X - UWSpace - University of Waterloo

SP~' has the same structure as the part one subproblem in the parallel two pari
decomposition method in Chapter 3, except for two more parts. thus having one more
proposal from the aggregated upper bound subproblem (parts 3 and 4) at each fint level
iteration. Also. SP:.J has the same structure as the part two subproblem in the panllel two
part decomposition except for two more pans, thus having one more cut from the aggregated
lower bound subproblem (parts 1 and 1) at each first ievel iteration. The subproblems spi"
and SP:+' utilize both proposals and cuts.
For fint level i tentions, the coordination is made through broadcasting proposals and
cuts. The proposais. which have the prima1 information of the previous subproblems. are
broadcasted to the other two subproblems and the cuts, which have dual information, are
broadcasted to the other two subproblems. During the second level iterations, the coordination
is made through exchanging prima1 and duai proposals only between the two subproblems
bi furcated from the same aggregated subpro blem.
At the fint itention of the paralle1 method, there is no information flow among the
subproblerns since no information is available. whiIe in concrast Lan's senal meihod begins
with the fint subproblem having no information from other subproblems. but al1 other
subproblems are solved with proposals or cuts from other subproblems, even in the first
itention.
From the second iteration of the parallel methoci, information is exchmged between
the aggregated subproblems of level 1. then level II subproblems are formed and solved with
new proposals or cuts exchanged between the immediate neighbor subproblerns bifurcated
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