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<p>Freight transportation in hilly areas is one of the major concerns for the decision-makers in any mountainous country. This study presents a cost-minimizing transportation problem considering road gradients, curvatures, and conditions. The concept of implementing penalty costs due to road gradients and curvatures is discussed and forecasted with the help of an artificial neural network (ANN) using the Levenberg-Marquardt feed-forward back-propagation (trainlm) learning algorithm by obtaining a (5-4-1) topology with logsig activation function using a single hidden layer. Then, a mathematical model for the solid transportation problem of hilly areas to minimize the total transportation cost is developed. The classification for road gradients and curvatures is considered as (0–15, 15–30, &gt;30) degrees of their elevation and (&lt;90, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ge \)</EquationSource> </InlineEquation>90) degrees of their turning angle, respectively. Earthen, Gravel, and Asphalt are three categories of road surface conditions that are considered. Considering all these aspects, decision-makers have to impose penalty costs for transportation. Finally, the model was suitably explained with an example. The problem has been solved with the help of the genetic algorithm and LINGO 13.0 optimizer solver.</p>

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An artificial neural network-based transportation problem in hilly areas considering geographical obstacles

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Akash Singh,
  • Amrit Das,
  • Saptadeep Biswas,
  • Tapan Senapati,
  • Uttam Kumar Bera

摘要

Freight transportation in hilly areas is one of the major concerns for the decision-makers in any mountainous country. This study presents a cost-minimizing transportation problem considering road gradients, curvatures, and conditions. The concept of implementing penalty costs due to road gradients and curvatures is discussed and forecasted with the help of an artificial neural network (ANN) using the Levenberg-Marquardt feed-forward back-propagation (trainlm) learning algorithm by obtaining a (5-4-1) topology with logsig activation function using a single hidden layer. Then, a mathematical model for the solid transportation problem of hilly areas to minimize the total transportation cost is developed. The classification for road gradients and curvatures is considered as (0–15, 15–30, >30) degrees of their elevation and (<90, \(\ge \) 90) degrees of their turning angle, respectively. Earthen, Gravel, and Asphalt are three categories of road surface conditions that are considered. Considering all these aspects, decision-makers have to impose penalty costs for transportation. Finally, the model was suitably explained with an example. The problem has been solved with the help of the genetic algorithm and LINGO 13.0 optimizer solver.