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Chapter 6 Conclusions and Future Research
6.1 Conclusions
In this thesis, the main objective is to develop a new parallel decomposition method for
rnulti-part linear prograrnmjng models. We focus on the proofs and demonsuation of the
convergence of the two-part and multi-part dgorithms. We repori in some test results that the
algonthms converge to an optimal solution of the original problems in a finite number of
decomposition i terations.
The idea of this thesis originally came frorn Lan [1993] for multi-stage nested decomposition.
however due to some infesibility problems on applying the nested decomposition in parallel, we
developed another parallel decomposition scheme for multi-part stxuctured models.
The parallel decomposition algorithm for two-part models consistently converged to an
optimal solution (and a convergence proof was formed). but our fint aigorithm for multi-pan
models did not always converge (we cal1 this algrithm a heuristic). Finally, we came up with a
convergent pûrallel primal-dual decomposi tion aleorithm for multi-part LPs. w hich convergeci
in al1 tests. by applying the two-part decomposition principle ~cursively in a hiemhical way.
The distinctions between Lads algorithm and the new parallel decomposition aigorithm
;ire summarized in Table 6.1.