, Artificial neural networks, Reliability, Hierarchical. Estimation of Route Reliability in Multimodal Hierarchical Hub Location Problem Using Lagrangian Relaxation and Artificial Neural Networks (ANN)Estimation of Route Reliability in Multimodal Hierarchical Hub Location Problem Using Lagrangian Relaxation and Artificial Neural Networks (ANN) Korani Ehsan Department of Industrial Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. 01 2025 24 01 2025 2 1 © 2025 REA Press 2025

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 Estimation of Route Reliability in Multimodal Hierarchical Hub Location Problem Using Lagrangian Relaxation and Artificial Neural Networks (ANN)

The present study has developed an Artificial Neural Networks (ANN) model to predict the route reliability in various structures of the Multimodal Hierarchical Hub Location Problem (MHHLP) utilizing Lagrangian relaxation; so that, initially, a mixed integer programming model was proposed for MHHLP and the, an efficient Lagrangian relaxation method was developed to solve the problem in different structures. The results obtained from problem solving were used as input and output data to create an ANN model using Multilayer Perceptron (MLP) neural network. As a result, an ANN model was designed by which, the reliability of the MHHLP route was predicted in large dimensions at different values ​​of the parameters. Computational analysis, ANN model validation and prediction process were conducted using CAB and IAD data.

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