## 3 Research Methodology
### CLP Optimization  
In the last step of the methodology, the PSO algorithm searches for the optimum values of CLP and the factors influencing it, using the predictive model proposed in the previous section. PSO is one of the swarm intelligence-based algorithms first proposed by [PERSON] and [PERSON] [64]. PSO is simple to implement and is able to find solutions with acceptable accuracy, which makes it popular [65]. Each particle maintains three D-dimension vectors: position vector, velocity vector, and personal best vector. A particle retains its current position in position vector \(X_{i}=(x_{i}^{1},\ x_{i}^{2},\ \dots,\ x_{i}^{D})\), for \(i=1\) to \(N\) (\(N\) = number of particles). Particles obtain their initial positions randomly in the search space. Velocity vector \(V_{i}=(v_{i}^{1},\ v_{i}^{2},\dots,\ v_{i}^{D})\) of the \(i\)th particle is utilized to update its position, and the particle also obtains its initial value randomly. The best position attained by the \(i\)th particle is preserved in personal best vector and denoted as \(\textit{Pbest}_{i}=(\textit{Pbest}_{i}^{1},\ \textit{Pbest}_{i}^{2},\ \dots,\ \textit{Pbest}_{i}^{D})\). Therefore, the swarm best position is evaluated as \(\textit{Gbest}=(\textit{Gbest}^{1},\ \textit{Gbest}^{2},\ \dots,\ \textit{Gbest}^{D})\). The movement of a particle is related to updating its velocity and position attributes in the \(i\)th iteration (\(t\) = 2, 3... ), based on Equations (7) and (8). \[v_{i}^{d}(t+1)=wV_{i}^{d}(t)+c_{1}r_{1}(\textit{Pbest}_{i}^{d}(t)-x_{i}^{d}(t) )+c_{2}r_{2}(\textit{Gbest}_{i}^{d}(t)-x_{i}^{d}(t) \tag{7}\]  
\[x_{i}^{d}(t+1)=x_{i}^{d}(t)+v_{i}^{d}(t+1) \tag{8}\]  
where \(w\) is the inertia weight, \(c_{1}\) is the cognitive acceleration coefficient, \(c_{2}\) is the social acceleration coefficient, and \(r_{1}\) and \(r_{2}\) are random values between 0 and 1. Figure 2 presents a flowchart of the PSO algorithm. The objective of the optimization phase of this study contained the following goals:  
* Goal 1: Predicted CLP (\(CLP_{\textit{Pred}}\)) has minimum deviation from \"targeted CLP\" (\(CLP_{\textit{tgt}}\)), as shown in Equation (9), where \(\omega\) is the relative importance of Goal 1, compared to Goal 2. \[\text{Goal 1}=\omega\times(CLP_{\textit{tgt}}-CLP_{\textit{Pred}})^{2}\] (9)
* Goal 2: Predicted CLP factors (\(F_{\textit{Pred}}\)) have minimum deviation from \"average value of factors\" (\(F_{\textit{Avgi}}\)) in the data set, among all the possible combinations of improvement scenarios, as shown in Equation (10). \[\text{Goal 2}=(1-\omega)\times\sum_{i=1}^{n}{(F_{\textit{Predi}}-F_{\textit{ Avgi}})^{2}}\] (10)  
In Goal 1, \"targeted CLP\" is the preferable CLP that a company tries to achieve. In this study, the value of CLP is between 0 and 1 after the normalization process, and greater CLP indicates better productivity in a project. Goal 1 tries to predict CLP considering the minimum distance from the targeted CLP. Goal 2 tries to minimize changes in factors that most influence CLP. Companies mostly prefer minimum changes and corrective measures to achieve the preferable CLP because of the cost of implementing new strategies and corrective measures. In Goal 2, the average value of each factor is achieved from the existing CLP data set, which is discussed in Section 4. Since obtaining a value near the average value of each factor in the data set is feasible, the goal is to have a minimum distance between the average and optimum values for each factor.