Table 4: Integer programming optimization test problems.

Test problem Problem definition
Problem 1 [51] FI1(x) = ||x| | 1  = | x 1 | + . . . + | x n |
Problem 2 [51] FI2(x) = x T x = [ x 1  . . .  x n ] [ x 1 ⋮ x n ]
Problem 3 [52] FI3(x) = [15 27 36 18 12] x + x T [ 35  -20 -10  32  -10 -20  40  -6  -31  32 -10  -6   11  -6  -10 32  -32  -6   38  -20 -10  32 -10  -20  31 ] x
Problem 4 [52] FI4(x) = (9 x 1 2  + 2 x 2 2  − 11) 2  +  (3 x 1  + 4 x 2 2  − 7) 2
Problem 5 [52] FI5(x) = ( x 1  + 10 x 2 ) 2  + 5  ( x 3   −  x 4 ) 2  +  ( x 2  −2 x 3 ) 4  + 10  ( x 1  −  x 4 ) 4
Problem 6 [53] FI6(x) = 2 x 1 2  + 3 x 2 2  + 4 x 1 x 2  − 6 x 1  − 3 x 2
Problem 7 [52] FI7(x) = −3803.84 − 138.08 x 1  − 232.92 x 2  + 123.08 x 1 2  + 203.64 x 2 2  + 182.25 x 1 x 2