## 4 Devised Configuration for the Integrated WT-ACO-FFANN Based ML Forecast Model
### Ant Colony Optimization (ACO)  
ACO is a probabilistic algorithm to solve optimization cost functions that are able to be represented for searching better paths via graphs. ACO is widely applied in computer science and operations research. Its development was motivated by the behavior of ants searching for the optimal path of a food location. The pheromone-based information exchange method of real ants is generally the major modeling framework of ACO [31]. Artificial ants represent heuristic optimization techniques motivated by the action of biological ants. Hybridizations of artificial ants and search methods has become an optional technique for several optimization works containing some kind of graph, for instance, vehicle and internet routing.  
ACO is a class of AI-based metaheuristic optimization algorithms established based on the behavior of colonies of biological ants [32]. Artificial ants are the simulating agents that trace the best solutions through the exploration of a parameter domain consisting of all possible solutions. Biological ants excrete pheromones communicating with each other for food when discovering their surroundings. The artificial ants in ACO likewise save their locations and the excellence of their solutions; thus, in future search steps, additional ants discover improved solutions [33].  
To increase the forecasting performance of wind power prediction models, the ACO is employed to search the global best parameter set of the models. Specifically, in this work, the ACO technique is employed to find the optimal parameters (neuron connection weights) of the FFANN wind power forecasting model.  
The ACO algorithm builds a full-directed graph via \(n\) FFANN model parameters. Initially, \(m\) ants are arbitrarily positioned in \(n\) parameter nodes (locations). The record list \(\mathit{record}_{k}\) saves the nodes that the ants have moved to, and \(\mathit{record}_{k}\) is set for each ant \(k\). The pheromone concentration \(\xi_{ij}(0)\) at each side is initially set at \(0\). The ant chooses the following node according to the pheromone concentration at each side. The probability \(\rho_{ij}^{k}(t)\) that the ant travels from parameter \(i\) to parameter \(j\) at the \(t\) step can be expressed as follows.  
\[\rho_{ij}^{k}(t)=\left\{\begin{array}{c}\frac{\xi_{ij}^{a}(t).\eta_{ij}^{b}( t)}{\sum_{\mathit{prewards}}\xi_{ia}^{a}(t).\eta_{ij}^{b}(t)},j\
otin\mathit{record}_{k} \\ 0,\mathrm{otherwise}\end{array}\right. \tag{6}\]  
Here, \(\eta_{ij}\) is a heuristic message that is normally calculated as \(1/d_{ij}\); where \(d_{ij}\) is the Euclidean distance between two parameters, \(\xi_{ij}(t)\) is the pheromone concentration on the route from parameter \(i\) to parameter \(j\) at the \(t\) step of the ACO running, and \(\alpha\) and \(\beta\) are the message heuristic coefficient and the anticipation heuristic coefficient that are employed to allocate the weights for the heuristic  
Figure 2: Multistep WT decomposition.  
message and the pheromone concentration. When the ant finishes its travel, the message (information) concentration on each route is modified as follows.  
\[\xi_{ij}\leftarrow(1-p).\xi_{ij}+p.\sum_{k=1}^{m}\Delta\xi_{ij}^{k} \tag{7}\]  
Here, \(p\in(0,1]\) is a weight coefficient, which is called the pheromone evaporation ratio. \(\Delta\xi_{ij}^{k}\) is the pheromone improvement of the route between parameter \(i\) and parameter \(j\) while traveling, and it is described as follows.  
\[\Delta\xi_{ij}^{k}=\left\{\begin{array}{c}\frac{Q}{L_{k}}\cdot(i,j)\in route \ of\ k\\ 0,\text{otherwise}\end{array}\right. \tag{8}\]  
Here, \(Q\) is a fixed-term known as pheromone intensity, and \(L_{k}\) is the route distance of the k_th_ ant in the travel. The ACO algorithm converges when all the ants arrive at a similar solution.  
Figure 3 shows the flowchart of the ACO.  
Figure 3: Flowchart of the ACO algorithm.