Multi-criteria decision-making optimization model for permeable breakwaters characterization

Mostafa Gandomi, Moharram Dolatshahi Pirooz, Banafsheh Nematollahi, Mohammad Reza Nikoo*, Iman Varjavand, Talal Etri, Amir H. Gandomi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Permeable breakwaters have always been of interest due to their advantages over the traditional types. This study proposed a stochastic multi-criteria decision-making model to optimize the geometry of permeable breakwaters. A multi-objective optimization algorithm was conducted using the non-dominated sorting genetic algorithm-II (NSGA-II) coupling with the estimations made by a well-known machine learning (ML) model, the multi-layer perceptron neural network (MLP-NN) to achieve the objective. Considering the inherent uncertainties in the wave characteristics using the conditional value-at-risk (CVaR) method, the presented risk-based model could determine optimal tradeoffs between wave transmission, wave reflection, and rockfill materials volume. This CVaR-based multi-objective optimization model was experimentally applied to a permeable breakwater with maximum significant wave heights of 1–3.5 m at confidence levels of 50%, 75%, 90%, and 99% for risk analysis. To rank several alternatives between the Pareto-optimal solutions, a decisive so-called multi-criterion decision-making (MCDM) approach was employed, which coupled the fuzzy decision-making trial and evaluation laboratory (DEMATEL) method and analytical network process (ANP) procedure. Results indicated that the heavier permeable breakwater was the most appropriate for greater wave heights. To this extent, the relative rockfill materials height and width increased to 1.1 from 0.77 and 1.1 from 0.41, respectively, by increasing the specific wave height from 2 to 3.5 m.

Original languageEnglish
Article number114447
JournalOcean Engineering
Publication statusPublished - Jul 15 2023


  • Analytical network process (ANP)
  • Conditional value-at-risk (CVaR)
  • Fuzzy decision-making trial and evaluation laboratory (DEMATEL)
  • Non-dominated sorting genetic algorithm-II (NSGA-II)
  • Permeable breakwater
  • Reflection and transmission coefficients

ASJC Scopus subject areas

  • Environmental Engineering
  • Ocean Engineering

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