# Qom--A New Hydroologic Prediction Model Enhanced with Multi-Objective Optimization
## 3 Related Work  
Since the last decade, the optimal parameter calibration of hydrologic models has been tackled with mono- and multi-objective metaheuristic algorithms, usually providing successful results for different approaches of decision variables and objective functions. In particular, two early surveys [2; 3] outlined the importance of using bio-inspired multi-objective approaches, as they are specially adapted to work as black-box optimizers with capabilities to explore the search space generated for each problem river basin scenario and for several objectives at the same time. In this regard, an interesting proposal was presented in Reference [24], where a sensitivity analysis and automatic calibration of a rainfall-runoff NedborAfstromnings model (NAM) [25] was carried out with nine decision variables to measure the quantitative and qualitative variation of results. In this work, an Elitist Non-dominated Sorting Differential Evolution (NSDE) [26] algorithm was used to optimize two objective functions consisting on Average Root Mean Squared-Error (RMSE) of peak and low flow Events. In Reference [27], a strategy that combined the principles of multi-objective optimization and depth-based sampling was presented with the title of Multi-Objective Robust Parameter Estimation (MOROPE). This algorithm applied multi-objective optimization to identify non-dominated robust model parameter vectors for the calibration of a distributed hydrologic model with a focus on flood events in a small pre-alpine and fast responding catchment in Switzerland. A thorough comparison was conducted in Reference [28] with a series of popular multi-objective algorithms (Borg, AMALGAM, GDE3, NSGA-II, OMOPSO, and SPEA2) for the calibration of the HBV (Hydrologiska Byrans Vattenbalansavdelning) conceptual rainfall-runoff model [29] with 14 real-valued decision variables and considering four objective functions. In this study, Borg and OMOPSO obtained, in overall, the best performance for the tackled instances. Also in 2013, the work presented in Reference [30] was centered on a river basin according to the distributed hydrologic model HEC-HSM (Hydrologic Engineering Center - Hydrologic Modeling System, [[https://www.hec.usace.army.mil/](https://www.hec.usace.army.mil/)]([https://www.hec.usace.army.mil/](https://www.hec.usace.army.mil/))), for which a number of 10 decision variables and 4 objectives were approached with a multi-objective particle swarm optimization algorithm. More recently, several variable balancing approaches for the exploration and exploitation of the NSGA-II, in the automatic parameter calibration of a HYdrological MODel (HYMOD) were evaluated in Reference [31]. These balancing approaches were compared with traditional static balancing methods (the two values are fixed during optimization) in a benchmark hydrological calibration problem for the Leaf River (1950 km\({}^{2}\)) near Collins, Mississippi. Another related study is found in Reference [32], where authors analyzed how adding daily Total Water Storage (dTWS) derived from the Gravity Recovery And Climate Experiment (GRACE) as extra observations, besides the traditionally used runoff data, improved the calibration of a conceptual hydrological model within the Danube River Basin. As calibration approach, four popular evolutionary optimization techniques (NSGA-II, MOPSO, PESA-II, SPEA2) were tested to calibrate the model. Results indicated that NSGA-II performed better than the other techniques for calibrating GR4J using GRACE dTWS and in situ runoff data. A common aspect in all these works is the use of already existing multi-objective optimizers (NSGA-II, SPEA2, MOPSO, etc.) with well-known hydrologic models usually requiring large number of parameters (HBV, HEC-HSM, GRACE, etc. ), trying to find the best performing algorithm. Our proposal differs not only in the definition of a novel hydrologic model (Qom), but also in how the calibration with metaheuristics is conducted.