Dual nested decomposition of staircase linear programs

An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling

“…We found the multicut method due to Birge and Louveaux [4] also yielded computational savings over its single cut counterpart. Consistent with earlier findings of Abrahamson [1] and Wittrock [15] (in the deterministic case) and Gassmann [7] (in the stochastic case) we found that the fastpass tree traversing strategy performed well. However, a new class of (-cautious tree traversing strategies produced comparable results to fastpass; further investigation of this class of strategies may be warranted for problems with many stages.…”

“…Tree Traversing Strategies For brevity, we refer to the nested Benders decomposition algorithm described in §3 as the shuffle tree traversing strategy. Abrahamson [1] and Wittrock [15] developed strategies other than shuffle for deterministic multistage linear programs; we consider two of these: fasipass and cautious. Gassmann [7] tested shuffle, fasipass, and cautious in the stochastic setting.…”

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

“…In this figure, the fast-forward fast-backward tree traversing strategy [18] is used. A discussion on alternative tree traversing strategies (Shuffle, Cautious) can be found in [10] for instance.…”

Simplicial with truncated Dantzig–Wolfe decomposition for nonlinear multicommodity network flow problems with side constraints

“…The idea of 'nesting', or recursively applying DW decomposition, is described earlier in [14,9] for staircase or multi-stage linear programs. (For additional enhancements, see [27] and references cited therein.) The term 'nesting' is used here because SD is essentially DW decomposition generalized to nonlinear problems.…”

“…He would like to also thank Prof. Hearn for providing the data for this research, Prof. Ramana for suggesting the use of system optimal solutions, and Prof. Morton for Ref. [27].…”