## 4 PUPSO Approach with the Objective Function of LCOE
### Objective Function  
With the start of bidding in wind power markets, LCOE, as the world's most commonly used index to evaluate the cost of electricity, has been favored by participants involved in wind power projects. [PERSON] et al. suggests that LCOE can be used as a basis for setting appropriate power purchasing agreement terms [44]. Based on the LCOE method, [PERSON] et al. studied the influence of deployable operating depth and other factors on offshore wind power platforms [45]. [PERSON] et al. proposed and optimized a distributed generation by adding a shroud to the wind turbine and assessed it by LCOE [46]. In this paper, the LCOE is chosen as the objective function and can be calculated by Equation (40):  
\[LCOE=\frac{\sum_{t=1}^{n}\frac{I_{t}+M_{t}+F_{t}}{(1+r)^{t}}}{\sum_{t=1}^{n} \frac{E_{t}}{(1+r)^{t}}} \tag{40}\]  
where \(I_{t}\) are the investment expenditures in year \(t\) (including financing); \(M_{t}\) is the operations and maintenance expenditures in year \(t\); \(F_{t}\) is the fuel expenditures in year \(t\); \(E_{t}\) is the electricity generation in year \(t\); \(r\) is the discount rate; and \(n\) is the life of the system. There are four types of wind energy resource areas in China and the LCOE of each area needs to be calculated separately.  
Table 2 shows the costs and fees of the wind farm, which are estimated based on official files and engineering experiences [16]. Management expenses and measure expenses are 33.3% and 15.3% of the total labor and machinery costs, respectively. However, due to the difficulties of considering extra costs during the project, such as wind curtailment, transportation, and road construction, these factors are not considered in the optimization.  
The geometry of a PCSH wind turbine tower, including the heights of the PC and steel segments, is optimized in this paper. Figure 3 shows the cost evaluation flow chart for the PCSH tower. As illustrated in Figure 3, the function of LCOE can be determined accordingly when the design is completed.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Title** & **Item** & **Unit Price** \\ \hline \multirow{6}{*}{Direct cost} & Concrete & 600 yuan/m\({}^{3}\) \\  & Reinforcement & 5500 yuan/ton \\  & Prestressing steel strand & 14,390 yuan/ton \\  & Sheeting & 50 yuan/m\({}^{2}\) \\  & Timber support & 15 yuan/m\({}^{2}\) \\  & Metallic pipe & 679 yuan/100 m \\  & Flange & 40,000 yuan/pcs \\  & Q345 & 1000 yuan/ton \\ \hline \multirow{6}{*}{Labor cost and mechanical cost} & Reinforcement & 1500 yuan/ton \\  & Prestressing steel strand & 1000 yuan/ton \\ \cline{1-1}  & Sheeting & 300 yuan/100 m\({}^{2}\) \\ \cline{1-1}  & Timber support & 15 yuan/m\({}^{2}\) \\ \cline{1-1}  & concrete & 60 yuan/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The comprehensive cost of LCOE.  
When the particle violates the constraint, measures need to be taken to orchestrate the motion of the particle. As shown in Figure 3, the penalty term is set to 0.5, which coordinates the movement of particles within the feasible region and cannot be treated as the ultimate goal of cost calculation. When a constraint violation occurs, the checking procedure is interrupted directly and the penalty term is employed to evaluate the fitness value for enhancing the computing efficiency of the optimal algorithm.