Benchmarks
Three sets of testing problems were used to perform the above-mentioned
numerical experiments. The first set is formed by the well-known Beasley’s
testing problems (Beasley (1990)) cap41, …, cap134, the sizes of which (ïIï´ú Jú) vary from 16´50 to 50´50 including three testing problems
capa, capb and capc of size 100´1000. The values of coefficients in
objective function were rounded to integers.
Since the standard Beasley’s
testing problems are relatively small we have generated two other sets, named K90 and G700. The set K90 consists of 90
testing problems derived from the railway network of Slovak Republic. These
medium sized problems are ordered in ten groups: 45´457, 91´457, 137´457, 182´457, 229´457, 274´457, 319´457, 365´457, 411´457 and 457´457. The set G700
consists of 700 problems derived from the road network of Slovak Republic. This
set consists from ten subgroups, sizes of which ranged from 100´2906, 200´2906, as large as 1000´2906. Each subgroup contained 70 benchmarks. For each
size of the benchmark 10 different random subgraphs of the road network graph
of corresponding size were generated. Each subgraph was used as a base for
creating seven benchmarks by modifying the coefficients cij
and fi to cover uniformly the whole spectrum of located
facilities in optimal solution. For instance, for a problem of size 100´2906 the optimal cardinality of located facilities
were 1,
17, 33, 50, 66, 83 and 100 respectively.