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# Table 5 Linear and non-linear functions

From: An efficient population-based multi-objective task scheduling approach in fog computing systems

Name | Function | Possible Effect | Diagram |
---|---|---|---|

Linear |
y=2−2x
| In the first half of the iterations, WOA is mostly devoted to global exploration, while in the other half iterations, it is mostly devoted to local exploitation. | |

Beta1 |
y=2−2x^{3}
| In more than half of the iterations, WOA is devoted to global exploration (about 4/5 of the iterations), while in the other iterations, it is devoted to local exploitation. Better global exploration capability. | |

Beta2 | \(y= 2 - \sqrt {4 - 4(x-1)^{2}}\) | In more than half of the iterations, WOA is devoted to local exploitation(more than 4/5 of the iterations), while in the other iterations, it is devoted to global exploration. Better local exploitation capability. | |

Beta3 | \(y = \left \{\begin {array}{lll} Beta1 & \qquad \text {if } x \leq 0.5 \\ Beta2 &\qquad \text {Otherwise } \\ \end {array} \right.\) | In the first half of the iterations, WOA is strictly devoted to global exploration, while in the other iterations, it is strictly devoted to local exploitation. | |

Beta4 | \(y = \left \{ \begin {array}{lll} Beta2 & \qquad \text {if } x \leq 0.5 \\ Beta1 &\qquad \text {Otherwise } \\ \end {array} \right.\) | In the first quarter of the iterations, WOA is devoted to global exploration, in the second quarter of the iterations, it is devoted to local exploitation. In the third quarter of the iteration, it is devoted to global exploration, while in the last quarter of iterations, it is devoted to local exploitation. |