The elements of this formula are calculated as follows. First, the values of the power spent by the cyclists, according to Eq. (6), are ranked. Then, the two weight coefficients for drag and gravitational power, \(k_{d}\) and \(k_{g}\), shown in Eq. (11), are calculated by normalizing \(F_{d}\) and \(F_{g}\) between 0.5 and 1.0, where 1.0 represents the cyclist with the lowest power.
Regarding the drag component, \(k_{d}\), this procedure reduces the step taken by the leading cyclists, which are closer to an optimal solution, thus resulting in a more specific local search around the leader position, \(X_{d}\), while the latter cyclists are rapidly pushed towards this point to benefit from the leaders drag.
With the gravitational component, \(k_{g}\), the purpose is to encourage the cyclists that are rapidly converging to a better solution,\(X_{g}\), to keep going in this direction, while cyclists going uphill or slowly improving are kept to explore with a more local search focus around their place.
Finally, instead of an inertia coefficient, as used in PSO, the gravity coefficient \(k_{g}\) is also used to give a weight to the cyclist current direction. Random values are also used to avoid a biased search.
The flowchart in Figure 1 summarizes the GTA optimization process.