In this work, the optimal dimensions of a double-layer perforated breakwater were determined by considering the risk of uncertainties in marine conditions, including wave height and wavelength. To do so, the CVaR-NINP technique combines Conditional Value-at-Risk (CVaR) and Nonlinear Interval Number Programming (NINP), which are useful in dealing with discrete interval uncertainties and probabilistic. Based on experimental data, two Extreme Learning Machine (ELM) models were developed to simulate the hydraulic behavior of the breakwater. To increase accuracy and performance, the parameters of these two models were optimized using single and multi-objective optimization algorithms. The obtained results indicate that the non-dominated sorting genetic algorithm (NSGA-II) exhibited better performance in optimizing ELM. Subsequently, optimized ELM, which better modeled the hydraulic performance of perforated breakwater, was selected to link to the NSGA-III algorithm to determine the trade-off between the defined objective functions based on the CVaR-NINP technique, namely, minimize CVaR of (Ct), minimize the radius of the interval number of (Ct), minimize CVaR of (Cr), minimize the radius of the interval number of (Cr). Pareto optimal solutions, obtained from NSGA-III, using the multi-attribute decision-making (MADM) method, also called the R-method, were ranked and applied to select the best solutions.
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