## 6 Experimental Results
### Solving the FLP Using Predictive Models  
The third alternative is to use predictive methods to estimate the solutions for incomplete data. Given a dataset with gaps or missing information, this approach aims to approximate the solutions that would have been obtained after multiple iterations of the algorithms.  
One of the critical considerations for researchers, corporations, and decision makers is the time required to solve complex problems. For instance, in the case of an emergency situation (such as a natural disaster), decision makers must respond quickly and make decisions on the placement of shelters (facilities) while taking into account the proximity of the affected population to ensure their safety.  
The use of machine learning techniques has demonstrated the capability of generating approximate or comparable results to those produced by sophisticated methods such as genetic algorithms, as evident from Figures 8-11. Implementing predictive machine learning models can provide a significant advantage for decision makers in emergency situations, as they enable an almost instantaneous reaction. In the context of the present study, this means that decision makers can quickly allocate refugee facilities to attend to people affected by emergencies within a city or state. The only prerequisites for such rapid responses are the availability of relevant data and the execution of fitting curves or machine learning models. The decision makers can then visualize the Pareto front produced by the various predictive methods, as depicted in Figures 8-11, and determine the most suitable solution based on the circumstances.  
Figures 8 and 9 present the results of the complete Pareto front achieved through the utilization of interpolation techniques such as cubic splines and exponential regression, respectively. It can be observed that the utilization of exponential regression leads to a more accurate approximation of the Pareto front compared to cubic splines. This is due to  
the fundamental nature of the regression method, which aims to fit the data trend in the most optimal manner. Conversely, the cubic splines technique necessitates the solutions to pass through the given points, which results in more oscillatory solutions and a higher number of dominated solutions.  
Figures 10 and 11 present the results obtained through the utilization of k-nearest neighbors (KNNs) and multiple imputation by chained equations (MICE), respectively. KNN is a supervised machine learning algorithm primarily used for solving classification and regression problems, whereas MICE is a statistical method for dealing with missing data. The results obtained through both methods may be similar as they employ similar strategies, such as using the values of similar observations or utilizing a model to predict missing values based on the available data.  
Figure 8: The Pareto set after solving the FLP complemented via exponential regression for: the Swain dataset (**left**), and the London dataset (**right**).  
Figure 9: The Pareto set after solving the FLP complemented via cubic spline for: the Swain dataset (**left**), and the London dataset (**right**).  
As depicted in Figure 11, the multiple imputation by chained equations (MICE) method utilizes a statistical model to generate several imputed datasets, which are then combined to produce a continuous curve. On the other hand, as shown in Figure 10, the k-nearest neighbors (KNNs) algorithm imputes missing data based on the information of its nearest neighbors, which results in a steeper or \"noisier\" curve due to the non-parametric nature of the algorithm.