


\chapter{Methodology for simulations}
\label{ch:Methodology for simulations}

Before the examination, we prepare the climate data base. For the present data we can download from EPWmap\cite{EPWMap}. However, for the predicted climate data in 2050s, we have to use a method \cite{CCWorldG,CCWorldG_Website} to predict it, which we will introduce in \cref{sec:Prediction for future climate}.

~\\
In the examination, we conduct 4 calculations, whose methodologies will be presented in the referring section:

\begin{itemize}
\setlength{\itemsep}{1pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}

\item \textbf{\glsxtrlong{EUI}} in \cref{sec:Approach for Energy simulation}
\item \textbf{Lighting} in \cref{sec: Approach for lighting simulation}
\item \textbf{Costing} in \cref{sec: Approach for economical analysis}
\item \textbf{Comfort metric} \cref{sec: Approach for comfort metrics}
\end{itemize}

in order to get the 3 \textbf{fitness values}.

~\\
And 1 \textbf{optimization}. in \cref{sec: GA in arhitecture design and NSGA-II}


~\\
The \glsxtrshort{EUI}, comfort metric and the optimization are conducted under the complete and mature programs, i.e. \glsxtrshort{EP} and \glsxtrshort{OS}\cite{OpenStudio_ow,EP}; \glsxtrshort{LBT}\cite{PollinationLB}; Wallacei\_X\cite{WALLACEI}.

~\\
The lighting simulation we operate with \glsxtrshort{HB} Radiance and also our arithmetic is combined\cref{eq:RoomIndex,eq:MaintenanceF,eq:IlluminaceLevel,eq:Efficay}. The economic simulation is calculated fully under our arithmetic\cref{eq:LCC,eq:GloblalCost,eq:GloblalCost2,eq:NPV}. This chapter is aiming at introducing these.



\section{Prediction for future climate}
\label{sec:Prediction for future climate}

Simulations are conducted utilizing weather files that incorporate climate projections for the year 2050, adhering to the A2 emissions scenario delineated in the Special Report on Emissions Scenarios (SRES) \cite{101} and other IPCC reports\cite{102}. The SRES articulates four principal scenario families—A1, A2, B1, and B2—encompassing a total of forty distinct scenarios. Each scenario envisions a different possible future trajectory for global development up to the year 2100, taking into account a multitude of factors such as demographic shifts, social, economic, and technological advancements, energy consumption patterns, and land-use changes, which collectively drive greenhouse gas emissions. ``Among these scenarios, the A2 scenario represents a high-impact future (though not the most severe), characterized by a substantial and continuously growing global population, a sluggish pace of technological and economic development (predominantly region-focused), and a pronounced reversion to coal utilization. These driving forces lead to a continuous rise in GHG emissions throughout the entire time horizon to 2100 \cite{101}, the highest projection among the four scenarios.''\cite[39]{rhino-gh} As expected, this scenario results in the highest temperature rise – see the \cref{fig:4Scenario}. 

\begin{figure}[h]
	\centering
	\includegraphics[width=\linewidth]{images/tables/IPCCProjections.jpg}
	\caption{4 Scenarios from Global warming report\cite{101}}
	\label{fig:4Scenario}
	\hfill
\end{figure}

~\\

Selected the scenario, we followed the instruction from Climate change world weather file generator manual \cite{CCWorld_Manual}, whose method is based on previous study around 2000\cite{CCW_3,CCW_4}.


\section{Approach for Energy simulation}
\label{sec:Approach for Energy simulation}
The main body of the exam is to do the \glsxtrfull{EI} simulation. Because it is difficult to do the \glsxtrshort{EI} simulation with a large amount of input parameters. We spend many steps, those introduced in \cref{ch:Methodology_B}, to complete and attune the parameters. So, the approach is congruent with the main work flow, and will be introduced in \cref{ch:Workflow}. 
But there's a lighting part that relates to the \glsxtrshort{EI}we can present here.



~\\
\subsection{Math of thermal transmittance}
\label{subsec:Math of thermal transmittance}
However, the basic formula to describe the thermal transmittance\cite{thermal_trans} is not difficult and can be written as follow \cite{thermal_trans}:


\begin{equation}
 \label{eq:thermal_U}
    U = \frac{1}{R_t}
\end{equation}

\begin{equation}
 \label{eq:thermal_Rt}
    R_t = R_{si} + \sum_{i=1}^{n}\ R_{i} + R_{se}
\end{equation}

\begin{equation}
 \label{eq:thermal_R}
    R = \frac{D}{\lambda}
\end{equation}

where:
\begin{conditions}
    U & Thermal Transmittance (W/m²·K) \\
    R_t & Total Thermal Resistance of the element (m²·K/W) \\
    R_{si} & Interior Surface Thermal Resistance (according to climatic zone) \\
    R_{se} & Exterior Surface Thermal Resistance (according to climatic zone) \\
     R_{i} & Thermal Resistance of i-th layer \\
    D & Material Thickness (m) \\
    \lambda & Thermal Conductivity of the Material (W/K·m)
\end{conditions}

~\\
This only consider one-dimensional situation, in reality, the heat transfers 3-dimensionally, see \cite{ThermalBridge,ThermalBridgeISO}. So we use the simulation program to help.

~\\
In the formula, we can see 2 main factors effect on \textit{\glsxtrshort{U-value}} the thermal transmittance, i.e. $\lambda$ and D. Those are the main role we consider for the insulation. And we further study it in \cref{sec:static-design}. And also because of this, D the thickness is one of the \textbf{objective} for optimization.





\section{Approach for lighting simulation}
\label{sec: Approach for lighting simulation}

\textbf{Lumen Method Calculations:}
~\\
This method\cite[p.~4]{LightingDG} uses ``the utilisation factor tables created from photometric measurement of each luminaire. Firstly, the Room Index (K) of the space must be calculated'', which is the relationship and measure of the proportions of the room:

\begin{equation}
    \label{eq:RoomIndex}
K=\frac{W\cdot L}{(W+L)\cdot H_{m}}
\end{equation}

where:
\begin{conditions}
 K      &   length of room \\
 W    &  width of room \\   
H_{m}    &  height of luminaire above working plane \\
\end{conditions}


With ``the room index and reflectances we can search for the utilisation factor in the table''\cite[6]{LightingDG}.

%\begin{comment}
\begin{table}[!ht]
\label{ch:RoomIndex}
    \centering
    \begin{tabular}{|ccc|ccccccccc|}
    \hline
    \toprule
    & \multicolumn{2}{c|}{Reflct.}  & \multicolumn{8}{c|}{Room Index} &\\ \hline
             C & W & F & 0.75 & 1.0 & 1.25 & 1.5 & 2.0 & 2.5 & 3.0 & 4.0 & 5.0 \\ 
     \midrule
        70 & 50 & 20 & N/A & 66 & 72 & 76 & 81 & 85 & 87 & 90 & 92 \\ 
        70 & 30 & 20 & N/A & 60 & 66 & 71 & 77 & 81 & 84 & 87 & 90 \\ 
        70 & 10 & 20 & N/A & 56 & 62 & 67 & 73 & 78 & 81 & 85 & 88 \\ \hline
        50 & 50 & 20 & N/A & 64 & 70 & 73 & 79 & 82 & 84 & 87 & 89 \\ 
        50 & 30 & 20 & N/A & 59 & 65 & 69 & 75 & 78 & 81 & 84 & 86 \\ 
        50 & 10 & 20 & N/A & 56 & 61 & 66 & 72 & 76 & 78 & 82 & 85 \\ \hline
        30 & 50 & 20 & N/A & 63 & 68 & 71 & 76 & 79 & 81 & 83 & 85 \\ 
        30 & 30 & 20 & N/A & 58 & 64 & 68 & 73 & 76 & 78 & 82 & 83 \\ 
        30 & 10 & 20 & N/A & 55 & 61 & 65 & 70 & 74 & 76 & 80 & 82 \\ \hline
        0 & 0 & 0 & N/A & 53 & 58 & 62 & 67 & 71 & 73 & 76 & 78 \\ \hline
        ~ & BZ & ~ & 1 & 2 & 2 & 2 & 2 & 2 & 3 & 3 & 3 \\ 
    \bottomrule
    \end{tabular}
    \caption{Utilisation factor to search}
\end{table}
%\end{comment}


The first 3 columns are the reflectances, the rest on the right are the room index in first row.
The last row are the BZ-class level, and where:
\begin{conditions*}
Reflct. & Reflectance\\
 C      &   Ceiling reflectances\\
W    & Wall reflectances \\   
F      &   Floor reflectances\\
BZ     &  British zonal classification\cite{Lynes1979}\\
\end{conditions*}



The result is used in conjunction with room reflectance values to obtain a  pecific utilisation factor for the surface illuminated from the tables.
This can then be used as part of the calculation to determine the average illuminance level, using the following formula:

\begin{equation}
    \label{eq:IlluminaceLevel}
E=\frac{F\cdot n\cdot N\cdot F_{M}\cdot F_{U}}{A}
\end{equation}

where:
\begin{conditions}
E & average luminance\\
F & initial lamp lumens\\
n & number of lamps in each luminaire\\
N & number of luminaires\\
F_{M} & maintenance factor\\
F_{U} & utilisation factor\\
A & area\\
\end{conditions}

The maintenance factor is a multiple of factors and is determined as follows:

\begin{equation}
    \label{eq:MaintenanceF}
F_{M} = F_{LLM}\cdot F_{LS}\cdot F_{LM}\cdot F_{RSM}
\end{equation}

where:
\begin{conditions*}
F_{M}    & \textit{maintenance factor}\\
F_{LLM}  & \textit{lamp lumen maintenance factor} - the reduction in lumen output after specific burning hours\\
F_{LS}   & \textit{lamp survival factor} - the percentage of lamp failures after specific burning hours\\
F_{LM}   & \textit{luminaire maintenance factor} - the reduction in light output due to dirt deposition on or in the luminaire\\
F_{RSM}  & \textit{room surface maintenance factor} - the reduction in reflectance due to dirt deposition in the room surfaces\\
\end{conditions*}

From now on, the quantity of lumen we need to produce in the light source is clear. We just need to convert it into energy usage. 

\begin{equation}
\label{eq:Efficay}
LEUI = \boldsymbol{\eta}^{-1}\cdot Lumen
\end{equation}
where the $\eta$ symbolizes efficacy, which is assumed to \cite{LedEfficacy} 100 lumen per watt. With it we can finally calculate the \glsxtrshort{EUI}.



\section{Approach for economical analysis} 
\label{sec: Approach for economical analysis}

We can know the methodology of evaluating a building or a project from theoretically to practically from the book\cite{fregonara2018evaluation}, which also gives us how the methodology has been developed.

The \glsxtrshort{LCC} approach advances the principles of "technical and economic" assessment of design/technology alternatives in case of works in the construction field. It is based on a research line developed in the United States in the 1960s and 1970s, which spread to other countries\cite[p.~79]{fregonara2018evaluation}. To encourage the development of this methodology, several factors must act together, like the cultural context in which it operates, its full maturity on the level of legislation, the support of the owners and the awareness of its limitations by using cost of construction as understood in the traditional sense (see \cite{Valutazione_valorizzazione}).
\glsxtrshort{LCC} allows one to determine the total cost of the project considering its entire life cycle\cite[p.~80]{fregonara2018evaluation}. The total cost could include its planning, design ,use, management, maintenance, disposal, the residual value must be included, considering it as possible income (see \cite[sections 3.1.4 and 4.4.7]{ISO_15686-5}).

In order to calculate the \textbf{cost} as the fitness values, we need to dive into the formula, and realize it in the \glsxtrshort{GH} platform.
With \glsxtrshort{LCC} method we can evaluates the project value in a future period. And the formula is as followed:

\begin{equation}
    \label{eq:LCC}
    LCC=\sum_{t=0}^{N}\frac{C_{o}+C_{m}}{{(1+r)}^{t}}\pm V_{r}\left (\frac{1}{(1+r)^{N}}\right )
\end{equation}
where:
\begin{conditions}
 LCC      &  Life Cycle Cost \\
 C_{i}    &  investment costs \\   
 C_{o}    &  operational costs \\
 C_{m}    & maintenance costs \\
 t        & the year when the cost is incurred \\
 N    & the number of years of the entire period considered for the analysis \\
 r    & discounted rate \\
 V_{r}    & residual value of the asset, materials or components \\
\end{conditions}

A diversity of "evolutions" of the mathematical models are presented, all of which come from the basic formula (see \cite{ISO_15686-5,Task_Group_4,D.Landon}). It can be generalized into mathematical model by distinguishing between continuous cost and the discontinuous ones.
And including costs for the substitution of building components or refurbishing of the envelop\\
es, etc. 

the formula can be written:


\begin{equation}
    \label{eq:NPV}
    NPV=c_{0}+\sum_{i}^{n} \sum_{t=0}^{T}c_{it}(1+r_{it})^{-t}+\sum \sum c_{jt}(1+r_{jt})^{-t}-d(1+r_{d})^{-T}
\end{equation}

where:
\begin{conditions}
 NPV      &  Net Present Value \\
 c_{0}    &  the \textit{procurement cost} at 0 moment in time\\   
 c_{it}    &  the annual cost of a period t support of the function i \\
 c_{jt}    & the cost at a moment t in time which refers the discontinuous costs j\\
 r_{it}     & discount rates applicable to support respectively the i function\\
 r_{jt}     & discount rates applicable to support respectively the j function\\
 d    & value of the asset to be disposed minus disposal costs \\
 r_{d}    & discounted rate applicable to the disposal of asset in period from 0 to T\\
\end{conditions}


However, we don't need to actually calculate the NPV for all the components, because our aim is the cost. In other words, we just need to calculate all the cost parts. That is, to calculate the initial cost and add up all the NPV for the future costs.
Notably, \glsxtrshort{LCC} are generally difficult to evaluate because the are significantly variable in terms of the discount and inflation rate, durability of the materials the number of substitutions needed and maintenance cycles during the useful life of the building (in this case expressed in the for of replacement and maintenance costs). Obviously, the actual estimation of the Global Cost depends on the availability of all the data necessary of each project/technology alternative, using methods such as the "stratigraphy" of costs. In our study this weakness is scaled up, as the financial state and material market diverse, and also the costs of labor vary. But at least, within the \glsxtrshort{EU} it's comparable. And also the methodology is universally adopted which can be apply in different environments, once we've input the value with higher accuracy, more assured result we can obtain. Lastly, using a same price database makes our result numbers in a similar scale. In a single study that benefits in the comparability and legibility.

~\\
This method can be extended into a deeper financial realm with a more cohesive GA. E.g. I can set leverage rate as a genotype, so the investment strategy would be optimized. More financial calculation can be brought in this mechanics. The matter is the balance whether the study is leaned more to the economy side or the energy simulation side. And also considered a bad legibility for too many financial numbers. I just keep a basic formula in the method, preserving it as simple as clear.

Considering only for the cost, formula turns into a direct way, only to calculate the Global Cost:
\begin{equation}
    \label{eq:GloblalCost}
 C_{G}(\tau) = C_{I} +\sum_{j} \left [ \sum_{i=1}^{\tau} \left (C_{a,i}(j)\cdot R_{d}(i)  \right ) - V_{f,\tau}(j)\right ]
\end{equation}
\begin{equation}
    \label{eq:GloblalCost2}
R_{d}=\frac{1}{(1+R_{r})^{p}}
\end{equation}

where:
\begin{conditions*}
 C_{G}(\tau)   &  the Global Cost, referred to in the initial year $\tau_{0}$ \\
 C_{I}         &  initial investment cost\\   
 C_{a,i}(j)    &  the annual cost at year i, for the j component (including running costs and the periodic or replacement costs)  \\
 R_{d}(i)        & the discount rate at the year i\\
 V_{f,\tau}(j)   & the final value of the j component at the end of the calculation period (referred to the initial year $\tau_{0}$)\\
 R_{d}    & discount factor\\
 R_{r}     & real discount rates \\
 p    & the reference period\\
 
\end{conditions*}
And in \cref{eq:LCC,eq:NPV,eq:GloblalCost,eq:GloblalCost2}, we can refer to \cite{EU-BankRate} for the market interest rate in real time. The bank rate flunctuates violently in 2023. But at the moment we began the experiment, this rate is 3.25\%, which is solidized in the to all the simulations and stay fixed to the end.



\section{Approach for comfort metrics}
\label{sec: Approach for comfort metrics}

Comfort, fundamental to human physical and mental well-being, stands as a primary gauge within the built environment\cite{107}. Given that individuals spend approximately 85\% of their lifetimes indoors\cite{84}, the microclimate indoors becomes a pivotal concern in architectural design, profoundly impacting occupants’ wellness, health, mood, productivity, work performance, and energy utilization. Indoor comfort, an amalgamation of thermal, visual, and acoustic elements, is subject to the influence of diverse environmental factors including temperature, humidity, lighting, and air quality. The model delineated in this study revolves around predicting occupants’ thermal and visual comfort by evaluating multiple parameters signifying individual satisfaction and adherence to regulatory benchmarks.

Initially, our primary focus was on investigating thermal comfort, particularly emphasizing the study of winter thermal comfort within the zone by conducting the \glsxtrshort{EP}energy simulation. Although our attention does extend to both thermal comfort and visual comfort, our primary emphasis remains directed towards understanding and enhancing winter thermal comfort. Design strategies that optimize one might inadvertently affect the other. For instance, a reduction in \glsxtrshort{WWR} could ostensibly enhance the building envelope's thermal performance. Paradoxically, this reduction may curtail daylight ingress, leading to escalated energy usage for artificial lighting. Conversely, elevating \glsxtrshort{WWR} could augment visual comfort while potentially increasing heat transfer through transparent surfaces, potentially culminating in excessive thermal dissipation or overheating, thereby amplifying energy requirements for heating/cooling systems.

This intertwined relationship underscores the indivisibility of control over thermal and visual comfort. Consequently, both facets are incorporated into consideration to provide a more comprehensive depiction of indoor comfort dynamics.


\subsection{Thermal comfort}
\label{subsec:Thermal comfort}
The \glsxtrfull{ASHRAE} Standard-55\cite{108} defines thermal comfort as ``that condition of mind that expresses satisfaction with the thermal environment and is assessed by subjective evaluation.''\cite[47]{rhino-gh} Hence, the perception of thermal comfort is highly individualistic, influenced by various personal factors like age, physical attributes, habitual tendencies, and acclimatization to specific climates. Essentially, these comfort-determining parameters may elicit different responses and sensations among individuals. However, established scientific methodologies enable the estimation of user satisfaction or dissatisfaction within a given environment. Two prevalent comfort models exist in literature: static (or steady-state) and adaptive\cite{109}.

The former, often referred to as the rational or heat balance model\cite{110}, was developed by P.O. Fanger in the early 1970s\cite{111}. This approach is widely employed in both national and international standards (e.g., ISO-7730:2005 \cite{112}) for evaluating indoor comfort. According to Fanger's model, thermal sensation emerges from the ``difference between the internal heat production and the heat loss to the actual environment for a person maintained at the comfort values for skin temperature and sweat production at the current activity level'' \cite{111}. ``Thermal comfort is influenced by six variables, four of which are environmental (air temperature, mean radiant temperature, relative humidity, and airspeed), while the other two are physiological (clothing insulation and activity level or metabolic rate).''\cite[46]{rhino-gh}

The collective impact of these variables on comfort is commonly assessed through the \glsxtrshort{PMV} index and the \glsxtrfull{PPD}. ``\glsxtrshort{PMV} is derived from a complex mathematical equation formulated based on controlled climate chamber experiments under stable conditions and regulated environmental (e.g., temperature, humidity, etc.) and physical variables (e.g., clothing).'' \cite[47,48,49]{rhino-gh}


\subsection{Predicted Mean Vote}
\label{subsec:Predicted Mean Vote}
It represents the average mean vote on thermal sensation of a group of people in a given environment. ``Mean vote can be associated with a seven-point scale that ranges from -3 (very cold) to +3 (very hot); 0 represents thermal neutrality. \glsxtrshort{PPD}, instead, is a statistical index that expresses the percentage of people in that same environment who are not satisfied with the indoor thermal conditions. ISO 7730 regulation suggests that \glsxtrshort{PPD} should be kept around 10\%, which corresponds to a \glsxtrshort{PMV} between -0.5 and +0.5.''\cite[47,48,49]{rhino-gh}


The static comfort model, as previously delineated, finds its application primarily within fully conditioned buildings where a controlled and stable indoor climate is rigorously upheld, relatively detached from the considerably variable outdoor conditions. ``Conversely, in naturally ventilated buildings where indoor temperatures continuously fluctuate in response to outdoor variations, Fanger’s method proves unsuitable, potentially introducing inaccuracies in evaluating occupants’ thermal perception.''\cite[47,48,49]{rhino-gh} De Dear et al. revealed substantial disparities between computed \glsxtrshort{PMV} values and actual comfort ratings in naturally ventilated structures, assembling the \glsxtrshort{ASHRAE} RP-884 thermal comfort database\footnote{RP-884 project represents a quality-controlled database built up assembling 21,000 samples from
thermal comfort field studies in 160 buildings, both naturally ventilated and with \glsxtrshort{HVAC} systems, across
different climate regions all over the world.} \cite{113,114}. Fundamentally, such contexts exhibit a tendency for the \glsxtrshort{PMV} index to overestimate occupants’ dissatisfaction, particularly in warmer conditions\cite{110}. This discrepancy may be attributed to occupants of naturally ventilated buildings under diverse climatic settings accepting a broader spectrum of comfort temperatures than presupposed by the heat balance model – as detailed in, for example, \cite{115}. Furthermore, occupants play an active role, adapting to dynamic thermal conditions by modifying clothing or adjusting openings when temperatures are less conducive. The adaptability of occupants underscores that maintaining indoor environments at uniform temperatures stipulated by standards can result in superfluous energy consumption and, paradoxically, discomfort (such as overheating during winter or excessive coldness in summer due to air conditioning). Even in buildings with advanced \glsxtrshort{HVAC} systems, discontentment with thermal environments remains prevalent \cite{110}.


``To address the limitations of the \glsxtrshort{PMV} method in free-running buildings, adaptive comfort models emerged, founded upon extensive field studies conducted in authentic settings. These investigations yielded a significant finding that the comfort (or neutral) temperature demonstrates a robust correlation with the prevailing outdoor mean temperature, as illustrated in \cref{fig:Neutral-temperatures}. Specifically, the neutral temperature aligns with the indoor operative temperature, itself subject to fluctuations mirroring changes in the mean outdoor air temperature.''\cite[49,50]{rhino-gh}

\begin{figure}[h]
    \centering
	\includegraphics[width=\linewidth]{images/tables/Neutral-temperatures-for-buildings-in-FR-mode-against-the-prevailing-mean-outdoor.png}
	\caption[Neutral temperatures for buildings in \glsxtrshort{FR} mode against prevailing mean outdoor temperature]{Neutral temperatures for buildings in \glsxtrshort{FR} mode against the prevailing mean outdoor temperature. Optimal comfort temperatures calculated from EN 15251 (single thick line) are shown for comparison though the outdoor temperature here is expressed in terms of prevailing mean temperature rather than the running mean so the comparison is only indicative. Source: Humphreys et al. (2010).}\cite{116,117}
	\label{fig:Neutral-temperatures}
    \hfill
\end{figure}

\subsection{Adaptive comfort}
\label{subsec:Adaptive comfort}
Adaptive comfort principles have integrated into various national and international regulations, including the American \glsxtrshort{ASHRAE} Standard-55\cite{108} and the European\glsxtrshort{CEN} Standard EN 15251\cite{118}, subsequently succeeded by EN 16798-1:2019\cite{119}. Notably, the latter standard specifies that the ``adaptive method only applies for occupants engaged in sedentary activities without stringent clothing regulations, where occupants primarily regulate thermal conditions by manipulating building envelope elements (e.g., windows, ventilation flaps, roof lights)'' (\cite[p.19]{118}). Therefore, the adaptive comfort model does not encompass considerations for clothing insulation, metabolic rate, or \glsxtrfull{RU}, despite the extensive investigations into \glsxtrshort{RU}'s influence on thermal comfort perception.

Although \glsxtrshort{RU}'s significance in comfort perception has been extensively explored, studies by Nicol\cite{120} and De Dear\cite{121} suggest its impact is generally minor and insufficient to significantly affect comfort. Givoni (2011) underscores the predominantly psychological nature of humidity's effect in a personal communication (\cite[p.58]{110}), with climatic adaptation playing a substantial role in its perception. However, in naturally conditioned buildings, outdoor \glsxtrshort{RU} profoundly influences internal humidity and, being beyond occupants' direct control, is anticipated to affect their thermal sensation, as evident in Vellei et al.\cite{109}. This research for the first time indicates that incorporating \glsxtrshort{RU} into the adaptive model causes a shift in the comfort range, indicating higher comfort temperatures and steeper gradients than predicted by the \glsxtrshort{ASHRAE} standard. Notably, elevated \glsxtrshort{RU} levels (>60\%) exhibit a pronounced impact, resulting in lower comfort temperatures and a narrower acceptability range\cite{109}.


Here, we derive the \glsxtrshort{RU} value post \glsxtrshort{EUI} simulation using the \textit{\glsxtrshort{HB} Read Room Comfort Result} component. Considering Torino as an example, we observe that during less than 9.7\% of all the hours, the \glsxtrshort{RU} exceeds 60\%. Given that our simulations do not encompass cities with excessively high humidity, we can reasonably assert the accuracy of the majority of the comfort metric predictions.

``The \glsxtrshort{LB} AdaptiveComfortCalculator component assesses the adaptive comfort of the zone during the occupancy period. Given the European context of this research, preference is given to the standard EN 15251 (now EN 16798-1) over the \glsxtrshort{ASHRAE} standard for evaluation. A notable divergence lies in the database used to establish the adaptive standard:\glsxtrshort{CEN} regulations draw from the European SCATs project database, aggregating comfort data recorded over the same period across five European countries, employing standardized instruments and methodologies\cite{110}. Standards EN 15251 and EN 16798 delineate buildings based on their conditioning system (mechanical or natural) and delineate three categories (I, II, III).''\cite[50]{rhino-gh} The tested building aligns with Category II, designated for "normal levels of expectation and suitable for new constructions and renovations"\cite{118}. For Category II, upper and lower limits of comfort temperatures are derived using formulas 1 and 2 \cite{119}. These limits are applicable only when the running mean outdoor temperature falls within the range of 10°C to 30°C - as depicted in \cref{fig:Comfort model based on EN-16798-1 2019}.

\begin{equation}
    \label{eq:UpperLimit}
\RaggedRight upper\  limit:
\centering
\theta_{o} = 0.33\ \theta_{rm}+18.8+3
\end{equation}
\begin{equation}
    \label{eq:LowerLimit}
\RaggedRight lower\  limit:
\centering
\theta_{o} = 0.33\ \theta_{rm}+18.8-4
\end{equation}
Optimal operative temperature is defined by formula \cref{eq:Opti_OperTemp}
\begin{equation}
    \label{eq:Opti_OperTemp}
\centering
\theta_{c} = 0.33\ \theta_{rm}+18.8
\end{equation}

where:
\begin{conditions}
\theta_{o}   &   indoor operative temperature [°C] \\
\theta_{rm}         &   running mean outdoor temperature [°C]\\   
\theta_{c}   &   optimal operative temperature [°C]  \\
\end{conditions}

\begin{figure}[h]
    \centering
	\includegraphics[width=\linewidth]{images/tables/Comfort-model-based-on-EN-16798-12019-Figure-5-quantifies-the-percentage-of-discomfort.png}
	\caption[Comfort model based on EN-16798-1 2019]{Comfort temperatures ranges for free-running building categories I, II and III as a function of the exponentially-weighted running mean of the outdoor temperature. Upper and lower limits define design values for indoor temperature during summer and winter seasons. Source: EN 16798-1}\cite{116,117}
	\label{fig:Comfort model based on EN-16798-1 2019}
    \hfill
\end{figure}

~\\
\subsection{Comfort visualization}
\label{subsec:Comfort visualization}

The \glsxtrshort{PMV} component assesses the comfort of the defined environmental conditions for occupants, determining the \glsxtrshort{PMV}. \glsxtrshort{PMV}, a scale ranging from cold (-3) to hot (+3), was utilized in comfort evaluations by P.O. Fanger. Each integer value within the scale represents distinct comfort levels: 
\begin{itemize}
\setlength{\itemsep}{1pt}
\setlength{\parskip}{0pt}
\setlength{\parsep}{0pt}
    \item[-3] - Cold
    \item[-2] - Cool
    \item[-1] - Slightly Cool
    \item[0] - Neutral
    \item[+1] - Slightly Warm
    \item[+2] - Warm
    \item[+3] - Hot
\end{itemize}
Each numerical value corresponds to an hour within the analysis period.


The developed \glsxtrshort{GH} script facilitates the creation of high-quality visualizations in the \glsxtrshort{RH} scene, aiding in a comprehensive interpretation of the outcomes. For instance, displaying the percentage of time spent in comfortable, hot, or cold conditions can be achieved by presenting colored meshes on an annual graph using the \textit{LB Hourly Plot} component. An illustrative example of this chart is depicted in \cref{fig:Comfort chart for Torino_A}. It give us a intuitive scan of the annual indoor thermal environment, which indicates us the need for pursuing the maximum comfort. It's a great tool for us to quickly obtain the global cognition for the environment.

\begin{figure}[h]
    \centering
	\includegraphics[width=\linewidth]{images/Climate & Map/PMV/PMV_TORINO_A.png}
	\caption[Comfort chart for Geneva - after]{3D chart generated with \glsxtrshort{LB}. It displays the percent of time comfortable, hot and cold that resulted from the simulation of the optimized solution for Geneva. Note that the ``global cognition'' is being of redundancy. Our \textbf{fitness value} is aiming at the comfort in the winter day during working hours. That's a range within 6 am. to 18 pm.}
	\label{fig:Comfort chart for Torino_A}
    \hfill
\end{figure}

``Another valuable output is the \textit{LB Psychrometric Chart} and \textit{LB PMV Polygon}. This chart visualizes the duration, within the considered occupancy period, during which temperatures fall between the upper and lower limits of the comfortable range for specific input conditions.''\cite[53]{rhino-gh} Unlike \cref{fig:Comfort chart for Torino_A} which indicates the indoor condition distribution among the day time, \cref{fig:Torino_Psycho_A} show the condition of \glsxtrshort{RU}, describing how long the distance from the status to the comfort zone. Although depicted as colored meshes similar to those in \cref{fig:Comfort chart for Torino_A}, the variables are different, hours are represented on the chart. The colored 'pixels' situated below the lower comfort limit indicate periods when occupants might feel cold, while those above the upper limit depict times when occupants might experience heat discomfort.

\begin{figure}[h]
    \centering
	\includegraphics[width=\linewidth]{images/tables/Torino_Psycho_A.png}
	\caption[Psychrometric Chart of Torino Optimized]{Psychrometric Chart of Torino Optimized with solution of \glsxtrshort{Gen}99 \glsxtrshort{Indi}01}
	\label{fig:Torino_Psycho_A}
    \hfill
\end{figure}


Lastly, we can analyse the human being. Rather than on the surface of building, this time we can analyse the thermal transmittance that take place of the human body, with the help of \textit{LB Hourly Plot}. In \cref{fig:TORINO-HL-A-1,fig:TORINO-HL-A-2}, we can know that in Torino the heat is taken away mainly by radiation and convection. And we can know when this happens.









\section{\glsxtrshort{GA}in arhitecture design and \glsxtrshort{NSGA2}}
\label{sec: GA in arhitecture design and NSGA-II}

Genetic algorithm is a stochastic optimization method developed based on the principles of natural selection and the simulation of biological evolution. It was created by Professor Holland and his students at the University of Michigan in 1975\cite{996017}.
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The history of it is almost as long as the personal computer.  It has been one of the top optimizer. However, due to the insufficient computing power, the theory of it wasn't evolved without the practice. Just as many other foreseeing algorithm, it merely became practical when reaching 21th century.

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Being as an "evolutionary algorithm", \glsxtrshort{GA} itself has evolved into a group of diversity. A comprehensive analysis\cite{Katoch2021} of recent advances in \glsxtrshort{GA}, which discusses the challenges and future research directions in the area of genetic operators, fitness function, and hybrid algorithms. The article also suggests some possible ways to improve the performance and efficiency of \glsxtrshort{GA}s.
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And we will discuss more about it in the last chapter, \cref{sec:AI in architecuture}, imagining about the future.
\subsection{Features and analogy of \glsxtrshort{GA}}
\label{subsec: Genetic algorithms' features and analogy}
\begin{minipage}[t]{1\linewidth}
\begin{itemize}
\setlength{\itemsep}{1pt}
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\item \textbf{Genetic Representation:} The genetic composition of a dog is symbolically represented as a chromosome, with each gene corresponding to distinct phenotypic traits. For example, individual genes may represent traits such as coat color, fur length, and activity level.

\item \textbf{Crossover:} The selected parental dogs engage in gene crossover, where genetic material from both the mother and father contributes to the genetic composition of the offspring. For instance, a resulting offspring may inherit the light coat color gene from the mother and the long fur trait gene from the father.

\item \textbf{Mutation:} During the reproductive process, genetic mutations may spontaneously occur, inducing slight alterations in specific traits. For example, a minor mutation may affect the activity level gene, resulting in a new generation of dogs exhibiting increased activity.

\item \textbf{Selection:} The fitness of each dog is rigorously evaluated, taking into consideration traits such as coat color, fur length, and activity level. Dogs exhibiting higher fitness levels are chosen as parental candidates for the process of reproduction.

\item Across successive generations of selection, crossover, and mutation, the optimization of specific traits within the dog breed is systematically achieved. Dogs with superior fitness levels are retained, while less favorable traits gradually diminish. Ultimately, a dog breed characterized by light coat color, longer fur, and heightened activity levels is selectively bred to align with the breeding objectives. \textbf{Genetic Representation} and \textbf{Crossover} the core of the whole algorithm, which take place in every solution generating. So I introduce it following in \cref{sebsec:SBX}.

\end{itemize}
\end{minipage}
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In this analogy, the genetic algorithm's core mechanism emulates the evolutionary process found in nature. It continuously refines candidate solutions through genetic operations, facilitating the attainment of a more suitable, optimal, or near-optimal solution.

\begin{figure}[h]
	\centering
	\includegraphics[width=\linewidth]{images/tables/TORINO-HL-A(1).png}
	\caption[Heat loss Chart of Torino Optimized part A]{Heat loss Chart of Torino Optimized with solution of \glsxtrshort{Gen}99 \glsxtrshort{Indi}01 Part-A}
	\label{fig:TORINO-HL-A-1}
	\hfill
\end{figure}
\begin{figure}[h]
	\centering
	\includegraphics[width=\linewidth]{images/tables/TORINO-HL-A(2).png}
	\caption[Heat loss Chart of Torino Optimized part B]{Heat loss Chart of Torino Optimized with solution of \glsxtrshort{Gen}99 \glsxtrshort{Indi}01 Part-B}
	\label{fig:TORINO-HL-A-2}
	\hfill
\end{figure}


\subsection{Mathematical process of \glsxtrlong{SBX}}
\label{sebsec:SBX}

\glsxtrfull{SBX} is a crossover operator used in \glsxtrshort{GA} for real-valued optimization problems. \glsxtrshort{SBX} is an extension of the binary crossover operator used in binary-coded \glsxtrshort{GA}s. The \glsxtrshort{SBX} operator simulates the single-point crossover operator of binary-coded \glsxtrshort{GA}s by using a probability density function to generate offspring solutions. The \glsxtrshort{SBX} operator is able to overcome the Hamming cliff, precision, and fixed mapping problems that are associated with binary-coded \glsxtrshort{GA}s\cite{Katoch2021}.
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As discussed in \cref{subsec: Genetic algorithms' features and analogy}, the core process is run under the \glsxtrshort{SBX} method. The complete algorithm refers to \cite{Seshadri_NSGA-II.pdf}. And core process \textit{\glsxtrlong{SBX}} is introduced in \cite{Real-Coded_Genetic_Algorithms}, which I've summarize in to following features:


\begin{itemize}
\setlength{\itemsep}{1pt}
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\setlength{\parsep}{0pt}

\item The gene values of offspring maintain an equal distance from the mean gene value of their parents.
\item Each chromosome position has an identical probability of being chosen as a crossover point.
\item Lower-bit crossovers result in minor alterations in gene values.
\item Offspring tend to be in close proximity to their parental genotypes.
\item \glsxtrshort{SBX} utilizes a probability density function that simulates the single-point crossover found in binary-coded \glsxtrshort{GA}.

\end{itemize}

\begin{figure}[h]
    \centering
	\includegraphics[width=\linewidth]{images/tables/sbx.png}
	\caption[Distribution of SBX]{Distribution of \glsxtrshort{SBX}, not that there's 0 possibility in the mean value \cite{sbx}}
	\label{fig:Distribution of SBX}
    \hfill
\end{figure}
Giving the parental value an additional Gaussian distribution, then there's the new one. 
It can be understood as 2 Gaussian distribution stacked together\cref{fig:Distribution of SBX}.


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These features are instrumental in preserving genetic diversity by ensuring that offspring values remain at an appropriate distance from one another. This prevents the dilution of filial values to an average level, which is beneficial for the subsequent selection phase, enabling an effective selection process.

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With this key characteristic, many variants are created. They can be categorized by \textit{ Fitness assignment}, \textit{Diversity mechanism}, \textit{Elitism}, etc. \cite{KONAK2006992,Kunkle2005ASA} Among them \glsxtrshort{SPEA2} and \glsxtrshort{NSGA2} are competitive\cite{10.1007/978-3-642-27207-3_22}.




\subsection[NSGA-II]{Non-dominated Sorting Genetic Algorithm II}
\label{subsec:Non-dominated Sorting Genetic Algorithm II}
\glsxtrshort{NSGA2} is a multi-objective optimization algorithm used to solve optimization problems with multiple objective functions. The algorithm was proposed by Kalyanmoy Deb and others in 2002\cite{996017}. It is a variant of \glsxtrshort{GA} designed to address multi-objective optimization problems where multiple conflicting objectives exist.

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The core idea of \glsxtrshort{NSGA2} is to maintain a set of non-dominated solutions by partitioning the candidate solutions into different non-dominated levels or fronts. These solutions are not dominated by other solutions. It then performs operations based on non-dominated sorting and crowding distance to maintain a set of high-quality solutions that are balanced across various objectives.

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The algorithm flow of \glsxtrshort{NSGA2} includes the following key steps:


\begin{enumerate}
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  \item \textbf{Population Initialization:} Create an initial population of candidate solutions.
  \item \textbf{Non-dominated Sorting:} Rank the solutions in the population through non-dominated sorting, dividing them into different front levels.
  \item \textbf{Crowding Distance Computation:} Calculate the crowding distance for each solution to measure the distribution density of solutions.
  \item \textbf{Elite Selection:} Select solutions from the front levels to ensure that the next generation's population contains high-quality solutions.
  \item \textbf{Crossover and Mutation:} Apply crossover and mutation operations to the selected solutions, generating the next generation.
  \item Repeat the above steps: Repeatedly execute the above steps until a stopping condition is met.
\end{enumerate}

\glsxtrshort{NSGA2} has become one of the widely used algorithms for solving multi-objective optimization problems\cite{Katoch2021}. It finds a set of Pareto-optimal solutions, allowing decision-makers to make trade-offs and selections among different objectives by maintaining diversity and balance in the solutions. This is exactly what we need for our project.

