Here \(g\) is the acceleration of gravity, \(I\) is the slope, defined
as the difference between the values for the objective function in two
successive iterations, and \(m\) is the cyclist mass.
As previously described, the objective function represents the
(vertical) distance to the finish line. And, as the race is downhill,
towards the minimum, the objective function is also the elevation of the
cyclist’s place on the terrain with respect to the minimum. Thus, when
cyclists are going downhill (negative slope), they need to put less
power, because the gravity is aiding. In contrast, a cyclist’s weight
causes an opposite force to the movement. This procedure avoids cyclists
to go uphill (positive slope), towards a worst solution, because they
would spend too much power in this case.
The value of the gravitational acceleration is constant, and the
cyclists’ mass is randomly defined at the beginning, in a range from 50
to 80 kg. This procedure allows lightweight cyclists, known as climbers,
not to be hardly affected by going uphill, i.e., with a direction
towards a worse solution. This guarantees better search capabilities.