Abstract
This study aims to approach the optimal design of the Sardasht rockfill dam, while two classic and three hybrid meta-heuristic adaptive nero-fuzzy inference systems (ANFIS) are utilized to estimate the seepage and factor of safety (FOS) according to the simulated values within SEEP/W and SLOP/W. The ANFIS is trained with classic gradient distance (CGD), hybrid back propagation and least square algorithm (BP&LS), particle swarm optimization (PSO), genetic algorithm (GA), and firefly optimization algorithm (FA). The non-dominated sorting genetic algorithm-III (NSGA-III) is employed to handle the multi-objective problem when the dam’s construction cost, seepage, and FOS are considered as objective functions. Thus, besides an extensive comparison among classic and hybrid meta-heuristic ANFISs, their influences on optimization results are investigated. Comparing the outcomes of ANFISs based on several statistical criteria and the Mann-Whitney test reveals that all ANFISs can estimate the seepage and FOS, and there is no significant difference between estimated and simulated values at 99% confidence level for all ANFISs. Nonetheless, hybrid meta-heuristic ANFISs report higher confidence than ANFIS-CGD and ANFIS-BP&LS, while the PSO improved the confidence of ANFIS more than other algorithms. The NSGA-III is executed 100 times, and optimization results are investigated in terms of the Hypervolume metric. It is found that utilizing meta-heuristic ANFISs, increases the convergence corresponding to the optimal Pareto front by 22.5%. Eventually, the NSGA-III provides two hundred optimal designs, all of which dominate the original design of the Sardasht dam.
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Acknowledgments
This work was supported by National Natural Science Foundation of China (No. 52079101) and Open Fund of Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station in China Three Gorges University (No. 2019KJX02).
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Mahmoud, A., Yuan, X. & Yua, Y. Hybrid Meta-heuristic Adaptive Fuzzy Inference Systems in Rockfill Dam Multi-objective Shape Optimization. KSCE J Civ Eng 25, 4913–4930 (2021). https://doi.org/10.1007/s12205-021-1504-9
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DOI: https://doi.org/10.1007/s12205-021-1504-9