## 2 Methods  
### ANN based Many-Objective Optimization Design Workflow  
The ANN based many-objective optimization design method includes three subprocesses: optimization design problem determination, ANN prediction modeling and many-objective optimization, as shown in Figure 1.  
Firstly, the designer should determine the optimization objectives, decision variables and constraints according to the conditions and requirements of the building design case. In this paper, Energy Use Intensity (EUI), Spatial Daylight Autonomy (sDA), Useful Daylight Illuminance (UDI) and Building Envelope Cost (BEC) were defined as four objectives to improve the energy, daylighting and cost performance of a large-scale public building. Ten building envelope design parameters were selected as decision variables and each within a certain constraint. Secondly, ANN models for EUI, sDA and UDI prediction were developed through four steps: step 1, Latin Hypercube Sampling (LHS) was used to get the samples of feasible solutions from the design space; step 2, a parametric simulation model was established based on the decision variables of the samples and with the consideration of objectives; step 3, energy and daylight simulations were performed for each sample and step 4, with the samples as the input data and the simulation results as the output data for ANN training, ANN models for EUI, sDA and UDI prediction were developed and trained. The prediction accuracy of the ANN models was optimized by minimizing the Mean Square Error (MSE) between the prediction and simulation results of the training data at the same time maximizing the correlation coefficients (R) between the prediction and simulation results of the validation data. Finally, BEC was calculated by adding up the cost of walls, windows and roofs, and the calculation program along with the ANN prediction models were coupled with the optimization engine to obtain the non-dominated solution set. To support the ANN based many-objective optimization design workflow, an optimization design model was developed based on the Rhinoceros and Grasshopper platform to achieve the process of ANN prediction modeling and many-objective optimization. Compared with MATLAB, modeFRONTIER, GenOpt and other non-architectural platforms, the Rhinoceros and Grasshopper platform has a friendly visual programming interface, and is widely used by architects. The proposed model is composed of five modules, which are the Latin Hypercube Sampling module, Parametric Simulation Modeling module, Energy and Daylight Simulation module, ANN Modeling and Training module and the Many-Objective Optimization module. Various software and plug-ins have been coupled with each other in the proposed model, as shown in Figure 2.  
1. Latin Hypercube Sampling module coupled Grasshopper components with the Design Space Exploration (DSE) plug-in, and a given number of samples that well represented the feasible solutions could be generated by performing LHS in the design space. The output data of this module was the decision variable values of the samples. 2. Parametric Simulation Modeling module coupled Grasshopper components with Honeybee plug-in, with the decision variable values of the samples as input data, a thermal zone model of the reference building could be built and sent to the Energy and Daylight Simulation module. 3. Energy and Daylight Simulation module coupled Grasshopper components, Ladybug and Honeybee plugin, energy simulation tool of EnergyPlus and daylight simulation tools of Radiance, Daysim. Energy and daylight simulation parameters were set by Grasshopper as well as Ladybug and Honeybee components, then simulations were performed with EnergyPlus, Radiance and Daysim. The output data of this module was the EUI, sDA and UDI values of the corresponding samples and was sent to the ANN Modeling and Training module. 4. ANN Modeling and Training module coupled grasshopper components, Crow and Octopus plug-ins.