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The Facilities

The optimization codes were compiled with the f77 compiler using the -O3 (aggressive code optimization) compilation flag on a Silicon Graphics Power Indigotex2html_wrap_inline3553 with Mips R8000 chip, 192 MB main memory and IRIX 6.0.1 operating system. The machine precision on this machine is approximately tex2html_wrap_inline3555. All facility distributions were computed on this machine. The computation times were obtained by the IRIX time command.

We computed facility distributions for problems with N facilities, tex2html_wrap_inline3377, tex2html_wrap_inline3561, and, additionally, tex2html_wrap_inline3563. The last set of distributions was computed for benchmarking reasons. The biggest problem solved had therefore N = 1600 facilities, which resulted in a nonlinear nonconvex global optimization problem with 3197 unknowns and 6394 constraints.

Figure 1 shows the computation time for the first (simulated annealing, SA) and the second (limited-memory BFGS, L-BFGS) phase in Stage 1. A detailed table of all computation times can be found in the appendix, see Table 2. As it can be seen, the bottle neck of the computation is the first part of the optimization process, i. e. obtaining a point distribution which is not too bad. Note that only one run of the simulated annealing algorithm in Phase I was needed to produce a good starting distribution for Phase II. The biggest problem took 722 minutes (about 12 hours) computation time in Phase I, followed by another 79 minutes for Phase II.

  =85mm Figure tex2html_wrap1619tex2html_wrap_inline3571 for the distribution calculated by the simulated annealing algorithm. The L-BFGS algorithm then refined this number to tex2html_wrap_inline3573. Detailed results can be found in Table 3 in the appendix.

  Figure tex2html_wrap1620
Figure tex2html_wrap1621
Figure tex2html_wrap1622
Figure tex2html_wrap1623
Figure tex2html_wrap1624tex2html_wrap_inline3575, tex2html_wrap_inline3577, but their algorithm nevertheless produced completely different facility distributions.

next up previous
Next: The Weights Up: Computational Results Previous: Computational Results

Joerg Fliege
Thu Dec 23 19:39:35 CET 1999