Table 3.
Properties of benchmark functions.
| f | f* | x* | Characteristics | Domain |
|---|---|---|---|---|
| f 1 | 0.0000 | (0,0,…, 0) | Highly multimodal | [−600,600] |
| f 2 | 0.0000 | (0,0,…, 0) | Highly multimodal | [−15,15] |
| f 3 | 0.0000 | (1,1,…, 1) | Several local optima | [−15,15] |
| f 4 | 0.0000 | (0,0,…, 0) | Highly multimodal | [−32.768,32.768] |
| f 5 | 0.0000 | (0,0,…, 0) | Highly multimodal | [−500,500] |
| f 6 | 0.0000 | (0,0,…, 0) | Unimodal, convex | [−600,600] |
| f 7 | −1.0000 | (π, π,…, π) | Several local optima | [−2π, 2π] |
| f 8 | −1.80131 | (2.20319,1.57049)1 | Several local optima | [0, π] |
| f 9 | 0.0000 | (0,0,…, 0) | Several local optima | [−2π, 2π] |
| f 10 | 0.0000 | (0,0,…, 0) | Unimodal | [−5,10] |
1Valid for 2-dimensional parameter space.