Hybrid Meta-heuristic Adaptive Fuzzy Inference Systems in Rockfill Dam Multi-objective Shape Optimization

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.