Table 1 Detailed information of fourteen benchmark functions
From: UAV-aided networks with optimization allocation via artificial bee colony with intellective search
f1 | \(\sum \limits _{i = 1}^{n} {{x_{i}}^{2}} \) | [ − 100,100] | 0 |
f2 | \(\sum \limits _{i = 1}^{n} {{{\left ({\sum \limits _{j = 1}^{i} {{x_{j}}}} \right)}^{2}}} \) | [ − 100,100] | 0 |
f3 | \({10^{6}}*{x_{1}}^{2} + \sum \limits _{i = 2}^{n} {{x_{i}}^{2}} \) | [ − 100,100] | 0 |
f4 | \(\sum \limits _{i = 1}^{n} {i*{x_{i}}^{2}} \) | [ − 100,100] | 0 |
f5 | \(\sum \limits _{i = 1}^{n} {{{\left \lfloor {{x_{i}} + 0.5} \right \rfloor }^{2}}} \) | [ − 100,100] | 0 |
f6 | \(\sum \limits _{i = 1}^{n} {i{x_{i}}^{4}} + random[0,1)\) | [ − 1.28,1.28] | 0 |
f7 | \(\sum \limits _{i = 1}^{n} {\left | {{x_{i}}} \right |} + \prod \limits _{i = 1}^{n} {\left | {{x_{i}}} \right |} \) | [ − 10,10] | 0 |
f8 | \(\sum \limits _{i = 1}^{n} {{x_{i}}^{2}} + \prod \limits _{i = 1}^{n} {{x_{i}}^{2}} \) | [ − 100,100] | 0 |
f9 | max(|x1|,|x2|,...,|xn|) | [ − 100,100] | 0 |
f10 | \(\sum \limits _{i = 1}^{n} {\left [ {{x_{i}}^{2} - 10\cos (2\pi {x_{i}}) + 10} \right ]} \) | [ − 5.12,5.12] | 0 |
f11 | \(\frac {1}{{4000}}\sum \limits _{i = 1}^{n} {{x_{i}}^{2}} - \prod \limits _{i = 1}^{n} {\cos (\frac {{{x_{i}}}}{{\sqrt i }})} + 1\) | [ − 600,600] | 0 |
f12 | \(\begin {array}{l} - 20\exp (- 0.2\sqrt {\frac {1}{n}\sum \limits _{i = 1}^{n} {{x_{i}}^{2}}})\\ + \exp (\frac {1}{n}\sum \limits _{i = 1}^{n} {\cos (2\pi {x_{i}})}) + 20 + \mbox{{e}} \end {array}\) | [ − 32,32] | 0 |
f13 | \(\frac {\pi }{{30}}\mbox{{\{ }}10 \cdot \sin [1 + 0.25{({x_{1}} + 1)^{2}}] + \sum \limits _{i = 1}^{n - 1} {} \{ {{\rm {[}}0.25\left ({{x_{i}} + 1} \right){\rm {]}}^{2}} [1 + 10(\sin (\pi (1 + 0.25\left ({{x_{i + 1}} + 1} \right)){)^{2}})]\} \} + \sum \limits _{i = 1}^{n} {{y_{i}}} \begin {array}{l} {y_{i}} = \\ \left \{ {\begin {array}{*{20}{c}} {100{{({x_{i}} - 10)}^{4}}}&{{x_{i}} > 10}&{}\\ 0&{ - 10 \le {x_{i}} \le 10}&{}\\ {100{{(- {x_{i}} - 10)}^{4}}}&{{x_{i}} < - 10}&{} \end {array}} \right. \end {array}\) | [ − 50,50] | 0 |
f14 | \(\begin {array}{l} 0.1\{ {\sin ^{2}}(3\pi {x_{1}}) + \\ \sum \limits _{i = 1}^{n - 1} {{{({x_{i}} - 1)}^{2}}} [1 + {\sin ^{2}}(3\pi {x_{i + 1}})]\\ + ({x_{n}} - 1)[1 + {\sin ^{2}}(2\pi {x_{n}})]\} \\ + \sum \limits _{i = 1}^{n} {{y_{i}}} \\ {y_{i}} = \\ \left \{ {\begin {array}{*{20}{c}} {100{{({x_{i}} - 10)}^{4}}}&{{x_{i}} > 5}&{}\\ 0&{5 \le {x_{i}} \le 5}&{}\\ {100{{(- {x_{i}} - 10)}^{4}}}&{{x_{i}} < - 5}&{} \end {array}} \right. \end {array}\) | [ − 50,50] | 0 |