k-Step Correction for Mixed Integer Linear Programming: A New Approach for Instrumental Variable Quantile Regressions and Related Problems

2018 ◽  
Author(s):  
Yinchu Zhu
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Instrumental Variable ◽  
Mixed Integer ◽  
Quantile Regressions ◽  
New Approach

A NEW APPROACH TO SELECT THE BEST SUBSET OF PREDICTORS IN LINEAR REGRESSION MODELLING: BI-OBJECTIVE MIXED INTEGER LINEAR PROGRAMMING

2019 ◽  
Vol 61 (1) ◽  
pp. 64-75 ◽  
Author(s):  
HADI CHARKHGARD ◽  
ALI ESHRAGH
Keyword(s):  
Linear Programming ◽  
Linear Regression ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Optimization Problem ◽  
Computational Study ◽  
Mixed Integer ◽  
Programming Approach ◽  
Objective Functions ◽  
New Approach

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.

scholarly journals A New Peak-Shaving Model Based on Mixed Integer Linear Programming with Variable Peak-Shaving Order

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 887
Author(s):  
Xianliang Cheng ◽  
Suzhen Feng ◽  
Yanxuan Huang ◽  
Jinwen Wang
Keyword(s):  
Linear Programming ◽  
Power Systems ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Mixed Integer ◽  
Time Interval ◽  
Renewable Energy Resources ◽  
Load Curve ◽  
Peak Shaving ◽  
Model Based

Peak-shaving is a very efficient and practical strategy for a day-ahead hydropower scheduling in power systems, usually aiming to appropriately schedule hourly (or in less time interval) power generations of individual plants so as to smooth the load curve while enforcing the energy production target of each plant. Nowadays, the power marketization and booming development of renewable energy resources are complicating the constraints and diversifying the objectives, bringing challenges for the peak-shaving method to be more flexible and efficient. Without a pre-set or fixed peak-shaving order of plants, this paper formulates a new peak-shaving model based on the mixed integer linear programming (MILP) to solve the scheduling problem in an optimization way. Compared with the traditional peak-shaving methods that need to determine the order of plants to peak-shave the load curve one by one, the present model has better flexibility as it can handle the plant-based operating zones and prioritize the constraints and objectives more easily. With application to six cascaded hydropower reservoirs on the Lancang River in China, the model is tested efficient and practical in engineering perspective.

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