Table 2.
Properties of benchmark functions.
| f | f* | x* | Bounds | Characteristics |
|---|---|---|---|---|
| f 1 | 0.0000 | (0,0,…, 0) | [−600,600] | Highly multi-modal |
| f 2 | 0.0000 | (0,0,…, 0) | [−15,15] | Highly multi-modal |
| f 3 | 0.0000 | (1,1,…, 1) | [−15,15] | Multiple local optima |
| f 4 | 0.0000 | (0,0,…, 0) | [−32.768,32.768] | Highly multi-modal |
| f 5 | 0.0000 | (0,0,…, 0) | [−500,500] | Highly multi-modal |
| f 6 | 0.0000 | (0,0,…, 0) | [−600,600] | Uni-modal, convex |
| f 7 | −1.0000 | (π, π,…, π) | [−2π, 2π] | Multiple local optima |
| f 8 | −1.80131 | (2.20319,1.57049)1 | [0, π] | Multiple local optima |
| f 9 | 0.0000 | (0,0,…, 0) | [−2π, 2π] | Multiple local optima |
| f 10 | 0.0000 | (0,0,…, 0) | [−5,10] | Uni-modal |
1These values are valid for dimensions D = 2.