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Currently, the presence of data uncertainty and noise raises critical issues to be handled on both theoretical and computational grounds. Therefore, robustification and robust optimization have gained attention from theoretical and practical points of view for the establishment of a modeling framework in mathematical optimization to immunize solutions against diverse uncertainties. Data of both the input and output variables, underlying the problems to be addressed, are affected by the noise of different kinds, such that standard statistical models alone may not be sufficient to ensure trustworthy results due to the complexity of the model. Consequently, we propose including parametric uncertainties reflecting future scenarios in multivariate adaptive regression splines (MARS), which, in turn, show great promise for fitting nonlinear multivariate functions, where additive and interactive effects of the predictors are employed to assess the response variable. We robustify MARS through the usage of robust optimization techniques. Due to the large complexity of the underlying model in prior studies, we applied a so-called weak robustification. Now, we exploit a geometrical and combinatorial approach to allow for a more complete robustification, by formulating Robust MARS (RMARS) under Cross-Polytope Uncertainty. In this study, we use RMARS for energy data and demonstrate its superior performance through a simulation study. [ABSTRACT FROM AUTHOR]

The multivariate adaptive regression splines (MARS) model is a flexible non-parametric sparse regression algorithm and provides an excellent promise to data fitting through nonlinear basis functions. During the last decades, it is employed in many fields of control design, finance, technology, and science. It can be regarded as an extension of linear models that automatically model interactions and nonlinearities. The least absolute shrinkage and selection operator (LASSO) analysis is a variable selection and shrinkage method to linear regression models. It proposes to construct the subset of explanatory variables which minimizes estimation error to a quantitative dependent variable. LASSO is applied to choose the variables and perform the regularization to improve the interpretability and robustness of the model. In this paper, we examine MARS and LASSO to generate natural gas demand forecasts of residential users for the distribution system operators who need both short- and long-term forecasts. We also compare the performance of MARS and LASSO with a simple multiple-linear regression (LR) commonly used in practice. Our analysis reveals that MARS outperforms LASSO and LR in both the average measures and in the worst-case analysis. For 1 day-ahead forecast, MARS provides a MAPE of around 4.8% while the same figure under LASSO and LR reaches 8.3 and 8.5% respectively. However, as the forecasting horizon increases, we observe that the performance of these proposed methods gets worse and for 1 year-ahead forecast, the MAPE values for MARS, LASSO, and LR are 13.4%, 24.8% and 26.3% respectively. [ABSTRACT FROM AUTHOR]

Residential customers are the main users generally need a great quantity of natural gas in distribution systems, especially, in the wintry weather season since it is particularly consumed for cooking and space heating. Hence, it ought to be noninterruptible. Since distribution systems have a restricted ability for supply, reasonable planning and prediction through the whole year, especially in winter seasons, have emerged as vital. The Ridge Regression (RR) is formulated mainly to decrease collinearity results through shrinking the regression coefficients and reducing the impact in the model of variables. Conic multivariate adaptive regression splines ((C)MARS) model is constructed as an effective choice for MARS by using inverse problems, statistical learning, and multi-objective optimization theories. In this approach, the model complexity is penalized in the structure of RR and it is constructed a relaxation by utilizing continuous optimization, called Conic Quadratic Programming (CQP). In this study, CMARS and RR are applied to obtain forecasts of residential natural gas demand for local distribution companies (LDCs) that require short-term forecasts, and the model performances are compared by using some criteria. Here, our analysis shows that CMARS models outperform RR models. For one-day-ahead forecasts, CMARS yields a MAPE of about 4.8%, while the same value under RR reaches 8.5%. As the forecast horizon increases, it can be seen that the performance of the methods becomes worse, and for a forecast one week ahead, the MAPE values for CMARS and RR are 9.9% and 18.3%, respectively. [ABSTRACT FROM AUTHOR]