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X - UWSpace - University of Waterloo
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Chapter 5 Preliminary Implementation and Results<br />
This chapter repons on some implementation procedures and prelirninary cornputational<br />
results <strong>of</strong> the parallel primal-dual decomposition algorithm for the multi-part problcms through<br />
the use <strong>of</strong> GAMS [ 19921. the Regex Libmy [ 19921, PVM (Pdlel Virnial Machine) 3.1 1 [ 19941<br />
and CPEX 6.0 [1997] on an iBM RS/60ûû workstation and a cluster <strong>of</strong> four PCs (Personal<br />
Cornputers) running the Solaris operating system. Severai multi-part LP models are implernented<br />
and in each <strong>of</strong> the tests. the new panllel decornposition algorithm (by the first method) converges<br />
to within a smail tolennce <strong>of</strong> the optimal \due in 3 finite number <strong>of</strong> iterations. The algorithm <strong>of</strong><br />
the second method somr~mes fails to converge. Therefore. we discuss oniy the first method in<br />
this chapter. except for a brief mention <strong>of</strong> the results for the second method. ît the end <strong>of</strong> the<br />
chapter.<br />
5.1 The Implementation Procedure<br />
In order to demonsuate the convergence and repon rhe computationd resuits <strong>of</strong> the new<br />
panilel decomposition algorithm. we coded the multi-part decomposition algorithm into C<br />
pro_gnms using GAMS. the Regex iibrary. the CPLEX Callable Library and PVM w hich are<br />
exetutable in one IBM RS/6ûûû with 128MB RA!! and a ciuster <strong>of</strong> four Pentiurn PCs, each with<br />
300MI-b processot and 118MB RAM. We chose the C language for coding because it cm utiiize<br />
bodi the CPLEX Cdlable Libnry and Pm. thus allowing implementation <strong>of</strong> the parailel<br />
decomposition aigorithm without worrying about the derails <strong>of</strong> coding a linear programming<br />
solver and paralle1 computing s<strong>of</strong>iwue. The network connectivity is shown in Fiam 5.1. The