# Qom--A New Hydroologic Prediction Model Enhanced with Multi-Objective Optimization
## 4 Hydrologic Calibration Strategy
### Optimization Approach  
Once we have formulated the calibration of the Qom model as a multi-objective optimization problem, the next step is to solve it to find an accurate approximation of the Pareto front and then take from it that solution providing the best overall result. Determining the _best_ metaheuristic for a given problem instance is far from being a trivial process; thus, the No Free Lunch Theorem [35] states  
\begin{table}
\begin{tabular}{l l} \hline
**Term** & **Description** \\ \hline \(Qd\) & initial river base streamflow (m\({}^{3}\)/s) \\ \(Qm\) & average output streamflow observed (m\({}^{3}\)/s) \\ \(O\) & vector of observed data \\ \(E\) & vector of estimated solution \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._that all optimization algorithms that search for a particular problem of a class perform the same when averaged over all the problems in the class.  
The experimental methodology we follow is not aimed at finding or designing a particular metaheuristic for the automatic calibration of Qom, but to make use of a set of existing algorithms and use all of them to get a Pareto front approximation. We want to avoid spending time in tuning the control parameters of the algorithms, so they will be configured with standard settings. Our approach is based on the assumption that each algorithm can efficiently explore a particular region of the search space, so running all of them independently and joining the results they provide is likely to yield a satisfactory set of solutions. To this end, we have selected a set of representative multi-objective metaheuristics which are included in the jMetal framework, namely: NSGAII [7], OMOPSO [8], SMS-EMOA [9], MOEA/D [10], AbYSS [11], SMPSO [12] and MOCell [13].  
The scheme we follow is illustrated in Figure 3. The starting point is, for each river basin, a dataset comprising 5 data files. A file with extension *.basin contains morphometric features with static parameters to characterize it, such as area, shape, percentage of permeable area %_p_, initial surface and soil moisture (_Ro_ and _So_, respectively), start and end dates of analysis, time slot between registers \(\Delta t\), and so forth. File *.var includes decision variables representing calibration parameters, as well as upper and lower bounds for algorithmic search. Information about total precipitations \(P\) is set in file *.rain, output flow data _Qo_ are in file with extension *.Qo and potential evapotranspiration data \(PEVT\) are in file *.pevt. These files register observed data for each time period \(\Delta t\). For each river basin, a problem instance is defined according to two or more series of data. One of these series is used for multi-objective optimization (calibration) and the remaining ones are used for validation, with regards to optimized solutions.  
Figure 3: Scheme of the optimization process using jMetal.  
All the used algorithms are configured to find a bounded set of solutions after performing a maximum number of evaluations over the problem calibration data. When they finish, the results are stored in two files, named VAR and FUN, which contain, respectively, the found solutions (i.e., the values of the decision variables) and the corresponding Pareto front approximation (i.e., the objective function values). A number of 30 independent runs for configuration have been executed, and all the solutions produced by all the algorithms have been joined, so after removing the dominated solutions a set of non-dominated solutions is obtained. This set is used as a reference front.  
After the optimization process, the next step is the decision making, consisting in the selection of one solution in the reference front that will allow the expert to compute an optimized prediction of the soil moisture state, volumes of looses and excesses and hydrographs. This step is described in the next section.