combinatorial-optimization

Some cases of combinatorial optimization solving with common decomposition algorithms. (# Gurobi 9 # Python3)

1.Intensity Modulated Radiation Therapy Problem

• Matrix segmentation problem
• Benders decomposition
• Article url: Benders decomposition[http://dx.doi.org/10.1002/9780470400531.eorms0104]

2.Fixed Charge Transportation Problem

• Mixed integer linear problem
• Benders decomposition
• Article url: Benders decomposition with GAMS[https://www.researchgate.net/profile/Erwin-Kalvelagen/publication/2552969_Benders_Decomposition_for_Stochastic_Programming_with_GAMS/links/0a85e5362481186d8c000000/Benders-Decomposition-for-Stochastic-Programming-with-GAMS.pdf]

3.Sheduling Problem

• Short term scheduling problem
• Event points
• Article url: Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes[https://doi.org/10.1021/ie990108r]

3.1 Example1 P2

3.2 Example2 P10

3.3 Example3 P13

3.4 Robust Scheduling problem:

• Robust processing time of each step
• Article url:A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization[https://doi.org/10.1021/ie200150p]

4.Robust Transportation Problem

• Right-hand-side parameters robust
• Column-and-constraint generation method
• Article url: Solving two-stage robust optimization problems using a column-and- constraint generation method[https://doi.org/10.1016/j.orl.2013.05.003]

4.1 3x3 P4

4.2 30x30 Random-Parameters P5

• Robust location transportation problems under uncertain demands, Discrete Applied Mathematics[https://doi.org/10.1016/j.dam.2011.09.015]

5.Cutting Stock Problems

• Steel cutting problem
• Column generation method