# Using Optimisation Meta-Heuristics for the Roughness Estimation Problem in River Flow Analysis
## 7 Conclusions and Future Work  
Hydraulic computational models are of paramount importance in preventing flood disasters. However, their accuracy heavily depends on the ability to estimate Manning's roughness coefficients at multiple cross-sections of the considered rivers. These coefficients are influenced by the conformation of the channel and other channel's features, thus making their calculation subject to uncertainty. This is why already existing deterministic Manning's coefficients estimation methods show a low accuracy. To avoid this problem, we propose a data-driven approach capable of returning optimal coefficients after minimising a purposely defined objective function that takes as input the coefficient values. These are used to run a flow simulation model to compute the (simulated) river depth at a given cross-section of the channel; finally, it compares the simulated river depth with the observed depth as measured at a gauge station deployed along the river. Therefore, the designed objective function can be used as a fitness function to drive the search of meta-heuristic algorithms. In this work, we considered five well-known algorithms, i.e., the evolutionary strategy (\(1+1\))-ES, DE, CMA-ES, PSO and BO. The proposed methodology was used in two case studies: the river Paglia and the river Aniene, both located in Italy. The experimental results clearly show that our method largely outperforms the standard methodology usually adopted in the hydraulic computation literature, thus allowing us to build much more accurate hydraulic computational models. The results from the comparative analysis among the five selected meta-heuristics have shown that, within the allocated computational budget (measured in fitness functional calls), the trajectory-based (\(1+1\))-ES is the most effective algorithm. In line with the No Free Lunch Theorems for stochastic optimisation [57], this proves the importance of applying multiple and heterogeneous meta-heuristic approaches as a 'universal' solver does not exist and sometimes, as in this case, the simpler method can outperform the more complex and sophisticated ones. Given the satisfactory results achieved in this piece of research, we recommend using this method and envisage further studies to improve upon it. A first improvement would be to validate our approach by considering a second hydraulic computational task, such as the case of a flow rate estimation [58]. This would let us analyse differences while performing this task with the estimated Manning's coefficients, as in our approach, with respect to the traditional strategy. Another interesting future development would be to increase the number of gauge stations or, alternatively, the number of target values of water elevations deployed along the river cross-sections. We speculate that this might improve the performance of the current system. We also plan on modifying the objective function in an attempt to find more adequate ways for expressing the distance between simulated and measured depth vectors. Conceptualization, A.A., C.B. and V.S. ; methodology, A.A., C.B. and V.S. ; software, V.S. ; validation, A.A., F.C. and V.S. ; formal analysis, A.A., F.C. and V.S. ; investigation, A.A.; resources, A.A.; data curation, A.A.; writing, A.A., M.B., C.B., F.C., A.M. and V.S. ; visualization, A.A. and V.S. ; supervision, A.A., C.B. and V.S. All authors have read and agreed to the published version of the manuscript.