X - UWSpace - University of Waterloo

esults of the parallel decomposition method using the simpiex and banier methods for solving
subproblems, respectively. Note that diffennt choices of subproblem type may give slightly
different solution time and decomposition iteration number. The results shown here are one
instance of what we have tried. Our experiences indicate that comctly identifying the parts, in
order to reduce the number of linking variables and constraints is vely important since the poor
performance we had at an earlier stage tumed out to be due to a poor definition of the parts. For
example. the performance of NAEP was improved by 3 minutes with a different grouping of
regions, which gave a smaller number of linking variables and constraints. Also. HEPGl was
solved 10 minutes faster by redefining the linking variables and consuoints. In our first attempt,
we defined al1 the water level variables. Uevel (hy-u, K), as the linking variables and dl the
water balance consaaints. LwûtBal(hydro-u.K. K), as the linking consaints However, it tumed
out that the water level variables of scenarios 1 to 3 and nodes 37 to 45 are not tmly linking
variables since they don't appear in other parts and the water balance constnints in nodes 1 to 12
are not trul y linking constraints because they don't include other parts' linking variables.
in "PD Steps" of Tables 5.5 and 5.6, "P W* means the number of information exchanges
between PL and Pu, and "Pr W' and "Pu #" represent the number of information exchanges in the
second level between Pu and PLU and between PUL and Pvu, respectively. Each subproblem's
simplex itention number is presented as the sum of al1 itentions. and "PD Time" is the longest
elqsed time taken. including setup time and idle time, arnong the 4 subproblerns by the parailel
decomposition in 4 PCs even though al1 processors finish almost at the same time. The speedup
is mesured as the ratio of the elapsed time taken by one processor over that of four processors