## 8 Load Optimization and Scheduling
### Scheduling Algorithm  
For researchers, nature is a wonderful source of imagination and inspiration for solving complex scientific problems in every domain. There have been different nature-inspired heuristic optimization algorithms proposed, such as genetic algorithm (GA) [40], differential evolution (DE) [41], particle swarm optimization (PSO) [42], ant colony algorithm (ACO) [43], cuckoo search (CS) [44], _etc._ These algorithms are successfully implemented, and satisfactory results are obtained. However, every algorithm has some pros and cons, and it is impossible that each algorithm from the nature-inspired family best solves all types of problems [45].  
The WDO is a novel and nature-inspired global optimization algorithm based on the atmospheric motion of wind particles. Moreover, it is a population-based iterative and heuristic optimization technique, in which constraints can be implemented in search domains, as compared to other heuristic algorithms (GA, PSO, _etc._). Infinitely small air particles move in an n-dimensional domain using [PERSON]'s second law of motion, which can also be used to analyse the motion of air particles in the Earth's atmosphere. Another major difference between WDO and other heuristic algorithms is additional velocity update parameters (gravitation and Coriolis forces), which lead to fast convergence [46,47]. Due to the three-dimensional coordinate system of our atmosphere, gravitational force \(F_{g}\) is a vertical force acting on the air particles to confine them to the centre.  
\[F_{G}=\rho\;\delta Vg \tag{20}\]  
The Coriolis force is included in the WDO algorithm due to the fact that the movement of air particles in the x-direction has a direct effect on the y-direction. Therefore, in the n-dimensional search space, this phenomenon is randomized. Mathematically, Coriolis force \(F_{C}\) can be defined as:  
\[F_{C}=-2(\Omega\times v) \tag{21}\]  
where \(\Omega\) and \(v\) denote the Earth rotation and velocity vector of the air particles, respectively. Now, it is clear that during the movement of air particles, the current position and \(v\) are updated using [PERSON]'s second law of motion. In WDO, the position and \(v\) of all air particles are updated with every movement of time. The velocity update equation can be written as:  
\[v_{new}=\underbrace{\left((1-\alpha)\times v_{old}\right)}_{1}-\underbrace{gx _{old}}_{2}+\underbrace{\left[\left|\frac{P_{max}}{P_{old}}-1\right|RT(x_{max}- x_{old})\right]}_{3}-\underbrace{\left[\frac{c\times v_{old}}{P_{old}}\right]}_{4} \tag{22}\]  
where the details of Equation (27) are given as follows:  
1. The first term shows that the air particles continue their movements to the previous path with some opposition of frictional force.
2. The second term is gravitational force, which attracts the air particles to the centre (in the coordinate system).
3. The third term describes the force exerted on air particles to move them towards the highest pressure location, which is the global best position in the WDO optimization problem.  
4. The fourth term shows the Coriolis force, which is a deflecting force, because the movement of air particles in one direction is affected by the movement in the second direction. Similarly, in PSO, weights \(w_{1}\) and \(w_{2}\) are used to control the movement of air particles in order to find the global best position.  
The variables used in the velocity update equation and WDO algorithm are given in Table 2. The pressure term used in the WDO algorithm is similar to the fitness term used in GA or PSO. However, the WDO algorithm consists of infinitely small air particles moving towards the highest pressure point in the _n_-dimensional search space. The new position of the air particles can be obtained after the velocity update (Equation (27)).  
\[x_{new}=x_{old}+(v_{new}\times\Delta t) \tag{23}\]