The usage of decomposition methods to reduce the size of problems is very important in the different applications. In the artificial intelligence applications, we face with the different problems that can be decomposed into some sub-problems. Just as some examples, the multi-commodity flow problem, the scheduling problem and resource assignment problems can be solved by decomposition methods efficiently. In our research group, we worked on the different decomposition methods under uncertain conditions. Our outcomes can be categorized as the following:
- Dantzig-Wolf Decomposition: In [ Niksirat, M., Hashemi, S. M., & Ghatee, M. (2016). Branch-and-price algorithm for fuzzy integer programming problems with block angular structure. Fuzzy Sets and Systems, 296, 70-96. ] two fuzzy decomposition methods have been developed under possibility and necessity measures.
- Benders Decomposition:
- In [ Fakhri, A., & Ghatee, M. (2016). Application of Benders decomposition method in solution of a fixed-charge multicommodity network design problem avoiding congestion. Applied Mathematical Modelling, 40(13-14), 6468-6476. ] a decomposition method for multi-commodity flow problem was developed.
- In [ Fakhri, A., & Ghatee, M. (2013) Solution of preemptive multi-objective network design problems applying Benders decomposition method. Annals of Operations Research, 210(1), 295-307. ] a decmposition method for bi-objective network design has been extended.
- In [ Fakhri, A., Ghatee, M., Fragkogios, A., & Saharidis, G. K. (2017). Benders decomposition with integer subproblem. Expert Systems with Applications, 89, 20-30. ] some local and global cuts have been proposed for general optimization problems with integer sub-problems.