## Two-Stage Building Information Modeling (BIM) Based Lighting Design Method
### Stage 1: Building Desing Optimziation
#### 2.1.2 Building Design Optimization  
In this study, a particle swarm optimization (PSO) algorithm was selected to generate the optimal design. This is because it has the advantages of evolutionary algorithms (i.e., inherent parallelism and the ability to exploit similarities in solutions through recombination [38]), and had the characteristics of directed mutation, population representation and operators, and others. The revised PSO algorithm used in this study ensures global convergence at a higher speed.  
As mentioned above, the two objectives of the optimization module were to minimize the project's life cycle energy (LCE) consumption and life cycle cost (LCC). The effects of the design and demolishment stages on the LCE and LCC were negligible, and data on these factors were difficult to obtain. As such, the life cycle of this study only included the construction and operation stages. Therefore, the LCE can be calculated using Equation (5):  
\[LCE=E_{cont}+E_{opt}=\sum\limits_{j=1}^{J}Q_{j}\times f_{j}+E_{sum}\times M \tag{5}\]  
In this expression, \(E_{cont}\) and \(E_{opt}\) represent the energy consumed at the construction stage and operation stage, respectively; \(j\) = 1, 2, 3,..., \(J\) is the number of building materials used in the design; \(Q_{j}\) is the quantity of the jth material; \(f_{j}\) is the energy intensity of the jth material; and \(M\) is the operation time for the project.  
Similarly, the LCC was composed of the construction cost and the operation cost. The LCC reflects cash flows at different stages, requiring the calculation of the time value of money. Consequently, all LCC elements were converted to the present value. The actual LCC was computed using Equation (6):  
\[\text{LCC}=C_{cont}+C_{opt}=\sum\limits_{j=1}^{J}(Q_{j}\times p_{j})+\sum \limits_{m=1}^{M}(C_{opt})_{m}\times(i+1)^{-m} \tag{6}\]  
In this expression, \(C_{cont}\) and \(C_{opt}\) are the costs of the construction stage and operation stage, respectively; \(p_{j}\) is the price of the jth material; and \(i\) is the real interest rate for a compounding period, which considered the effect of inflation.  
Decision variables were another important aspect of optimization. In this study, design factors, which significantly influenced lighting and thermal performances, were set as decision variables. Many studies have demonstrated that wall types, glazing types, and window-to-wall ratio were the most significant design factors [39; 40; 41; 42]. Artificial lighting types was also an important factor in illumination and energy consumption [25; 43]. Therefore, these 4 design factors were selected as the decision variables in the optimization module.  
For clients, project costs were a crucial element impacting decisions. As such, the constraints set in the optimization module included both the construction cost and the design's LCC, which cannot exceed their respective budgets.  
The output of the proposed optimization system was a Pareto-optimal solution set, which contained several optimal design schemes. The solutions were non-dominated with each other; as such, the client must select the solution that can fulfill most of the project requirements for the following processes.