Network-Based Approximate Linear Programming for Discrete Optimization

2017 ◽  
Author(s):  
Selvaprabu Nadarajah ◽  
Andre Augusto Cire
Keyword(s):  
Linear Programming ◽  
Discrete Optimization ◽  
Approximate Linear Programming

Network-Based Approximate Linear Programming for Discrete Optimization

2020 ◽  
Vol 68 (6) ◽  
pp. 1767-1786
Author(s):  
Selvaprabu Nadarajah ◽  
Andre A. Cire
Keyword(s):  
Linear Programming ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Linear Programs ◽  
Solution Quality ◽  
Marketing Analytics ◽  
Dynamic Programs ◽  
Approximate Linear Programming ◽  
Commercial Solver ◽  
Discrete Optimization Problems

Several prescriptive tasks in business and engineering as well as prediction in machine learning entail the solution of challenging discrete optimization problems. We recast the typical optimization formulation of these problems as high-dimensional dynamic programs and approach their approximation via linear programming. We develop tractable approximate linear programs with supporting theory by bringing together tools from state-space aggregations, networks, and perfect graphs (i.e., graph completions). We embed these models in a simple branch-and-bound scheme to solve applications in marketing analytics and the maintenance of energy or city-owned assets. We find that the resulting technique substantially outperforms a state-of-the-art commercial solver as well as aggregation-heuristics in terms of both solution quality and time. Our results motivate further consideration of networks and graph theory in approximate linear programming for solving deterministic and stochastic discrete optimization problems.

scholarly journals Cyclic Cleaning Scheduling of Industrial Boiler Based on Steepest Descent Approximate Linear Programming

2013 ◽  
Vol 46 (13) ◽  
pp. 478-483
Author(s):  
Yan Zhaoyang ◽  
Ma Xin ◽  
Gao Dong ◽  
Liu Pingping ◽  
Zhang Beike
Keyword(s):  
Linear Programming ◽  
Steepest Descent ◽  
Industrial Boiler ◽  
Approximate Linear Programming

scholarly journals THE PROBLEM OF DISCRETE OPTIMIZATION ON THE CONSTRUCTION OF A SLIDING SCHEDULE OF EMPLOYEES SHIFTS

2020 ◽  
Vol 7 (3) ◽  
pp. 038-043
Author(s):  
A. N. Shingareva ◽  
◽  
M. N. Rasskazova ◽  
Keyword(s):  
Mathematical Model ◽  
Linear Programming ◽  
Programming Problem ◽  
Integer Linear Programming ◽  
Discrete Optimization ◽  
Linear Programming Problem ◽  
Target Function ◽  
Work Schedules ◽  
Integer Linear Programming Problem ◽  
Shift Schedules

This article discusses a linear programming problem on the construction of rolling shift schedules for warehouse employees. A mathematical model of an integer linear programming problem has been developed. The target function can be either minimization of the total number of employees or minimization of wages. Experiments were carried out for various work schedules, which showed the effectiveness of the proposed approach.

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