# A Hybridized Flower Pollination Algorithm and Its Application on Microgrid Operations Planning
## 4 Application of the HSFPA for Microgrid Operations Planning
### Multi-Object HSFPA (MHSFPA) Configuring Steps  
There are several techniques dealing with the multiobjective optimal operation model, e.g., the Pareto front [50] and weighting ways [51; 52]. The Pareto optimality is used to figure out the feasible solutions of the microgrid optimization operation planning. Then, the best points are selected to provide the suitable weighting values for applying the weighting method objective function. The optimal dominance of the Pareto optimality is denoted as an \(\overset{\rightarrow}{x}\prec\overset{\rightarrow}{y}\) that is determined in the feasible solutions [53]. An optimal dominance definition as \(\overset{\rightarrow}{x}\) is the dominance solution (\(\overset{\rightarrow}{y}\)) iff: \(F_{1}\left(\overset{\rightarrow}{x}\right)<=F_{2}\left(\overset{\rightarrow}{y}\right)\) for entire feasible sites and \(F_{1}\left(\overset{\rightarrow}{x}\right)<F_{2}\left(\overset{\rightarrow}{y}\right)\) for at least a site in the feasible area.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**The Emissions** & & \(CO_{2}\) & \(SO_{2}\) & \(NO_{x}\) & \(CO\) \\ \hline \multirow{2}{*}{The coefficient/\(\left(\text{g}/\text{kW}^{-1}\right)\)} & MT & 179 & 0.00089 & 0.621 & 0.16 \\ \cline{2-6}  & FC & 635 & 0 & 0.023 & 0.054 \\ \hline \multirow{2}{*}{Related operations} & \multirow{2}{*}{\(\cos\text{ts}/\left(\text{$\$/\$/kg^{-1}\right)}\)} & \multirow{2}{*}{0.0052} & \multirow{2}{*}{0.693} & \multirow{2}{*}{1.19} & \multirow{2}{*}{0.201} \\ \cline{1-1  
The economic operation and environmental pollution costs are used to construct the multiobjective optimal operation model for the minimizing objective cost function. It means that \(F_{1}\) and \(F_{2}\) are two variables that are mutually exclusive. The environmental cost will rise as the economic cost decreases. The environmental benefits will be reduced if the economic cost is increased. However, the minimum economic cost and the maximum ecological benefit are mutually exclusive, so we use the minus technique for converting maximum environmental benefit into minimizing harm ones. The solution set in the object space is often built a ranging set 0 to 1, so a safe checking boundary is stated as the following expression:  
\[\begin{cases}S_{F_{1}}=\frac{F_{1}-F_{1}^{min}}{F_{1}^{max}-F_{1}^{min}}\\ S_{F_{2}}=\frac{F_{2}-F_{2}^{min}}{F_{2}^{max}-F_{2}^{min}}\end{cases}, \tag{27}\]  
where \(S_{F_{1}}\), and \(S_{F_{2}}\) are two solution sets of checking measure parameters \(\in\) [0, 1] as considering checking boundary factors. The meaning parameters are used with most satisfied and dissatisfied values ranging set 0 to 1 or [0, 1]. The weighting method for a multiobjective function can be expressed as follows:  
\[Min\;F_{3}=\omega\times F_{1}+(1-\omega)\times F_{2}, \tag{28}\]  
where \(\omega\) is a variable of weight considering the proportion of the relevant economic cost and the practical environmental benefits, respectively. The comprehensive benefit of the optimal solution set generated by the optimization algorithm is the chosen best sites. The best points are selected from the Pareto optimal front to provide suitable weighting values for the weight responding, respectively, facts. Figure 5 depicts the HSFPA's flowchart for planning microgrid operations.  
The optimizing applying steps of the HSFPA for the microgrid operation planning problem is described as follows:  
Step 1: Input the microgrid model parameters: \(P_{d}(t),\;P(t)\), and (T): daily load demand, power output curves, unit generating set respectively; \(C_{i}(t)\): time-of-use energy costs; and \(CO_{2},\;CO_{2},\;NO_{x},\;CO\) for MT, FC: as various pollution cost treatment factors shown in Tables 5 and 6.  
Figure 5: The HSFPA’s flowchart for microgrid operations planning.