Mixed integer nonlinear goal programming approach to variable selection in linear regression

Author(s):  
Mohammed Albassam ◽  
Ali El Hefnawy ◽  
Emad E. A. Soliman
2009 ◽  
Vol 26 (05) ◽  
pp. 587-604 ◽  
Author(s):  
H. HASSANPOUR ◽  
H. R. MALEKI ◽  
M. A. YAGHOOBI

Many researches have been carried out in fuzzy linear regression since the past three decades. In this paper, a fuzzy linear regression model based on goal programming is proposed. The proposed model takes into account the centers of fuzzy data as an important feature as well as their spreads. Furthermore, the model can deal with both symmetric and non-symmetric data. To show the efficiency of proposed model, it is compared with some earlier methods based on simulation studies and numerical examples. Moreover, the sensitivity of the model to outliers is discussed.


2019 ◽  
Vol 61 (1) ◽  
pp. 64-75 ◽  
Author(s):  
HADI CHARKHGARD ◽  
ALI ESHRAGH

We study the problem of choosing the best subset of $p$ features in linear regression, given $n$ observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem. We explain the main weaknesses of existing approaches and, to overcome their drawbacks, we propose a bi-objective mixed integer linear programming approach. A computational study shows the efficacy of the proposed approach.


Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 483
Author(s):  
Chia-Nan Wang ◽  
Nhat-Luong Nhieu ◽  
Trang Thi Thu Tran

Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective mixed-integer optimization model is developed to ensure production efficiency in uncertainty conditions and satisfy the requirements of sustainable development. The efficiency of the production system is ensured through objective functions that optimize backorder quantity, machine uptime and customer satisfaction. The other three objective functions of the proposed model are related to optimization of profits, emissions, and employment changing. The objective functions respectively represent the three elements of sustainable development: economy, environment, and sociality. The proposed model also assures the production manager’s discretion over whether or not to adopt production options such as backorder, overtime, and employment of temporary workers. At the same time, the resource limits of the above options can also be adjusted according to the situation of each production facility via the model’s parameters. The solutions that compromise the above objective functions are determined with the Chebyshev goal programming approach together with the weights of the goals. The model is applied to the multinational production system of a Southeast Asian supplier in the textile industry. The goal programming solution of the model shows an improvement in many aspects compared to this supplier’s manufacturing practices under the same production conditions. Last but not least, the study develops different scenarios based on different random distributions of uncertainty demand and different weights between the objective functions. The analysis and evaluation of these scenarios provide a reference basis for managers to adjust the production system in different situations. Analysis of uncertain demand with more complex random distributions as well as making predictions about the effectiveness of scenarios through the advantages of machine learning can be considered in future studies.


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