Mathematical Problems in Engineering

Research Article

New Bounds for Ternary Covering Arrays Using a Parallel Simulated Annealing

Table 1

(a) A set of 7 covering arrays configurations. (b) Performance of ESSA. Columns 3–9 show the time taken to construct each of the covering arrays.
(a)
Id CA description
c a 1 C A ( 1 9 ; 2 , 3 0 , 3 )
c a 2 C A ( 3 5 ; 3 , 5 , 3 )
c a 3 C A ( 5 8 ; 3 , 1 0 , 3 )
c a 4 C A ( 8 6 ; 4 , 5 , 3 )
c a 5 C A ( 2 0 4 ; 4 , 1 0 , 3 )
c a 6 C A ( 2 4 3 ; 5 , 5 , 3 )
c a 7 C A ( 1 0 4 0 ; 5 , 1 5 , 3 )
(b)
ℙ 𝟏 ℙ 𝟐 Covering arrays
c a 1 c a 2 c a 3 c a 4 c a 5 c a 6 c a 7
0 1 4789.763 3.072 46.989 12.544 3700.038 167.901 0.102
0.1 0.9 1024.635 0.098 0.299 0.236 344.341 3.583 0.008
0.2 0.8 182.479 0.254 0.184 0.241 173.752 1.904 0.016
0.3 0.7 224.786 0.137 0.119 0.222 42.950 1.713 0.020
0.4 0.6 563.857 0.177 0.123 0.186 92.616 3.351 0.020
0.5 0.5 378.399 0.115 0.233 0.260 40.443 1.258 0.035
0.6 0.4 272.056 0.153 0.136 0.178 69.311 2.524 0.033
0.7 0.3 651.585 0.124 0.188 0.238 94.553 2.127 0.033
0.8 0.2 103.399 0.156 0.267 0.314 81.611 5.469 0.042
0.9 0.1 131.483 0.274 0.353 0.549 76.379 4.967 0.110
1 0 7623.546 15.905 18.285 23.927 1507.369 289.104 2.297