Search Space Reduction for Genetic Algorithms Applied to Drainage Network Optimization Problems

In recent years, a significant increase in the number of extreme rains around the world has been observed, which has caused an overpressure of urban drainage networks. The lack of capacity to evacuate this excess water generates the need to rehabilitate drainage systems. There are different rehabilitation methodologies that have proven their validity; one of the most used is the heuristic approach. Within this approach, the use of genetic algorithms has stood out for its robustness and effectiveness. However, the problem to be overcome by this approach is the large space of solutions that algorithms must explore, affecting their efficiency. This work presents a method of search space reduction applied to the rehabilitation of drainage networks. The method is based on reducing the initially large search space to a smaller one that contains the optimal solution. Through iterative processes, the search space is gradually reduced to define the final region. The rehabilitation methodology contemplates the optimization of networks using the joint work of the installation of storm tanks, replacement of pipes, and implementation of hydraulic control elements. The optimization model presented uses a pseudo genetic algorithm connected to the SWMM model through a toolkit. Optimization problems consider a large number of decision variables, and could require a huge computational effort. For this reason, this work focuses on identifying the most promising region of the search space to contain the optimal solution and to improve the efficiency of the process. Finally, this method is applied in real networks to show its validity.

Search Space Reduction for Determination of Earthquake Source Parameters Using PCA and k-Means Clustering

The characteristics of an earthquake can be derived by estimating the source geometries of the earthquake using parameter inversion that minimizes the L2 norm of residuals between the measured and the synthetic displacement calculated from a dislocation model. Estimating source geometries in a dislocation model has been regarded as solving a nonlinear inverse problem. To avoid local minima and describe uncertainties, the Monte-Carlo restarts are often used to solve the problem, assuming the initial parameter search space provided by seismological studies. Since search space size significantly affects the accuracy and execution time of this procedure, faulty initial search space from seismological studies may adversely affect the accuracy of the results and the computation time. Besides, many source parameters describing physical faults lead to bad data visualization. In this paper, we propose a new machine learning-based search space reduction algorithm to overcome these challenges. This paper assumes a rectangular dislocation model, i.e., the Okada model, to calculate the surface deformation mathematically. As for the geodetic measurement of three-dimensional (3D) surface deformation, we used the stacking interferometric synthetic aperture radar (InSAR) and the multiple-aperture SAR interferometry (MAI). We define a wide initial search space and perform the Monte-Carlo restarts to collect the data points with root-mean-square error (RMSE) between measured and modeled displacement. Then, the principal component analysis (PCA) and the k-means clustering are used to project data points with low RMSE in the 2D latent space preserving the variance of original data as much as possible and extract k clusters of data with similar locations and RMSE to each other. Finally, we reduce the parameter search space using the cluster with the lowest mean RMSE. The evaluation results illustrate that our approach achieves 55.1~98.1% reductions in search space size and 60~80.5% reductions in 95% confidence interval size for all source parameters compared with the conventional method. It was also observed that the reduced search space significantly saves the computational burden of solving the nonlinear least square problem.