Spatial prediction of groundwater spring potential mapping based on an adaptive neuro-fuzzy inference system and metaheuristic optimization

Groundwater is one of the most valuable natural resources in the world (Jha et al., 2007). However, it is not an unlimited resource; therefore understanding groundwater potential is crucial to ensure its sustainable use. The aim of the current study is to propose and verify new artificial intelligence methods for the spatial prediction of groundwater spring potential mapping at the Koohdasht–Nourabad plain, Lorestan province, Iran. These methods are new hybrids of an adaptive neuro-fuzzy inference system (ANFIS) and five metaheuristic algorithms, namely invasive weed optimization (IWO), differential evolution (DE), firefly algorithm (FA), particle swarm optimization (PSO), and the bees algorithm (BA). A total of 2463 spring locations were identified and collected, and then divided randomly into two subsets: 70&thinsp;% (1725 locations) were used for training models and the remaining 30&thinsp;% (738 spring locations) were utilized for evaluating the models. A total of 13 groundwater conditioning factors were prepared for modeling, namely the slope degree, slope aspect, altitude, plan curvature, stream power index (SPI), topographic wetness index (TWI), terrain roughness index (TRI), distance from fault, distance from river, land use/land cover, rainfall, soil order, and lithology. In the next step, the step-wise assessment ratio analysis (SWARA) method was applied to quantify the degree of relevance of these groundwater conditioning factors. The global performance of these derived models was assessed using the area under the curve (AUC). In addition, the Friedman and Wilcoxon signed-rank tests were carried out to check and confirm the best model to use in this study. The result showed that all models have a high prediction performance; however, the ANFIS–DE model has the highest prediction capability (AUC&thinsp; = &thinsp;0.875), followed by the ANFIS–IWO model, the ANFIS–FA model (0.873), the ANFIS–PSO model (0.865), and the ANFIS–BA model (0.839). The results of this research can be useful for decision makers responsible for the sustainable management of groundwater resources.</p

Adaptive ridge regression system for software cost estimating on multi-collinear datasets

10.1016/j.jss.2010.07.032Journal of Systems and Software83112332-2343JSSO

Evaluation of estimators for ill-posed statistical problems subject to multicollinearity

Multicollinearity is a significant problem in economic analysis and occurs in any situation where at least two of the explanatory variables in a model are related to one another. The presence of multicollinearity is problematic, as changes in the dependent variable cannot be accurately attributed to individual explanatory variables. It can cause estimated coefficients to be unstable and have high variances, and thus be potentially inaccurate and inappropriate to guide management or policy. Due to this problem, many alternative estimators have been developed for the analysis of multicollinear data. The primary objective of this thesis is to compare and contrast the performance of some of these common estimators, as well as a number of new estimators, and test their prediction accuracy and precision under various circumstances. Through the use of non-trivial Monte Carlo experiments, the estimators are tested under 10 different levels of multicollinearity, with regressors and errors drawn from different distributions (normal, student t, chi-squared, and in the case of errors, mixed Gaussian). Insights are gained through response surface analysis, which is conducted to help summarise the output of these simulations. A number of key findings are identified. The highest levels of mean square error (MSE) are generally given by a Generalised Maximum Entropy estimator with narrow support bounds defined for its coefficients (GMEN) and the One-Step Data Driven Entropy (DDE1) model. Yet, none of the estimators evaluated produced sufficiently high levels of MSE to suggest that they were inappropriate for prediction. The most accurate predictions, regardless of the distributions tested or multicollinearity, were given by Ordinary Least Squares (OLS). The Leuven-2 estimator appeared relatively robust in terms of MSE, being reasonably invariant to changes in condition number, and error distribution. However, it was unstable due to variability in error estimation arising from the arbitrary way that probabilities are converted to coefficient values in this framework. In comparison, MSE values for Leuven-1 were low and far more stable than those reported for Leuven-2. The estimators that produced the least precision risk, as measured through mean square error loss (MSEL), were the GMEN and Leuven-1 estimators. However, the GMEN model requires exogenous information and, as such, is much more problematic to accurately apply in different contexts. In contrast, two models had very poor precision in the presence of multicollinear data, the Two-Step Data Driven Entropy (DDE2) model and OLS, rendering them inappropriate for estimation in such circumstances. Overall, these results highlight that the Leuven-1 estimator is the most appropriate if a practitioner wishes to achieve high prediction accuracy and precision in the presence of multicollinearity. Nevertheless, it is critical that more attention is paid to the theoretical basis of the Leuven-1 estimator, as relating estimated probabilities to coefficients using concepts drawn from the theory of light appears highly subjective. This is illustrated through the differences in empirical results obtained for the Leuven-1 and Leuven-2 estimators

Software Size and Effort Estimation from Use Case Diagrams Using Regression and Soft Computing Models

In this research, we propose a novel model to predict software size and effort from use case diagrams. The main advantage of our model is that it can be used in the early stages of the software life cycle, and that can help project managers efficiently conduct cost estimation early, thus avoiding project overestimation and late delivery among other benefits. Software size, productivity, complexity and requirements stability are the inputs of the model. The model is composed of six independent sub-models which include non-linear regression, linear regression with a logarithmic transformation, Radial Basis Function Neural Network (RBFNN), Multilayer Perceptron Neural Network (MLP), General Regression Neural Network (GRNN) and a Treeboost model. Several experiments were conducted to train and test the model based on the size of the training and testing data points. The neural network models were evaluated against regression models as well as two other models that conduct software estimation from use case diagrams. Results show that our model outperforms other relevant models based on five evaluation criteria. While the performance of each of the six sub-models varies based on the size of the project dataset used for evaluation, it was concluded that the non-linear regression model outperforms the linear regression model. As well, the GRNN model exceeds other neural network models. Furthermore, experiments demonstrated that the Treeboost model can be efficiently used to predict software effort