Stochastic optimization model for determining support system parameters of a subway station

Elahe Mohammadi, Mojtaba Jahanandish*, Arsalan Ghahramani, Mohammad Reza Nikoo, Sina Javankhoshdel, Amir H. Gandomi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The process of designing the support system of a subway station using a concrete arch pre-supporting system (CAPS) construction method includes an estimation of design variables based on intuition and experience. However, this process may often lead to controversial and economically unfavorable designs. In this regard, developing an optimization model to determine design variables (support system parameters) is necessary. In this study, a stochastic optimization model is developed to determine the support system parameters of a subway station constructed using CAPS. To estimate the risk of uncertainties of the soil properties, the concept of conditional value at risk (CVaR) is used. A Python script is programmed in cooperation with a 2D Finite Element Method (FEM) software to provide the dataset. Then, the results are applied to prepare multi-layer perceptron (MLP) models, which are subsequently used as meta-models and linked to a reference-point-based non-dominated sorting genetic algorithm III (NSGA-III). It should be noted that the selection of the NSGA-III algorithm was based on comparing its performance with a few other meta-heuristic algorithms such as NSGA-II, MOPSO, and MOMBIII considering metrics such as hypervolume (HV), inverted generational distance (IGD), spread, and pure diversity (PD). Finally, all optimal solutions are ranked using the ELECTRE multi-criteria decision-making method. Various weighting scenarios for the objectives are considered to evaluate the importance of the selected design criteria. The results of the numerical modeling confirm that the proposed algorithm can provide worthwhile information for a logical decision about the support system parameters of a subway station. Thus, the outcome of this study is to achieve an appropriate and economical design by minimizing four following objectives: the risk of instability, risk of the maximum surface settlement, risk of the maximum displacement throughout the station structure, and the concreting volume. The presented algorithm could also alter the prioritization of design goals based on the project's sensitivity and the designer's judgment. On the other hand, by considering the uncertainty in soil parameters, the optimal parameters of the support system are determined more accurately in comparison with an assumption of homogenous soil. Therefore, the main contribution of this article to the design of a subway station constructed by the CAPS method is to increase the accuracy of the design of support system parameters by considering the risk of uncertainties in soil parameters, the importance of the project, and goals of the designer. In this way; the overly conservative designs in practice would be avoided.

Original languageEnglish
Article number117509
Number of pages1
JournalExpert Systems with Applications
Publication statusPublished - Oct 1 2022


  • Artificial neural network
  • Conditional Value at Risk
  • Finite Element Method
  • Subway station design

ASJC Scopus subject areas

  • Engineering(all)
  • Computer Science Applications
  • Artificial Intelligence


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