Wind Driven Optimization Algorithm (WDO)
The WDO was developed by Bayraktar et al. [12-14]. The core equations of WDO are inspired by the wind in the Earth’s atmosphere where the motion of an infinitesimally small air parcel is analyzed. To find the velocity and position displacement of the air parcel, the Newton’s second law of motion is used. There are four major forces that can either cause the wind to move in a certain direction or deflect it from its existing path. These forces are the pressure gradient force, the friction force, the gravitational force and the Coriolis force. The physical equations that govern each of these forces and detailed descriptions are given in [13]. The sum of these forces can be inserted into Newton’s second law of motion and then the velocity and position displacement of each air parcel can be computed. The parcel’s velocity is calculated using the following equation [14]:
(33)
where is the current iteration velocity, is the current position of the air parcel in the search space, is the optimum position of the air parcel’s in the search space at the current iteration, irepresents the ranking among all air parcels (the best solution has the lowest pressure with rank 1), is the velocity in one of the other dimensions, α is the friction coefficient, g is the gravitational constant, R is the universal gas constant, Tis the temperature, and c is a constant that represents the rotation of the Earth. The coefficients α , g , RT , and c are the algorithm parameters that must be specified prior to starting an optimization.
At each iteration, the velocity and the position of all parcels need to be updated. Once the new velocity is calculated according (33), the position can be updated as follows:
(34)
where is the new position of the air parcel in the search space for the next iteration.