Table 3 Description of unimodal benchmark functions.

_F1

\(f(x) = \sum\nolimits_{i = 1}^{n} {x_{i}^{2} }\)

[100, 100]

_F2

\(f(x) = \sum\nolimits_{i = 1}^{n} {\left| {x_{i} } \right|} + \prod\nolimits_{i = 1}^{n} {\left| {x_{i} } \right|}\)

[10, 10]

_F3

\(f(x) = \sum\nolimits_{i = 1}^{n} {\left( {\sum\nolimits_{j - 1}^{i} {x_{j} } } \right)^{2} }\)

[100, 100]

_F4

\(f(x) = \max_{i} \left\{ {\left| {x_{i} } \right|,\,1 \le i \le n} \right\}\)

[100, 100]

_F5

\(f(x) = \sum\nolimits_{i = 1}^{n - 1} {\left[ {100\left( {x_{i + 1} - x_{i}^{2} } \right)^{2} + (x_{i} - 1)^{2} } \right]}\)

[30, 30]

_F6

\(f(x) = \sum\nolimits_{i = 1}^{n} {\left( {\left[ {x_{i} + 0.5} \right]} \right)^{2} }\)

[100, 100]

_F7

\(f(x) = \sum\nolimits_{i = 1}^{n} {ix_{i}^{4} + random(0,1)}\)

[1.28, 1.28]