sustainability

Article Building Optimization through a Parametric Design Platform: Using Sensitivity Analysis to Improve a Radial-Based Algorithm Performance

Nayara R. M. Sakiyama 1,2,*, Joyce C. Carlo 3, Leonardo Mazzaferro 4 and Harald Garrecht 1

1 Materials Testing Institute (MPA), University of Stuttgart, Pfaffenwaldring 2b, 70569 Stuttgart, Germany; [email protected] 2 Institute for Science, Engineering and Technology (ICET), Federal University of the Jeq. and Muc. Valleys (UFVJM), R. Cruzeiro, 01-Jardim São Paulo, Teófilo Otoni 39803-371, Brazil 3 Architecture and Urbanism Department (DAU), Federal University of Vicosa (UFV), Av P. H. Rolfs, Viçosa 36570-900, Brazil; [email protected] 4 Laboratory of Energy Efficiency in Buildings (LabEEE), Federal University of Santa Catarina (UFSC), Caixa Postal 476, Florianópolis 88040-970, Brazil; [email protected] * Correspondence: [email protected]

Abstract: Performance-based design using computational and parametric optimization is an effective strategy to solve the multiobjective problems typical of building design. In this sense, this study investigates the developing process of parametric modeling and optimization of a naturally ventilated house located in a region with well-defined seasons. Its purpose is to improve its thermal comfort



 during the cooling period by maximizing Natural Ventilation Effectiveness (NVE) and diminishing annual building energy demand, namely Total Cooling Loads (TCL) and Total Heating Loads (THL). Citation: R. M. Sakiyama, N.; C. Following a structured workflow, divided into (i) model setting, (ii) Sensitivity Analyses (SA), and Carlo, J.; Mazzaferro, L.; Garrecht, H. (iii) Multiobjective Optimization (MOO), the process is straightforwardly implemented through Building Optimization through a a 3D parametric modeling platform. After building set up, the input variables number is firstly Parametric Design Platform: Using reduced with SA, and the last step runs with an innovative model-based optimization algorithm Sensitivity Analysis to Improve a Radial-Based Algorithm Performance. (RBFOpt), particularly appropriate for time-intensive performance simulations. The impact of design Sustainability 2021, 13, 5739. https:// variables on the three-performance metrics is comprehensively discussed, with a direct relationship doi.org/10.3390/su13105739 between NVE and TCL. MOO results indicate a great potential for natural ventilation and heating energy savings for the residential building set as a reference, showing an improvement between Academic Editors: José L. Vivancos 14–87% and 26–34% for NVE and THL, respectively. The approach meets the current environmental and Carolina Aparicio-Fernández demands related to reducing energy consumption and CO2 emissions, which include passive design implementations, such as natural or hybrid ventilation. Moreover, the design solutions and building Received: 29 March 2021 orientation, window-to-wall ratio, and envelope properties could be used as guidance in similar Accepted: 13 May 2021 typologies and climates. Finally, the adopted framework configures a practical and replicable Published: 20 May 2021 approach for studies aiming to develop high-performance buildings through MOO.

Publisher’s Note: MDPI stays neutral Keywords: parametric design; multiobjective optimization; natural ventilation; model-based algo- with regard to jurisdictional claims in rithm; energy demand published maps and institutional affil- iations.

1. Introduction Passive design and building optimization are attractive alternatives considering the Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. contemporary sustainable goals involving reducing energy consumption and CO2 emis- This article is an open access article sions [1]. The solutions include improving the building envelope, implementing passive distributed under the terms and strategies, and taking advantage of natural light and ventilation. They aim to produce a conditions of the Creative Commons high-performance building that fulfills comfort and energy efficiency requirements [2–4]. Attribution (CC BY) license (https:// Moreover, for the climates where natural ventilation is restricted to a period of the year, creativecommons.org/licenses/by/ implementing mixed-mode or hybrid ventilation systems is a more sustainable solution [5]. 4.0/). Additionaly, these goals are mostly conflicting, also defined as a multiobjective problem.

Sustainability 2021, 13, 5739. https://doi.org/10.3390/su13105739 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 5739 2 of 25

Thus, performance-oriented design through computational and parametric optimization is a way to solve them that is becoming increasingly popular [6–8]. Optimization methods applied to building performance simulation, or simple BSO (Building Simulation Optimization), are beneficial since many variables affect building per- formance, such as form, layout, envelope materials, orientation, and landscape design [9]. These variables are usually defined qualitatively and mainly considered in the conceptual design phase [10]. Consequently, designers lack sufficient information to make effective and appropriate decisions that lead to high-performance buildings, and the subject has been the focus of many investigations [11–13]. Furthermore, although optimizing the energy-efficient building design is encouraging, many applications demand skills that most architects are unfamiliar with, and a smooth connection with standard and parametric modeling programs is still missing [10]. In this sense, using the available tools must happen with parsimony. On the one hand, they are credited to assist the design and decision process, optimizing the final building performance with relatively low cost [14]. On the other hand, the tools also present limitations and may not accurately represent the study’s objective [15]. Therefore, the more structured the processes and the more substantiated the variables considered in the project, the greater the chances of finding optimal solutions.

Building Performance Optimization through Simulation and Parametric Design BSO has been explored to find optimum alternatives among potential combinations of several parameters that involve passive design or responsive climate strategies. Tian et al. [16] studied the integration of optimization algorithms into simulation-based de- sign processes and summarized the different procedures that can be applied within the technique (Table1), which involve multiple steps, described in a tutorial form by Konak et al. [17]. A review of computational optimization methods applied to building per- formance design can be found in [6,18,19], which provide a classification of building optimization problems and algorithms.

Table 1. Typical optimization methods applied in building performance simulation. Adapted from Tian et al. [16].

Optimization Procedures Description The optimization process occurs in three phases: Three-phase optimization preprocessing, running the optimization, and postprocessing Building performance simulation with optimization Multitime design optimization methods is applied at each stage of building design Sensitivity analyses are used to narrow the variables range, determine the significant ones, and filter those Sensitivity analyses and optimization with little impact on the objectives. Optimization is then conducted with a narrow variable range.

Generally, the most investigated parameters are related to building envelope [20–22] and consider material properties, orientation, Window-to-Wall Ratio (WWR), shape, and in- ternal space. The impact from different Heating, Ventilating, and Air Conditioning (HVAC) systems and controls are also explored, combined with the aforementioned items [23,24]. Some studies focused on improving natural ventilation, assessed different window po- sitions, sizes, and shapes [25–27]; roof types [28]; and also testing ventilation controls to improve Phase Change Materials (PCM’s) efficiency [29–31]. Nevertheless, when addressing the BSO thematic from the architects’ perspective, Shi et al. [10] point out some limitations regarding its design practice application. The authors state that a common approach regarding the techniques or platforms used to perform the optimization combines energy models and an optimization algorithm, mostly implemented through GenOpt [32] and MatLab [33]. A more friendly and attractive option to integrate BSO into the design process would be by using the same program where the project is Sustainability 2021, 13, 5739 3 of 25

developed, such as Building Information Modelling (BIM) [34,35], or parametric modeling platform [36–38]. In that context, Díaz et al. [39] explored some strategies and challenges and concluded that parametrization is crucial to integrating BSO into the construction industry. A review about integrating performance simulation in parametric 3D modeling is presented by Touloupaki and Theodosiou [40], which also proposed a methodology to accomplish design optimization in the project’s early stages. According to the authors, software such as Rhinoceros (Robert McNeel & Associates, Seattle, WA, USA) [41], Dynamo BIM (Autodesk, Inc., Mill Valley, CA, USA) [42], and GenerativeComponents (Bentley Systems, Exton, PA, USA) [43] have increased parametric 3D modeling application into design practice by nonprogrammers. Predominant is the plugin for the Rhinoceros software, the Grasshopper [44]. Pub- lished studies that use the 3D parametric platform include building optimization concern- ing both its overall passive performance and energy efficiency [45,46], or more specific goals, such as solar radiation [47,48], natural ventilation [49,50], and daylighting [51–54]. Although growth in the application of parametric 3D modeling is noticed, the diffusion of a simplified approach to optimization tools is still timid. Given this gap, by failing to incorporate MOO into the design process, solutions for multiobjective problems may underperform rather than provide the best passive or low-energy alternatives. In this context, parametric 3D modeling and BSO-based process guided this research development. Both procedures are implemented within the design platform to facilitate optimization practice in the early design stages. The study aims to optimize the passive design of a residential building with hybrid ventilation located in a region with well-defined seasons (see Section3). The problem can be characterized as multiobjective optimization (MOO) since the objectives include improve thermal comfort during the cooling period and reduce annual building energy demand. The focus is on natural ventilation use expansion and heating and cooling consumption minimization employing a parametric design platform. Moreover, establishing a general approach that involves performance-based design is a secondary goal. Therefore, the proposed methodology is a practical strategy that supports high-efficiency building development. It contributes to spreading and encouraging the use of optimization tools when dealing with conflict objectives so that the designer can propose quantitatively based solutions. The workflow is universal, replicable, and can be implemented for any building and location. Moreover, this study’s results can be considered evidence that geometric aspects provided a greater solution diversity among the parameters investigated. Finally, this paper’s contents are as follows: Section2 provides the optimization framework adopted in the study, organized in three steps. The experimental house used as a reference case and its corresponding numerical model are presented in Section3, while Section4 summarizes the selected influential variables based on sensitivity analysis. Problem description, results’ presentation, and discussions are the Section5 themes. At last, Section6 closes the paper with the mains conclusions found, remarks, and future works.

2. Optimization Framework Following the structure presented in [3], Figure1 shows this study workflow, divided into three significant steps: model setting with objectives definition, sensitivity analysis, and multiobjective optimization (MOO), which are described in detail in the following sections. Differently from other similar procedures carried out through multiple programs, the approach uses a 3D parametric modeling platform. It allows performing passive design optimization with a single canvas, easing its application into practice. Sustainability 2021, 13, 5739 4 of 25 Sustainability 2021, 13, x FOR PEER REVIEW 4 of 28

FigureFigure 1. 1.Multiobjective Multiobjective optimizationoptimization framework. framework.

2.1.2.1. StepStep 1:1: ModelModel SettingSetting forfor MultiobjectiveMultiobjective OptimizationOptimization First,First, anan experimentalexperimental househouse waswas parametricallyparametrically modeledmodeled asas aa basebase case. case. WithWith this this approach,approach, the the modifiable modifiable variables variables are are linked linked totospecific specificarchitectural architecturalelements elementsand andforms, forms, enablingenabling directdirect visualizationvisualization ofof thesethese changes,changes, significantlysignificantly aidingaiding complexcomplex geometrygeometry designdesign [[55].55]. Thus,Thus, differentdifferent designdesign alternativesalternatives cancan bebe easilyeasily testedtested inin thethe initialinitial phase,phase, makingmaking itit possiblepossible to to find find the the best best solution solution according according to to the the established established goals. goals. InIn thisthis study,study, RhinocerosRhinoceros waswas selectedselected asas aa modelingmodeling tooltool andand GrasshopperGrasshopper asas aa commandcommand platform.platform. HoneybeeHoneybee (HB),(HB), aa plug-inplug-in runningrunning insideinside Grasshopper,Grasshopper, is is used used as as an an engineengine toto performperform thethe energy energy simulations simulations through through EnergyPlus EnergyPlus (E+) (E+) andand Open Open Studio. Studio. AA detaileddetailed descriptiondescription of of the the model model is is provided provided in in Section Section3 .3.

Sustainability 2021, 13, 5739 5 of 25

2.1.1. Optimization Objectives • Natural Ventilation Effectiveness (NVE) The number of hours the outdoor airflows can be used to cool space is estimated through the performance metric Natural Ventilation Effectiveness (NVE) [56], expressed in Equation (1). It calculates the weighted averaged of hourly ratios (αi) between the available natural ventilation air changes per hour (ACH)—ACHavai to the required ones (ACHreq) of zone i, where n is the total number of considered building zones, equal to 4.  α = 1, i f ACH ≥ ACH  avai req n n  V α α = 1, i f ACH = 0 NVE = ∑i=1 i i/∑i=1 Vi req (1)   α = 0, otherwise

ACHavai corresponds to the hourly E+ output AFN Zone Infiltration Air Change Rate calculated for the Living room and Bedrooms 1–3, while the ACHreq is calculated through Equations (2) and (3). × ACHreq/min = 3600 AFreq/min/V (2)

q AFreq = /ρ c (Tcom f − Tout) (3) 3 where AFreq is the required airflow to offset cooling load, expressed in m /s, which is converted to ACH, considering the volume of the room (V); q is the heat rate (kj/s) calculated by the energy simulation (air-infiltration, solar radiation, heat gains from people, equipment, and light); ρ is the density of air (kg/m3), set as 1.27; and c is the specific heat ◦ capacity of the air (KJ/kg C), equal to 1050. Tcom f is used instead of Tin because it is assumed that when natural ventilation cannot provide sufficient comfort, occupants rely on mechanical systems. ASHRAE Standard 55 [57] is used at the Tcom f calculations. 3 Moreover, the minimum airflow (AFmin) in m /s is calculated by Equation (4) and converted to ACH by Equation (2), following the design ventilation requirements for the breathing zone of occupiable spaces, according to ASHRAE 62.1 [58].

AFmin = QpP + Qa A (4)

where Qp is the outdoor airflow rate required per person, set as 2.5 L/s.person; P is the zone population (the most extensive number of people expected to occupy the zone during 2 typical usage); Qa is the outdoor airflow rate required per unit area, set as 0.3 L/s·m ; and A is the zone floor area. Minimum and required airflow is compared; therefore, if ACHmin is greater, it is set as a reference, rather than ACHreq. In this study, as NVE is evaluated in the living room and bedrooms, the performance metric was measured through the weighted average among the four considered spaces. • Total Cooling Loads (TCL) and Total Heating Loads (THL) The building energy demand was separately calculated as the sum of the cooling and heating loads (kWh) of the considered rooms (Living room, Bedrooms 1–3), expressed respectively by Equations (5) and (6) as: n TCL = ∑ Eci (5) i=1

n THL = ∑ Ehi (6) i=1

where Eci and Ehi are E+ outputs from the energy consumption due by the cooling coil and the heat pump for zone i cooling and heating, respectively, and n is the total number of considered zones, equal to 4. The cooling and heating loads were considered separately since they can be supplied by different energy matrices and present heterogeneous consumption. Therefore, evalu- Sustainability 2021, 13, 5739 6 of 25

ating them together would lead to a limited understanding of their respective demands and solutions.

2.1.2. Input Variables As this study aims to find optimal passive design solutions for a residential building in a temperate climate in terms of NVE, TCL, and THL, the considered input variables for the reference building involve six variables categories: building orientation, Window-to- Wall Ratio (WWR), opaque and translucid envelope material properties, external window shading, natural ventilation, and HVAC system setpoints and AFN parameters (discharge coefficient and the fraction of glazed area operable). The finally predefined 32 input variables are presented in Table2 with their respective description, lower and upper limits.

Table 2. Input values and their ranges for sensitivity analysis.

Probability Density Base-Case Lower Upper Category Variable Description Variable Name Function Value Limit Limit Building orientation 1 Building long axis azimuth (o) x01_orient Discrete 345 0 315 Window-to-Wall North WWR (%) x02_glzRn Continuous uniform 3.5 3.5 75 Ratio (WWR) East WWR (%) x03_glzRe Continuous uniform 13 3.5 75 South WWR (%) x04_glzRs Continuous uniform 34 3.5 75 West WWR (%) x05_glzRw Continuous uniform 10 3.5 75 Material properties Window U-value (W/m2K) x06_windowU Continuous uniform 1.3 1.05 5.7 Window Solar Heat Gain Coefficient x07_shgc Continuous uniform 0.3 0.21 0.81 Aerogel thickness (m) x08_aeroT Continuous uniform 0.04 0.04 0.12 Roof thermal conductivity (W/mK) x09_roofC Continuous uniform 0.055 0.03 0.15 Window Shade Opening multiplier factor x10_shdOp Continuous uniform 0 0 1 Fraction of the shade surface open x11_shdAir Continuous uniform 0 0 0.8 to airflow Shading control setpoint—Solar x12_shdSp Continuous uniform 0 400 600 radiation on the window (W/m2) Minimum indoor air SetPoint temperature—AFN ventilation x13_minAirT Continuous uniform 20 20 22 control strategy (◦C) Maximum indoor air temperature—AFN ventilation x14_maxAirT Continuous uniform 27 25 28 control strategy (◦C) Heating setpoint (◦C) x15_setPoint Continuous uniform 19 18 19 Cooling system operation (on-off) x16_onOff Discrete False True False AFN Parameter Discharge coefficient 2 x17_disCoef Continuous uniform 0.6 0.33 0.84 Ventilation area x window ratio 3 LWindE Window VWR x18_LWindE Continuous uniform 0.75 0.5 1 Fraction of operable glazed area LwindS1 Window VWR x19_LwindS1 Continuous uniform 0.75 0.5 1 LPorteS2 Window VWR x20_LPorteS2 Continuous uniform 0.75 0.5 1 LPorteW Window VWR x21_LPorteW Continuous uniform 0.75 0.5 1 LDoorH Window VWR x22_LDoorH Continuous uniform 0.75 0.5 1 LDoorC Window VWR x23_LDoorC Continuous uniform 0.75 0.5 1 R1WindN Window VWR x24_R1WindN Continuous uniform 0.75 0.5 1 R1WindW Window VWR x25_R1WindW Continuous uniform 0.75 0.5 1 H2W1door Window VWR x26_H2W1door Continuous uniform 0.75 0.5 1 R2WindW Window VWR x27_R2WindW Continuous uniform 0.75 0.5 1 R2WindS Window VWR x28_R2WindS Continuous uniform 0.75 0.5 1 R2Ndoor Window VWR x29_R2Ndoor Continuous uniform 0.75 0.5 1 R3WindE Window VWR x30_R3WindE Continuous uniform 0.75 0.5 1 R3SWind Window VWR x31_R3SWind Continuous uniform 0.75 0.5 1 R3Sdoor Window VWR x32_R3Sdoor Continuous uniform 0.75 0.5 1 Note: 1 The smaller of the angles, measured clockwise, between the true north and the long building axis. 2 Measured discharge coefficient values from different window types (Table3). 3 VWR.

The probability density functions of input variables can affect sensitivity analyses and optimization results. Therefore, although the parameters are intrinsically discrete, they were considered to be continuously uniform, with exception to the building orienta- tion, which is restricted to eight discrete values (from 0–315◦, every 45◦) and the cooling Sustainability 2021, 13, x FOR PEER REVIEW 8 of 28

Sustainability 2021, 13, x FOR PEER REVIEW 8 of 28

Sustainability 2021, 13, x FOR PEER REVIEW 8 of 28

Sustainability 2021, 13, x FOR PEER REVIEW Continuous 8 of 28 R3Sdoor Window VWR x32_R3Sdoor 0.75 0.5 1 Sustainability 2021, 13, x FOR PEER REVIEW Continuousuniform 8 of 28 R3Sdoor Window VWR x32_R3Sdoor 0.75 0.5 1 Note: 1 The smaller of the angles, measured clockwise, between the true north and the long building axis. 2 Measured Sustainability 2021, 13, x FOR PEER REVIEW uniformContinuous 8 of 28 Sustainability 2021, 13, 5739 3 7 of 25 discharge1 coefficient R3Sdoorvalues from Window different VWR window types x32_R3Sdoor (Table 3). VWR. 0.75 0.52 1 SustainabilityNote: 2021 The, 13smaller, x FOR ofPEER the REVIEW angles, measured clockwise, between the trueContinuousuniform north and the long building axis. Measured8 of 28 3 Sustainability discharge 12021 coefficient, 13, x FOR R3SdoorPEERvalues REVIEW from Window different VWR window types x32_R3Sdoor (Table 3). VWR. 0.75 0.52 18 of 28 Note: The smaller of the angles, measured clockwise, between the trueContinuousuniform north and the long building axis. Measured Sustainability 2021, 13, x FOR PEER REVIEWMass flow through openings is directly3 affected by the wind pressure coefficient8 ( of𝐶 28), Note:discharge 1 The coefficient smaller R3Sdoorof values the angles, from Window different measured VWR window clockwise, types x32_R3Sdoor between (Table 3). the VWR. true north and the long building0.75 axis.0.5 2 Measured 1 Continuousuniform systemdischargeMass operation, flowcoefficient through defined (𝐶 openings), as and true window-opening (1) is directly3 or false af (0)—on/off.fected factor. by the Each The wind operable range pressure limits opening coefficient of Window area (was𝐶), discharge1 coefficient R3Sdoor values from Window different VWR window types x32_R3Sdoor (Table 3). VWR. 0.75 0.52 1 Note: The smaller of the angles,dischargeconsidered measured coefficient individually clockwise, (𝐶 ),at betweenand this window-opening stage the truetouniformContinuous provide north and factor. a morethe longEach practical building operable and axis. opening detailed Measured area passive was R3SdoorU-value WindowMass and flow window VWR through Solar x32_R3Sdooropenings Heat Gain is directly3 Coefficient Continuous affected (SHGC) by the were wind0.75 determined pressure 0.5 coefficient according 1 to(𝐶), Note:discharge 1 The coefficient smaller of R3Sdoorvalues the angles,natural from Window different measured ventilation VWR window clockwise, design types x32_R3Sdoor between (Tablesolution, 3). the VWR.truetotalinguniform north 14 and apertures the long building0.75or subvariables. axis. 0.52 Measured Similarly,1 theconsidereddischarge valuesMass from flowcoefficient individually the through reference (𝐶 openings ),at and buildingthis window-opening stage is directly and touniformContinuous theprovide af availablefected factor.a moreby products the Each practical wind operable in pressure the and building opening detailed coefficient material area passive (was𝐶), dischargeNote: 1 The coefficient smaller R3Sdoorofvalues the angles, althoughfrom Window different measured the VWR literaturewindow clockwise, types suggests x32_R3Sdoor between (Table that 3). the 3 VWR.𝐶 true values north rangeand the between long building0.75 0.60–0.65 axis. for0.5 2 Measured sharp-edged1 1 market.naturaldischargeconsidered Regarding ventilation coefficient individually the design ( external𝐶 ),at and thissolution, walls’window-opening stage thermal totalingto provide performance, 14 factor. aapertures more Each practical the oroperable approachsubvariables. and opening detailed adopted2 Similarly, area passive was was Note: The smaller of the angles,Mass measured flow through clockwise, openings between is the directly3 trueuniform north affected and bythe thelong wind building pressure axis. coefficient Measured (𝐶 ), discharge coefficient valuesopenings from different [60–62], window the valuetypes (Table can vary 3). dependinVWR. g on the opening porosity, shape, location dischargeNote: 1 The coefficient smaller ofvalues thelimited angles,althoughconsidered naturalfrom different to measured theventilation the individually exterior literature window clockwise, design render types suggests at between (Table this thickness,solution, thatstage 3). the 3 𝐶VWR. truetotalingto instead valuesprovide north of 14 rangeand considering aapertures morethe between long practical buildingor a 0.60–0.65 broadsubvariables. and axis. thermal detailedfor 2 Measured sharp-edged conduc-Similarly, passive dischargeMass flowcoefficient through (𝐶 openings), and window-opening is directly affected factor. by the Each wind operable pressure opening coefficient area ( was𝐶), tivityopeningsinnaturalalthough the range, façade, ventilation [60–62],the as literature performedwind the designangle, value suggests with andcansolution,the vary Reynoldsthat roof.3 dependin 𝐶totaling values In number this g14 rangeon sense, apertures [63].the between opening wallTherefore, compositionor 0.60–0.65 porosity,subvariables. a broader for shape, remains sharp-edged rangeSimilarly, location the was discharge coefficient valuesconsidered fromMass different flow individually window through types openings at (Tablethis stage 3).is directly VWR. to provide affected a moreby the practical wind pressure and detailed coefficient passive (𝐶 ), same,dischargeinconsidered the and façade, opaque coefficient in thewind envelope investigation, angle,(𝐶), optimizationand and window-opening Reynoldsbased involveson numberwind-tunnel findingfactor. [63]. theEachandTherefore, ideal on-site operable aerogel-based aassessments. broader opening range exteriorarea Table waswas 3 naturalalthoughopeningsMass ventilation the[60–62], flow literature through the design value suggests openings cansolution, varythat is directly 𝐶dependintotaling values affected g14 range on apertures theby between theopening wind or 0.60–0.65 porosity,pressuresubvariables. for coefficientshape, sharp-edged Similarly, location (𝐶), renderconsideredsummarizesdischarge thickness coefficient individually the [59 ].measured (𝐶 ),at and this discharge window-opening stage to coefficienprovide factor.ats, more literature Each practical operable sources, and opening detailed and respective area passive was considereddischargeopeningsin theMass façade, [60–62], coefficientflow in thewind through theinvestigation, angle, (value𝐶 openings), and andcan window-opening varyReynoldsbased is directly dependin on wind-tunnelnumber affectedg onfactor. [63].the by theopeningand EachTherefore, wind on-site operable porosity,pressure aassessments. broader opening coefficientshape, range area locationTable (waswas𝐶 ),3 althoughconsidered the individually literature suggests at this thatstage 𝐶 to valuesprovide range a more between practical 0.60–0.65 and detailedfor sharp-edged passive naturalwindow ventilation types. The design 𝐶 values solution, are automaticallytotaling 14 apertures calculated or bysubvariables. E+ using the Similarly, surfaceC summarizesconsideredindischarge Massthe façade, flow coefficient individuallyin throughthe thewind measuredinvestigation, angle,( openings𝐶 ),at and and thisdischarge window-opening is Reynoldsstagebased directly to oncoefficien provide affected numberwind-tunnel factor. ts, bya [63]. more theliterature andEachTherefore, wind practical on-site operable pressuresources, aandassessments. broader opening coefficient detailedand rangerespective area passiveTable ( pwas), 3 althoughopeningsnatural ventilation the[60–62], literature the design value suggests cansolution, varythat 𝐶 dependintotaling values g 14range on apertures the between opening or 0.60–0.65 porosity,subvariables. for shape, sharp-edged Similarly, location dischargewindownaturalaverageconsideredsummarizes coefficientcalculationventilationtypes. inindividually the the The measuredinvestigation, (methodC designd𝐶), andatvalues this [64]solution, window-openingdischarge stageimplementedbasedare automatically totalingto oncoefficien provide wind-tunnel through factor.14 ts,aapertures calculatedmore literature Each theand practicalE+ operable on-site orAFN by sources,subvariables. E+ model.andassessments. opening using detailedand the area respectiveSimilarly, Tablepassivesurface was 3 openingsinalthough the façade, [60–62],the literature wind the angle, value suggests andcan vary Reynoldsthat dependin𝐶 values numberg rangeon [63].the between opening Therefore, 0.60–0.65 porosity, a broader for shape, sharp-edged range location was consideredaverage calculation individually method𝐶 at this [64] stage implemented to provide through a more the practical E+ AFN and model. detailed passive consideredalthoughsummarizesnaturalwindow ventilation thetypes. in literaturethe the The measuredinvestigation, design suggests values solution,discharge thatbasedare 𝐶automaticallytotaling on coefficien values wind-tunnel 14range ts,apertures calculated literaturebetween and on-siteor 0.60–0.65by sources,subvariables. E+ assessments. using forand sharp-edged the respectiveSimilarly, Tablesurface 3 naturalinTableopenings the 3. ventilationfaçade, Discharge [60–62], wind coefficients/window designthe angle, value solution, and can Reynoldsvary totaling types dependin fornumber 14 sensitivity aperturesg on [63]. the analyses. openingTherefore, or subvariables. porosity, a broader shape, Similarly, range location al-was summarizesopeningswindowalthoughaverage calculation types.the[60–62], literaturethe The measuredthe method 𝐶value suggests values can[64]discharge vary thatimplementedare dependinautomatically𝐶 coefficien values throughg range onts, thecalculated literature between theopening E+ AFN 0.60–0.65by sources,porosity, E+model. using for andshape, sharp-edged therespective locationsurface thoughconsideredTablein the 3. thefaçade, Discharge literature in thewind coefficients/window investigation, suggestsangle, and that ReynoldsbasedC typesvalues on for wind-tunnelnumber rangesensitivity between[63]. analyses. and Therefore, on-site 0.60–0.65 assessments.a broader for sharp-edged range Table was 3 inaverageopenings the façade, calculation [60–62], wind theWindow method angle, value andcan [64]Type varyReynoldsimplemented d dependin number throughg on [63].the theopening Therefore, Measured E+ AFN porosity, model.a 𝑪broader shape, rangeSource location was summarizeswindowconsidered types. in the the The measuredinvestigation, 𝐶 values discharge basedare automatically oncoefficien wind-tunnelts, calculatedliterature and on-site bysources, E+ assessments. 𝒅using and therespective Tablesurface 3 openingsconsideredinTable the 3. façade, [Discharge60– in62 ],thewind the coefficients/window investigation, value angle, can and vary Reynoldsbased depending types on for numberwind-tunnel sensitivity on the [63]. opening analyses. andTherefore, on-site porosity, aassessments. broader shape, range location Table was 3 windowaveragesummarizes calculationtypes. the The measuredWindow method 𝐶 values [64]Typedischarge implementedare automatically coefficien throughts, calculated literature the Measured E+ AFN bysources, E+ model. 𝑪 𝒅using and the Sourcerespective surface insummarizesTableconsidered the façade, 3. Discharge in windthe the coefficients/window measured angle,investigation, and discharge Reynolds based types on numbercoefficien for wind-tunnel sensitivity [63ts,]. literature Therefore,analyses. and on-site sources, a broaderassessments. and range respective Table was 3 consideredaveragewindow calculation types. in the investigation,The Windowmethod 𝐶 valuesSide-hung [64] Type based implementedare casement onautomatically wind-tunnel through calculated and the Measured on-siteE+ 0.47–0.81 AFN by assessments. E+model. 𝑪 𝒅using theSource Table surface3 windowTablesummarizes 3. Discharge types. the The coefficients/windowmeasured 𝐶 values discharge are typesautomatically coefficien for sensitivityts, calculated literature analyses. bysources, E+ using and the respective surface summarizesaverage calculation the measuredWindow method dischargeSide-hung [64]Type implemented coefficients,casement through literature the Measured sources,E+ 0.47–0.81 AFN andmodel. 𝑪𝒅 respective Source win- averagewindow calculation types. The method 𝐶 values [64] implementedare automatically through calculated the E+ AFN by E+model. using the surface dowTable types. 3. Discharge The C coefficients/windowvalues are automatically types for calculated sensitivity byanalyses. E+ using the surface average[65] average calculationp Window methodSide-hung [64]Type implemented casement through the Measured E+ 0.47–0.81 AFN model. 𝑪 𝒅 Source calculationTable 3. Discharge method coefficients/window [64] implementedSide-hung throughtypescasement for thesensitivity E+ AFN analyses. model. 0.47–0.81 [65] Table 3. Discharge coefficients/windowWindowBottom-hung Type types casement for sensitivity analyses. Measured 𝑪𝒅 Source [65] Table 3. Discharge coefficients/windowWindowSide-hung Type typescasement for sensitivity analyses. Measured 0.47–0.81 𝑪 𝒅 Source Table 3. Discharge coefficients/windowWindowBottom-hung Type types casement for sensitivity analyses. Measured 𝑪 Source 𝒅 [65] WindowBottom-hungSide-hung Type casement casement Measured 0.47–0.81 𝑪𝒅 Source Window TypeSide-hung casement Measured 0.47–0.81Cd Source[65] Bottom-hungSide-hungTilted casement 45° casement 0.47–0.810.45 [65] Bottom-hungSide-hung casement casement 0.47–0.81 Side-hungTilted casement 45° 0.47–0.810.45 [65] Bottom-hungTilted 45°casement 0.45 [65] [65] [65] Bottom-hungTilted 90°45° casement 0.710.45 Bottom-hung casement casement

Bottom-hungTilted 90°45° casement 0.710.45 TiltedTilted 45°90° 0.450.71 TiltedHoles 90°45°◦ 0.710.45 TiltedTilted 45 45° 0.45 0.450.64 (open)Holes Tilted 90°45° 0.640.710.45 (open)Holes TiltedTilted 90 90°◦ 0.71 0.710.64 Tilted(open)Holes 90° 0.71 TiltedHoles 90° 0.710.64 (open) 0.06 (closed)HolesHoles [66] Tilted 90° 0.64 0.640.71 (open)(open)Holes 0.06 [66] (closed)Holes 0.64 (open)Holes 0.06 [66] (closed)Holes 0.64 Holes(open)Flaps 0.640.06 [66] (closed)(open)Holes 0.06 0.61 [66] (closed)(open)Holes 0.64 Flaps 0.06 [66] (closed)Holes(open) 0.61 Flaps(open)Flaps 0.06 (closed)Holes 0.61 0.61 [66] (open)(open)HolesFlaps 0.06 (closed)Flaps 0.060.61 [66] (open) 0.24 [66] (closed)HolesFlaps FlapsFlaps 0.610.06 [66] (closed)(open) 0.24 0.24 (closed)(closed)FlapsFlaps 0.610.24 (closed)(open)Flaps Flaps 0.240.61 (closed)Roof(open)Roof 0.25 0.610.25 (open)Flaps Roof 0.250.240.61 (closed)(open)Flaps Roof 0.240.25 (closed)Flaps 2.2. Step 2: Sensitivity Analyses—ReducingFlaps Input Variables Number 0.24 (closed)Roof 0.240.25 (closed)Flaps Before the optimization, SensitivityRoof Analyses (SA) were performed0.250.24 to identify the influential passive design variables(closed) in terms of the three objective functions previously Roof 0.25 described in Section 2.1. Implementing SA at the early stage of this study reduced the num- Roof 0.25 ber of variables for the optimizationRoof procedure, improving the algorithm0.25 performance and

making the process more effective. TianRoof et al. [67] reviewed sensitivity0.25 analysis methods in

Sustainability 2021, 13, 5739 8 of 25

building energy investigations, which can be local and global. The authors commented which options might be adequate concerning the research purpose, computational cost, number of input variables, and familiarity with the methods. While local SA evaluates the output variability changing one factor at a time, global SA ponders several factors simultaneously, allowing for the interaction between elements, the effect of factor range, and the shape of the factor probability density function to be considered. To analyze the relationship between the design (or input) parameters on the optimization objective (or output), the “sdo.analyze” function from Simulink® Design OptimizationTM [33] was implemented in a MatLAB script using the Partial Ranked Correlation (PRC). The global method was chosen because it analyzes how a model parameter and the outputs are correlated, adjusting to remove the other parameters’ effect. First, a sample of 607 cases with raw values (0–1) was generated using the Sobol sampling method. The sample size was defined following the recommendation in [68], which states that the minimum sample size should de 15–19 times the variables number considered in the analysis. Sobol quasirandom sequences are drawn from the probability distributions specified for the parameters, using Equation (7):
Varv = Llow + Lup − Llow × x (7)

where Varv is the variable value; x is the raw value, varying from 0 to 1; Llow is lower limit; and Lup is the upper limit of the variable range. Sampling-based on Sobol’ sequences pro- vides a highly systematic space-filling with low discrepancy, showing a better performance than other sample techniques [69]. The 607 cases were run using Colibri components, a tool that performs parametric simulations distributed with TT Toolbox [70]. A slider controls the case changes, and the resulting impact of each run is recorded into a .csv file. Regarding the simulation time, the 607 runs took around 21 h (≈2 min for simulation) using an Intel i7-7500U Core laptop, up to 3.2 GHz.

2.3. Step 3: Multiobjective Optimization (MOO) with Model-Based Algorithm Instead of using an evolutionary MOO algorithm, such as HypE [71], SPEA [72], or NSGA-II [73], commonly employed in similar investigations [11,17], the last step uses a Ra- dial Basis Function Multiobjective Optimization (RBFMOpt). This machine-learning-related MOO algorithm won the “Two Objectives Expensive” track of the Black Box Optimization Competition (BBCOMP) 2019 [74]. Moreover, a benchmark study presented in [75,76] showed its good performance compared to other algorithms, finding reasonable solu- tions with fewer simulations. It has proven efficient and robust, while genetic algorithms perform poorly [77], and therefore was chosen to run this study optimization phase. In single-objective optimization, the goal is to find a single point, e.g., a design so- lution, that best answers a sole performance metric or a project requirement. On the other hand, MOO aims to find the best solution points according to multiple conflicting objectives. These points or optimal solutions are non-dominated, meaning that one point’s objectives cannot be improved without harming the others. When connected, the points form a curve, which illustrates the optimization results, known as the Pareto surface or front. According to Ciftcioglu and Bittermann (2009) the Pareto ranking is this solution surface in a multidimensional solution space formed by several criteria, representing the objectives. Although the solutions are diverse on this surface, they are assumed to be valid in an identical way. Thus, the Pareto front graph supports designers’ decision-making since it allows visualization of the trade-off among objectives [78]. In that light, the RBF- MOpt’s goal, also known as a model-based method, is to find the nondominated points in the Pareto front. The algorithm builds and iteratively refines surrogate models of the unknown objective function that predict simulation results [79] and approximates the set of points in the solution surface by iterating over a series of weights based on a Halton sequence [80]. Wortmann and Natanian [75] explain that RBFMOpt exploits this property by resuming RBFOpt and feeding it at each iteration with all known points, reweighted Sustainability 2021, 13, x FOR PEER REVIEW 10 of 28

since it allows visualization of the trade-off among objectives [78]. In that light, the RBFMOpt’s goal, also known as a model-based method, is to find the nondominated points in the Pareto front. The algorithm builds and iteratively refines surrogate models of the unknown objective function that predict simulation results [79] and approximates the set of points in the solution surface by iterating over a series of weights based on a Halton sequence [80]. Wortmann and Natanian [75] explain that RBFMOpt exploits this property by resuming RBFOpt and feeding it at each iteration with all known points, reweighted according to the up-to-date set of weights. Hence, with every iteration, the initial RBFOpt surrogate model becomes increasingly accurate, leading to more effective optimization cycles. With this approach, model-based optimization is considered an attractive alternative for performance-oriented design [81] because it is seen as Sustainability 2021, 13, 5739 particularly effective for optimizing problems with complex associations between9 of 25 variables and objectives and time-expensive simulations [82]. Aimed for BSO Practitioners, the RBFOpt Algorithm Is Available in Grasshopper via the Plug-in Opossum [83]. according to the up-to-date set of weights. Hence, with every iteration, the initial RBFOpt surrogate model becomes increasingly accurate, leading to more effective optimization 3. Base-Case Building Model cycles. With this approach, model-based optimization is considered an attractive alterna- tive forThe performance-oriented base-case building (Figure design 2) [comprises81] because one it isof seenthe experimental as particularly houses effective from for the optimizingINCAS platform problems facility with [84, complex85], developed associations by the between French variables National and Institute objectives for Solar and time-expensiveEnergy—INES simulationsfacility located [82]. in Aimed Bourget-du-Lac, for BSO Practitioners, France (45°38’38.5 the RBFOpt″ N, Algorithm 5°52’27.4″ IsE, Availablealtitude 270 in Grasshopper m). The region via is the characterized Plug-in Opossum by warm [83]. summers (mean and max. temp of 20 and 34 °C), cold and wet winters (mean and min. temp. of 5 and −4 °C), and partly 3.cloudy Base-Case year-round Building (Köppen: Model temperate climate, warm summer—Cfb [86]). The reference building,The base-case also known building as I-MA (Figure house,2) is comprises a low-energy one oftwo-story the experimental rectangular houses construction from the(7.5 INCAS × 8.5 m), platform with an facility opaque [84 envelope,85], developed made of by cavity the French bricks National (42 cm thick) Institute covered for Solar with Energy—INESan aerogel-based facility exterior located insulating in Bourget-du-Lac, rendering. The Francebuilding (45 is◦ 38taken038.5 as00 aN, base 5◦52 case027.4 in00 thisE, altitudestudy because 270 m). one The of region its purposes is characterized is to assist by numerical warm summers validation (means, being and equipped max. temp with of 20numerous and 34 ◦ C),sensors cold andand wetfeaturing winters a simple (mean anddesign, min. which temp. favors of 5 andsimulation−4 ◦C), process and partly and cloudyverification. year-round Moreover, (Köppen: it is temperatea passive climate,building warm [87], summer—Cfbwhose design [represents86]). The reference a single- building,family residence also known typically as I-MA found house, in the is a regi low-energyon. Passive two-story Houses rectangular have been constructionexpanding in (7.5the ×market,8.5 m), as with they an present opaque themselves envelope made as a so oflution cavity to bricks the challenges (42 cm thick) related covered to energy with anefficiency aerogel-based [88–90]. exterior In this sens insulatinge, the base rendering. building The is also building representative is taken asand a basecharacterizes case in thisa movement, study because at least one in of Europe, its purposes to build is tounder assist strict numerical energy validations,standards. being equipped with numerousBased on a sensors one-week and monitoring featuring a campaign simple design, (19–25 which August favors 2014), simulation an E+ numerical process andmodel verification. was created, Moreover, calibrated, it is and a passive used to building perform [87 annual], whose energy design and represents natural ventilation a single- familyassessments residence in [91,92], typically which found also in theprovide region. a detailed Passive Housesdescription have of been the expandingmeasurement in theequipment, market, asexperimental they present protocol, themselves construction, as a solution and to the the climatic challenges data related recorded to energy on-site efficiencyand used [ 88at –the90]. simulation. In this sense, Moreover, the base buildingthe complete is also settings representative of the E+ and model, characterizes including a movement,the occupancy at least schedule in Europe, and the to build.idf file, under are available strict energy in the standards. Data in Brief article [93].

FigureFigure 2. 2.I-MA I-MA house: house: base-case base-case building. building.

Based on a one-week monitoring campaign (19–25 August 2014), an E+ numerical model was created, calibrated, and used to perform annual energy and natural ventilation assessments in [91,92], which also provide a detailed description of the measurement equipment, experimental protocol, construction, and the climatic data recorded on-site and used at the simulation. Moreover, the complete settings of the E+ model, including the occupancy schedule and the .idf file, are available in the Data in Brief article [93]. Model creation within the optimization framework begins by importing the .idf file available in [93] using the Honeybee component HB_Import idf. The base-case building geometry is translated into the 3D modeling parametric platform (Rhino + Grasshopper) through HB-Energy components. Figure3 shows the nine thermal zones modeled with the HB Model: three on the ground (Living room, Cellar, Hall 1), four on the first floor (Bedrooms 1–3, Hall 2), and an attic and a staircase zone. Natural ventilation can be used as a cooling strategy in all zones; therefore, the openings, either windows or external/internal Sustainability 2021, 13, x FOR PEER REVIEW 11 of 28

Model creation within the optimization framework begins by importing the .idf file available in [93] using the Honeybee component HB_Import idf. The base-case building geometry is translated into the 3D modeling parametric platform (Rhino + Grasshopper)

Sustainability 2021, 13, 5739 through HB-Energy components. Figure 3 shows the nine thermal zones modeled10 with of 25 the HB Model: three on the ground (Living room, Cellar, Hall 1), four on the first floor (Bedrooms 1–3, Hall 2), and an attic and a staircase zone. Natural ventilation can be used as a cooling strategy in all zones; therefore, the openings, either windows or doors,external/internal were modeled doors, as AirflowNetworkwere modeled as(AFN) AirflowNetwork objects. However, (AFN) objects. just the However, Living room just and the theLiving Bedrooms room and have the HVAC Bedrooms system, have modeled HVAC with system, the HBmodeled Apply Setpointwith the ValuesHB Applycomponent Setpoint thatValues uses component the E+ Ideal that Loads uses Air the System E+ Ideal. Loads Air System.

Bedroom 1 Bedroom 2 Bedroom 3 Hall 2

I-M A H ou . Stairs se . Hall 1 r loo t F . Cellar rs Fi A . Living I-M room

r oo Fl nd ou Gr A M I- Figure 3. Thermal zones of the building simulation model. Figure 3. Thermal zones of the building simulation model.

TheThe externalexternal openings, openings, either either windows windows or doors, or were doors, assumed were to haveassumed parametrically to have adjustableparametrically dimensions. adjustable Their dimensions. size varies inTheir a window-to-wall-ratio size varies in a functionwindow-to-wall-ratio using the HB Aperturesfunction using by Ratio thecomponent, HB Apertures which by Ratio depends component, on façade which orientation depends (HB on Façadefaçade Parametersorientation). Moreover,(HB Façade external Parameters shading). Moreover, devices wereexternal modeled shading with devices the HB were Window modeled Construction with the Shade HB component,Window Construction controlled Shade based component, on the solar controlled radiation based incidence on the solar on the radiation window, incidence with a parametricon the window, setpoint with varying a parametric from 400–600 setpoint W/m varying2. from 400–600 W/m2. OpeningsOpenings operationoperation regardingregarding naturalnatural ventilationventilation andand building’s building’s heating/cooling heating/cooling systemsystem waswas established,established, configuringconfiguring aa hybridhybrid behavior.behavior. VentilationVentilation controlcontrol dependsdepends onon occupancyoccupancy andand waswas basedbased onon aa temperaturetemperature setpoint,setpoint, whichwhich waswas parametrizedparametrized andand variedvaried fromfrom 20–2220–22◦ C.°C. The The living living room room apertures apertures can be can operated be operated only when only the when room the is occupied, room is whereasoccupied, the whereas bedrooms’ the windowsbedrooms’ are windows operable wheneverare operable someone whenever is in thesomeone house. is Regard- in the inghouse. the Regarding heating system the heating control, system its activation control, it happenss activation if the happens occupied if the room’s occupied operative room’s temperatureoperative temperature is below 18–19 is below◦C (parameterized 18–19 °C (parameterized value) so that value) the indoor so that temperature the indoor is maintainedtemperature at is 21 maintained◦C. Oncein at operation,21 °C. Once the in heater operation, is only the turned heater off is only when turned the occupancy off when inthe the occupancy room is null, in the and room whenever is null, the and windows whenever are open,the windows mechanical are ventilation open, mechanical cannot happen,ventilation as wellcannot as thehappen, contrary. as well as the contrary. Moreover,Moreover, an an extra extra operational operational condition condition was was considered considered to turn to on turn the coolingon the systemcooling insystem the conditioned in the conditioned spaces when spaces natural when ventilationnatural ventilation is insufficient is insufficient to maintain to maintain the indoor the ◦ temperatureindoor temperature within the within established the established parameterized parameterized limited (25–28 limitedC). (25–28 This hybrid°C). This behavior hybrid wasbehavior modeled was through modeled the throughEnergy the Management Energy Management System (EMS) System object (EMS) [94] byobject adding [94] additional by adding stringsadditional to the stringsHB Model to the to OpenStudioHB Model Modelto OpenStudiocomponent. Model The controlscomponent. developed The controls in the EMSdeveloped are presented in the EMS in [ 93are]. presented in [93]. 4. Selection of the Influential Variables and Sensitivity Analyses Results The relation between the design parameters on the outputs was analyzed through the Partial Ranked Correlation so that the most influential variable could be determined. With this approach, the performance of the radial-based algorithm can be improved, and the search for optimal solutions is therefore enhanced. Figure4 shows the calculated PRC of the 32 variables for the three objectives (NVE, TCL, and THL), sorting from the largest to the smallest absolute value. The higher the PRC absolute value, the more influential variable. The PRC positive/negative value indicates the proportional/inverse relationship between an input parameter and the outputs. Sustainability 2021, 13, x FOR PEER REVIEW 13 of 29 Sustainability 2021, 13, 5739 11 of 25

(a)

(b)

Figure 4. Cont. Sustainability 2021, 13, x FOR PEER REVIEW 14 of 29 Sustainability 2021, 13, 5739 12 of 25

(c)

Figure 4. Sensitivity Figurerankings 4. ofSensitivity PRC for NVE rankings (a), THL of PRC (b), for and NVE TCL (a ),(c) THL of the (b ),reference and TCL building. (c) of the reference building.

The figures show thatThe the figures order show and magnitude that the order of the and input magnitude variables of theslightly input diverge variables slightly diverge between the threebetween objectives. the Based three onobjectives. the PRC Basedanalysis, on the half PRC of the analysis, top 10 halfinfluential of the top 10 influential variables for the threevariables objectives for the overlapped three objectives. Table overlapped.4 shows the sensitivity Table4 shows analy thesis sensitivity results analysis results straightforwardly, illustrating the relationships between each input variable and the three straightforwardlySustainability, illustrating 2021, 13, x FOR PEER the REVIEW relationships between each input variable and the three 15 of 28 goals (i.e., positive goals or negative) (i.e., positive and each or negative) input variable and each’s sensitivity input variable’s ranking. sensitivity ranking. Based on these results and aiming to reduce the input variables number, Figure5 Table 4. Results of sensitivity analysis andshows locally the-improvements PRC’s sumBased for foron the these the remaining results three andobjectives, less aiming influential to redu sortingce variables the input the .variables numbers number, according Figure 5 to their absolute value andshows finding the PRC’s a newsum for arrangement the three objectives index., sorting the numbers according to their absolute value and finding a new arrangement index. Locally- PCR for NVE PCR for TCL PCR for THL Variable Description Variable Name Improved (Ranking) (Ranking) (Ranking) Solution Building long axis azimuth (o) x01_orient Negative (10) Positive (13) Positive (04) North WWR (%) x02_glzRn Positive (11) Positive (09) Positive (09) East WWR (%) x03_glzRe Positive (05) Positive (04) Positive (20) South WWR (%) x04_glzRs Positive (09) Positive (03) Negative (06) West WWR (%) x05_glzRw Positive (08) Positive (11) Negative (18) Window U-value (W/m2K) x06_windowU Negative (02) Positive (32) Positive (02) Window Solar Heat Gain x07_shgc Positive (04) Positive (10) Negative (05) Coefficient Aerogel thickness (m) x08_aeroT Positive (12) Negative (14) Negative (03) Roof thermal conductivity x09_roofC Negative (14) Negative (28) Positive (28) base-case (W/mK) Opening multiplier factor x10_shdOp Positive (13) Positive (23) Negative (07) HB E+ default Fraction of the shade surface x11_shdAir Positive (31) Negative (30) Negative (12) minimum open to airflow Figure 5. Sensitivity rankings of the PRC sum for NVE, TCL, and THL of the reference building. Figure 5. Sensitivity rankings of the PRC sum for NVE, TCL, and THL of the reference building. Lastly, the influential variables regarding all objectives were screened out to be analyzed in the next optimization step, keeping the balance between the three considered goals. The finally selected parameters are listed in Table 5, and the locally improved values are established for the less influential parameters. All 12 remained variables presented a PRC absolute result bigger than 0.1. The number of parameters could be drastically reduced because many had a low impact on objective functions, such as all those related to Ventilation area x Window Ratio (VWR). Adopting a unique value for such parameters makes the optimization problem more effective.

Table 5. Input variables and their ranges for multiobjective optimization.

Probability Base-Case Locally Improved Lower Upper Variable Description Variable Name Density Function Value Values Limit Limit Building long axis azimuth x01_orient Discrete 345 0 315 (o) Continuous North WWR (%) x02_glzRn 3.5 3.5 75 uniform Continuous East WWR (%) x03_glzRe 13 3.5 75 uniform Continuous South WWR (%) x04_glzRs 34 3.5 75 uniform Continuous West WWR (%) x05_glzRw 10 3.5 75 uniform Continuous Window U-value (W/m2K) x06_windowU 1.3 1.05 5.7 uniform Sustainability 2021, 13, 5739 13 of 25

Table 4. Results of sensitivity analysis and locally-improvements for the remaining less influential variables.

PCR for NVE PCR for TCL PCR for THL Locally-Improved Variable Description Variable Name (Ranking) (Ranking) (Ranking) Solution Building long axis azimuth (o) x01_orient Negative (10) Positive (13) Positive (04) North WWR (%) x02_glzRn Positive (11) Positive (09) Positive (09) East WWR (%) x03_glzRe Positive (05) Positive (04) Positive (20) South WWR (%) x04_glzRs Positive (09) Positive (03) Negative (06) West WWR (%) x05_glzRw Positive (08) Positive (11) Negative (18) Window U-value (W/m2K) x06_windowU Negative (02) Positive (32) Positive (02) Window Solar Heat Gain x07_shgc Positive (04) Positive (10) Negative (05) Coefficient Aerogel thickness (m) x08_aeroT Positive (12) Negative (14) Negative (03) Roof thermal conductivity x09_roofC Negative (14) Negative (28) Positive (28) base-case (W/mK) Opening multiplier factor x10_shdOp Positive (13) Positive (23) Negative (07) HB E+ default Fraction of the shade surface x11_shdAir Positive (31) Negative (30) Negative (12) minimum open to airflow Shading control setpoint—Solar x12_shdSp Positive (07) Positive (05) Negative (11) radiation on the window (W/m2) Minimum indoor air temperature—AFN ventilation x13_minAirT Negative (01) Positive (07) Positive (32) control strategy (◦C) Maximum indoor air temperature—AFN ventilation x14_maxAirT Positive (06) Negative (02) Negative (21) control strategy (◦C) Heating setpoint (◦C) x15_setPoint Positive (15) Negative (25) Positive (01) Cooling system operation x16_onOff Negative (3) Positive (01) Negative (30) (on-off) Discharge coefficient x17_disCoef Positive (28) Positive (19) Negative (31) minimum LWindE Window VWR x18_LWindE Positive (30) Positive (18) Negative (22) base-case LwindS1 Window VWR x19_LwindS1 Positive (20) Negative (31) Negative (15) base-case LPorteS2 Window VWR x20_LPorteS2 Positive (17) Negative (22) Positive (19) base-case LPorteW Window VWR x21_LPorteW Positive (19) Negative (15) Negative (14) base-case LDoorH Window VWR x22_LDoorH Positive (24) Positive (24) Positive (16) base-case LDoorC Window VWR x23_LDoorC Positive (27) Negative (06) Positive (08) base-case R1WindN Window VWR x24_R1WindN Positive (22) Negative (17) Positive (23) base-case R1WindW Window VWR x25_R1WindW Negative (16) Negative (27) Positive (13) base-case H2W1door Window VWR x26_H2W1door Positive (21) Positive (20) Negative (17) base-case R2WindW Window VWR x27_R2WindW Negative (32) Negative (12) Positive (29) base-case R2WindS Window VWR x28_R2WindS Positive (26) Positive (26) Positive (27) base-case R2Ndoor Window VWR x29_R2Ndoor Positive (23) Negative (21) Positive (25) base-case R3WindE Window VWR x30_R3WindE Positive (25) Positive (29) Negative (24) base-case R3SWind Window VWR x31_R3SWind Positive (18) Negative (08) Negative (10) base-case R3Sdoor Window VWR x32_R3Sdoor Negative (29) Negative (16) Positive (26) base-case Note: The bold items are less influential variables and are supposed to be locally improved.

Lastly, the influential variables regarding all objectives were screened out to be an- alyzed in the next optimization step, keeping the balance between the three considered goals. The finally selected parameters are listed in Table5, and the locally improved values are established for the less influential parameters. All 12 remained variables presented a PRC absolute result bigger than 0.1. The number of parameters could be drastically reduced because many had a low impact on objective functions, such as all those related to Ventilation area x Window Ratio (VWR). Adopting a unique value for such parameters makes the optimization problem more effective. Sustainability 2021, 13, 5739 14 of 25

Table 5. Input variables and their ranges for multiobjective optimization.

Probability Density Base-Case Locally Lower Upper Variable Description Variable Name Function Value Improved Values Limit Limit Building long axis azimuth (o) x01_orient Discrete 345 0 315 North WWR (%) x02_glzRn Continuous uniform 3.5 3.5 75 East WWR (%) x03_glzRe Continuous uniform 13 3.5 75 South WWR (%) x04_glzRs Continuous uniform 34 3.5 75 West WWR (%) x05_glzRw Continuous uniform 10 3.5 75 Window U-value (W/m2K) x06_windowU Continuous uniform 1.3 1.05 5.7 Window Solar Heat Gain Coefficient x07_shgc Continuous uniform 0.3 0.21 0.81 Aerogel thickness (m) x08_aeroT Continuous uniform 0.04 0.04 0.12 Roof thermal conductivity (W/mK) x09_roofC Continuous uniform 0.055 0.055 Opening multiplier factor x10_shdOp Continuous uniform 0 0.5 Fraction of the shade surface open to x11_shdAir Continuous uniform 0 0 airflow (permeability) Shading control setpoint—Solar x12_shdSp Continuous uniform 0 400 600 radiation on the window (W/m2) Minimum indoor air temperature—AFN ventilation x13_minAirT Continuous uniform 20 20 22 control strategy (◦C) Maximum indoor air temperature—AFN ventilation x14_maxAirT Continuous uniform 27 25 28 control strategy (◦C) Heating setpoint (◦C) x15_setPoint Continuous uniform 19 18 19 Cooling system operation (on-off) x16_onOff Discrete False True Discharge coefficient x17_disCoef Continuous uniform 0.5 0.6 LWindE Window VWR x18_LWindE Continuous uniform 0.75 0.75 LwindS1 Window VWR x19_LwindS1 Continuous uniform 0.75 0.75 LPorteS2 Window VWR x20_LPorteS2 Continuous uniform 0.75 0.75 LPorteW Window VWR x21_LPorteW Continuous uniform 0.75 0.75 LDoorH Window VWR x22_LDoorH Continuous uniform 0.75 0.75 LDoorC Window VWR x23_LDoorC Continuous uniform 0.75 0.75 R1WindN Window VWR x24_R1WindN Continuous uniform 0.75 0.75 R1WindW Window VWR x25_R1WindW Continuous uniform 0.75 0.75 H2W1door Window VWR x26_H2W1door Continuous uniform 0.75 0.75 R2WindW Window VWR x27_R2WindW Continuous uniform 0.75 0.75 R2WindS Window VWR x28_R2WindS Continuous uniform 0.75 0.75 R2Ndoor Window VWR x29_R2Ndoor Continuous uniform 0.75 0.75 R3WindE Window VWR x30_R3WindE Continuous uniform 0.75 0.75 R3SWind Window VWR x31_R3SWind Continuous uniform 0.75 0.75 R3Sdoor Window VWR x32_R3Sdoor Continuous uniform 0.75 0.75

5. MOO through RBFMOpt In this step, the goal was to find the optimal values of the 12 selected influential passive design parameters for maximizing cooling ventilation (NVE) while minimizing the building energy demand (THL and TCL). Although more than forty parameters control the RBFOpt, the Opossum’s graphical user interface reduces its complexity into three tabs that afford increasing the control levels and offers presets based on intensive testing with mathematical test functions [76]. Table6 shows the adopted settings within Opossum in the optimization runs (Run 1, Run 2, and Run 3). Most of them were left as default, following the predetermined plug-in configurations. Each variable is modeled in the Grasshopper canvas with a number slider, floating the value according to the predetermined lower and upper limits. Opossum saves each interaction run in a single log file, and after performing all function evaluations, it sum- marizes the results in a table, which makes it easy to revisit all optimization outcomes by double-clicking the entries in it. Among the results is the hypervolume from each simu- lation, which measures the objective space’s volume dominated by the set of points, e.g., design solutions [75]. Within MOO, the hypervolume must be maximized as all objectives are to be minimized. The goal is to dominate as much of the objective space as possible since, mathematically, if one set is better than the other, it spans a larger hypervolume [95]. Sustainability 2021, 13, 5739 15 of 25

Table 6. Adopted settings with the Opossum optimization process.

Configuration Description Input Data One is limited to either minimize or maximize the objective functions. Optimization type Minimize If controversial, the one to be adjusted is multiplied by −1. Algorithm Algorithm chosen from those available in the plug-in RBFOpt Max iterations Stop the simulation if the iterations exceed this number 500 Number of optimizations runs Number of times the simulations will be repeated 3 Number of cycles Determines how long the algorithm spends optimizing each set of weights 6

The former procedures resulted in Figure6, which shows a 3D representation of the three optimization objectives results. Each run generated respectively 268, 147, and 168 cases, totaling 588 function evaluations or model regenerations. It took about 20 h to run them all, with the same laptop configurations mentioned in item 0. The Pareto front Sustainability 2021, 13, x FOR PEER REVIEW 18 of 28 is depicted in Figure7, where the best solutions found in each run can be observed at the curve formed at the lower-left corner. Sustainability 2021, 13, x FOR PEER REVIEW 18 of 28

Figure 6. 3D representation of the multiobjective optimization results for the I-MA house. Figure 6. 3D representation of the multiobjective optimization results for the I-MA house. Figure 6. 3D representation of the multiobjective optimization results for the I-MA house.

FigureFigure 7. 7. Pareto Pareto solutions onon aa 2D 2D representation. representation. Figure 7. Pareto solutions on a 2D representation. TheThe hypervolume hypervolume calculated inin eacheach of of the the three three runs runs is isthe the metric metric used used to findto find the the optimizedoptimized solution.solution. InIn this regard, FigureFigure 88 groups groups the the three three runs runs according according to theto the hypervolumehypervolume generated, generated, which showsshows stability stability (convergence) (convergence) of ofthe the results results between between 100 100 and 150 interactions. The numbers in the graph correspond to the NVE, TCL, and THL and 150 interactions. The numbers in the graph correspond to the NVE, TCL, and THL results of the three runs’ optimal solutions, which are also summarized in Table 7. results of the three runs’ optimal solutions, which are also summarized in Table 7. Sustainability 2021, 13, 5739 16 of 25

Sustainability 2021, 13, x FOR PEER REVIEWThe hypervolume calculated in each of the three runs is the metric used to find 19 of 28 the optimized solution. In this regard, Figure8 groups the three runs according to the Sustainability 2021, 13, x FOR PEER REVIEW 19 of 28 hypervolume generated, which shows stability (convergence) of the results between 100 and 150 interactions. The numbers in the graph correspond to the NVE, TCL, and THL results of the three runs’ optimal solutions, which are also summarized in Table7.

Figure 8. Hypervolume calculated by the RBFOpt algorithm vs. function evaluations and optimal FigureFiguresolutions 8. Hypervolume 8. Hypervolume for each run. calculated by by the the RBFOpt RBFOpt algorithm algorithm vs. function vs. function evaluations evaluations and optimal and optimal solutionssolutions for for each each run. run.

Moreover,Moreover, Figure Figure9 allows 9 allows a comparison a comparison of these results of these variability results over variability the runs, over the runs, presentingpresentingMoreover, their theirFigure normalized normalized 9 allows values, a va whilecomparisonlues, Figure while 10 illustratesofFigure these 10 normalizedresults illustrates variability values, normalized but over of values,the runs, but of presentingthethe parameters parameters their ofnormalized RBFOpt of RBFOpt solutions va lues,solutions according while according toFigure the ranges. 10 to illustrates the ranges. normalized values, but of the parameters of RBFOpt solutions according to the ranges.

FigureFigure 9. Comparison9. Comparison of the of variability the variability of the results of the in the results three runs.in the three runs. Figure 9. Comparison of the variability of the results in the three runs. Table 7. Range of optimization variables in base-case and RBFOpt solutions and their respective objective functions Tableresults. 7. Range of optimization variables in base-case and RBFOpt solutions and their respective objective functions results. Selected Influential Variables Variable Name Base-Case Ranges Run 1 Run 2 Run 3 BuildingSelected long axis Influential azimuth Variables(o) Variable x01_orient Name Base-Case 345 Ranges (0.315) Run 1 315 Run 2 90 Run 3 90 BuildingNorth long WWR axis (%) azimuth (o) x01_orient x02_glzRn 345 3.5 (0.315) (5.75) 315 17 90 57 90 15 NorthEast WWR WWR (%) (%) x02_glzRn x03_glzRe 3.5 13 (5.75) (5.75) 17 5 57 62 15 64 East SouthWWR WWR(%) (%) x03_glzRe x04_glzRs 13 34 (5.75) (5.75) 5 7 62 7 64 34 SouthWest WWR WWR (%) (%) x04_glzRs x05_glzRw 34 10 (5.75) (5.75) 7 5 7 12 34 42 WestWindow WWR (%) U-value (W/m2K) x05_glzRw x06_windowU 10 1.3 (5.75) (1.05, 5.7) 5 1.09 12 1.08 42 1.06 WindowWindow U-value Solar (W/m Heat2K) Gain Coefficient x06_windowU x07_shgc 1.3 0.3 (1.05, (0.21, 5.7) 0.81)1.09 0.391.08 0.301.06 0.70 WindowAerogel Solar thickness Heat Gain (m) Coefficient x07_shgc 0.3 0.04 (0.21, (0.04, 0.81) 0.12) 0.39 0.12 0.30 0.10 0.70 0.11 x08_aeroT Aerogel thickness (m) 2 0.04 (0.04, 0.12) 0.12 0.10 0.11 Wall U-value (W/m K) x08_aeroT 0.71 (0.71, 0.26) 0.26 0.31 0.28 Wall ShadingU-value (W/mcontrol2K) setpoint—Solar radiation on the 0.71 (0.71, 0.26) 0.26 0.31 0.28 x12_shdSp 0 (400, 600) 590 490 520 Shading control setpoint—Solar2 radiation on the window (W/m ) x12_shdSp 0 (400, 600) 590 490 520 window (W/m2) Sustainability 2021, 13, 5739 17 of 25

Table 7. Range of optimization variables in base-case and RBFOpt solutions and their respective objective functions results.

Selected Influential Variables Variable Name Base-Case Ranges Run 1 Run 2 Run 3 Building long axis azimuth (o) x01_orient 345 (0.315) 315 90 90 North WWR (%) x02_glzRn 3.5 (5.75) 17 57 15 East WWR (%) x03_glzRe 13 (5.75) 5 62 64 South WWR (%) x04_glzRs 34 (5.75) 7 7 34 West WWR (%) x05_glzRw 10 (5.75) 5 12 42 Window U-value (W/m2K) x06_windowU 1.3 (1.05, 5.7) 1.09 1.08 1.06 Window Solar Heat Gain Coefficient x07_shgc 0.3 (0.21, 0.81) 0.39 0.30 0.70 Aerogel thickness (m) 0.04 (0.04, 0.12) 0.12 0.10 0.11 x08_aeroT Wall U-value (W/mSustainability2K) 2021, 13, x FOR PEER REVIEW 0.71 (0.71, 0.26) 0.26 0.31 0.28 20 of 28

Shading control setpoint—Solar radiation x12_shdSp 0 (400, 600) 590 490 520 on the window (W/m2) Minimum indoor air temperature—AFN Minimum indoor◦ air temperature—AFNx13_minAirT ventilation 20 (20, 22) 20.3 20 20 ventilation control strategy ( C) x13_minAirT 20 (20, 22) 20.3 20 20 Maximum indoorcontrol air temperature—AFN strategy (°C) x14_maxAirT 27 (25, 28) 28 28 28 ventilation controlMaximum strategy indoor (◦C) air temperature—AFN ventilation ◦ x14_maxAirT 27 (25, 28) 28 28 28 Heating setpointcontrol ( C) strategy (°C) x15_setPoint 19 (18, 19) 18 18 18 NVEHeating setpoint (°C) 585 x15_setPoint 19 665 (18, 19) 933 18 1096 18 18 THLNVE 11.238 585 7.924 8.359665 7.455933 1096 TCLTHL 10 11.238 4 26 7.924 788.359 7.455 TCL 10 4 26 78

Figure 10. Comparison between solution variables. Figure 10. Comparison between solution variables.

Additionally,Additionally, Figure 11 shows Figure the 11 respective shows the optimizedrespective geometryoptimized generatedgeometry generated for the for the three runs’ selectedthree runs’ solutions selected (Figure solutions 11b–d) (Figure and 11b–d) the base and case the (Figure base case 11 a).(Figure The images11a). The images are automaticallyare automatically generated with generated the Honeybee with the component HoneybeeHB component Visualyze byHB Type Visualyzeand show by Type and show the changes related to building orientation and openings size. Thus, the significant the changes related to building orientation and openings size. Thus, the significant WWR WWR variations that were firstly numerically attested are also visualized. variations that were firstly numerically attested are also visualized.

(a) (b) Sustainability 2021, 13, x FOR PEER REVIEW 20 of 28

Minimum indoor air temperature—AFN ventilation x13_minAirT 20 (20, 22) 20.3 20 20 control strategy (°C) Maximum indoor air temperature—AFN ventilation x14_maxAirT 27 (25, 28) 28 28 28 control strategy (°C) Heating setpoint (°C) x15_setPoint 19 (18, 19) 18 18 18 NVE 585 665 933 1096 THL 11.238 7.924 8.359 7.455 TCL 10 4 26 78

Figure 10. Comparison between solution variables.

Additionally, Figure 11 shows the respective optimized geometry generated for the three runs’ selected solutions (Figure 11b–d) and the base case (Figure 11a). The images are automatically generated with the Honeybee component HB Visualyze by Type and

Sustainability 2021, 13, 5739 show the changes related to building orientation and openings size. Thus, the significant18 of 25 WWR variations that were firstly numerically attested are also visualized.

Sustainability 2021, 13, x FOR PEER REVIEW 21 of 28

(a) (b)

(c) (d)

FigureFigure 11. 11. E+ geometryE+ geometry models models of the of(a) thebase( casea) base and case(b–d) and optimized (b–d) optimizedsolutions (b solutions) Run 1, (c) ( bRun) Run 2, 1, and (d) Run 3. (c) Run 2, and (d) Run 3.

InIn sum, sum, when when comparing comparing all all runs runs to to the the base base case, case, an an improvement improvement between between 14–87%14–87% andand 26–34% 26–34% occurs inin NVENVE and and THL, THL, respectively. respectively. As forAs TCL,for TCL, a reduction a reduction of 60% of concern- 60% concerninging the reference the reference is restricted is restricted to Run to 1, Run with 1, an with increase an increase of 160% of for 160% Run for 2 andRun 680% 2 and in 680%Run 3in. Nevertheless,Run 3. Nevertheless, cooling consumption cooling consumption presents nearly presents negligible nearly values. negligible Thus, values. turning Thus,on the turning air conditioning on the air conditioning system can be system disregarded, can be disregarded, meaning that meaning the I-MA that building the I-MA can buildingrely on coolingcan rely natural on cooling ventilation natural duringventilation the warm during seasons. the warm seasons.

6.6. Discussion Discussion AA fast fast convergence convergence can can be be noted noted regarding regarding the the number number of of runs runs presented presented in in Figure Figure 88 (less(less than than 150 150 interactions). interactions). Finding Finding optimal optimal solutions solutions with with few few simu simulationslations is is one one of of the the RBFMOptRBFMOpt algorithm algorithm advantages advantages pointed pointed in in benchmark benchmark studies studies [75,76] [75,76 ]when when compared compared to to otherother algorithms. algorithms. Observing Observing the the object object function function results results individually individually in in Figure Figure 8,8 ,the the total total heatheat loads loads (THL) (THL) present present a aslight slight variation variation in in all all runs, runs, ranging ranging from from 7455 7455 to to 8359 8359 kWh. kWh. RegardingRegarding the the objectives relatedrelated toto natural natural ventilation, ventilation, NVE, NVE, and and total total cooling cooling loads loads (TCL), (TCL),the values the values show moreshow significant more significant variability, variability, ranging ranging from 665 from to 1096 665 h/year to 1096 for h/year NVE for and NVEfrom and 4 to from 78 kWh 4 to for78 kWh TCL. for Simultaneously, TCL. Simultaneously, there is a there direct is relationshipa direct relationship between between these two theseresults, two where results, the where greater the the greater number the of number NVE hours, of NVE the greaterhours, thethe energygreater consumption the energy consumptiondue to cooling due (TCL). to cooling By contrast, (TCL). such By contra associationst, such is not association observed is among not observed the heating among loads theand heating other objectives.loads and other objectives. WhenWhen analyzing analyzing each ofof thethe variable variable outcomes outcomes for for the the optimal optimal alternatives, alternatives, thebuild- the θ ◦ θ ◦ buildinging long long axis axis azimuth azimuth (x01) (x01) presents presents for for runs runs 2 2 and and 3 3 θ= =90 90°,, whilewhile Run 1 1 has has θ == 315°, 315 , representingrepresenting a aminor minor difference difference regarding regarding the the base base case. case. On On the the other other hand, hand, in in all all solutions, solutions, the long axis changes so that the façades are more exposed. The base case has a north–south the long axis changes so that the façades are more exposed. The base case has a north–south orientation, where the south façade is the one with the most significant solar incidence orientation, where the south façade is the one with the most significant solar incidence and and the one with the most extensive opening area. When observing the three optimized the one with the most extensive opening area. When observing the three optimized solutions, solar distribution is more balanced among the façades, which also have different solutions, solar distribution is more balanced among the façades, which also have different WWR. Thus, it is evident that with a heterogeneous distribution of the glazed areas, the WWR. Thus, it is evident that with a heterogeneous distribution of the glazed areas, the proposed implantation in the optimized solutions enhances the solar gains through the different building translucent facades. On the other hand, compared to the base-case values (Figure 9), the optimized solutions show a clear improvement in NVE and THL of all runs and for TCL in Run 1. The NVE-bars show an increasing behavior for all runs, but the THL-bars show a decreasing one. As for the TCL, on the other hand, the bars only diminish in run 1. Besides showing the objective results for each run, Table 6 also outlines the scope of the optimization variables from both base case and optimal solutions. Figure 10 presents the solution variables, except for the building orientation, within a box plot graph with normalized values centered on median 0, allowing for a direct results’ correlation. Sustainability 2021, 13, 5739 19 of 25

proposed implantation in the optimized solutions enhances the solar gains through the different building translucent facades. On the other hand, compared to the base-case values (Figure9), the optimized solu- tions show a clear improvement in NVE and THL of all runs and for TCL in Run 1. The NVE-bars show an increasing behavior for all runs, but the THL-bars show a decreasing one. As for the TCL, on the other hand, the bars only diminish in run 1. Besides showing the objective results for each run, Table6 also outlines the scope of the optimization variables from both base case and optimal solutions. Figure 10 presents the solution variables, except for the building orientation, within a box plot graph with normalized values centered on median 0, allowing for a direct results’ correlation. Some parameters show a low variation, while others present a high range. Wort- mann [76] comments in this regard that repeated runs of stochastic algorithms for identical settings and problems can have very different results. In this sense, parameters related to the temperature and shading setpoints, aerogel thickness, and window U-Value present more cohesive results, while geometric variables are more dispersed. Therefore, it can be seen that concerning the physical properties, the values remain within a narrow range. On the other hand, the variables related to the building shape and form welcomed more alternatives, presenting a wider variance. As a result, during the early design stages, the variables associated with the physical properties could be restricted to a known range, focusing the search for optimized solutions on the geometric aspects. With considerable discrepancies, the four WWRs (x02, x03, x04, and x05) vary sig- nificantly in all runs, where Run 1 presents the closest values to the base case, which is reflected in the objective function’s outputs. Similarly, bigger WWRs lead to a higher NVE and TCL, which is the Run 3 case. On the other hand, the same Run also presents the lowest heating consumption (THL). That is because the Window U-values (x06) remained within small values, allowing solar entry with low thermal losses in periods without radiation. In high Window U-values, oversized windows would negatively impact heating loads since the opaque/isolated surfaces would decrease, and the losses due to a low-performance glass could surpass solar gains. Moreover, concerning the insulating thickness (x08), its value in Run 3 was not the largest one found, at 11 cm, while Run 1 remains with the maximum range, 12 cm, and still had a greater THL. In this sense, the aerogel layer’s optimized values were left between 10 and 12 cm, more than double compared to the base case. When converting the corre- sponding thickness values (cm) to Wall U-values (W/m2K), the wall thermal transmittance varies from 0.71–0.26 W/m2K, for an aerogel thickness of 4–12 cm, respectively. The Wall U-Value found in Run 2 and 3 correspond to 0.31 W/m2K and 0.28 W/m2K. Therefore, when relating the Walls and Windows U-values for the three solutions, a inversely pro- portional relationship is perceived in Run 1, where the transparent surface presents the worst performance and the opaque surface the best. However, this is not the case for Run 2 or 3, although both values are close. Nonetheless, a relationship between the different envelope systems (opaque vs. translucid) is observed, which seeks to compensate each other to achieve the desired building performance. No clear relationship was observed between the SHGC (x07) and Window U-value (x06) variables. The Window U-value shows a slight variance while SHGC presents a broader range. Run 3 has both the best Window U-value and the worst SHGC, which might indicate compensation, but it is not the case with the other two solutions. Furthermore, Table6 results show that the setpoint temperatures are at their limit and that the minimum (x13) and maximal (x14) optimized air temperatures for natural ventilation represent their respective lowest and highest possible values. Likewise, the heating setpoint (x15) stays within its lower limit. This low variance and even constancy are also observed in Figure 10, showing that the temperature range for the window’s operation resulted in a good NV performance (20–28 ◦C). On the other hand, setting a higher upper limit, bis 31 ◦C for instance, might also be acceptable and could be considered, as exposed in studies in hot and humid climates [96–98]. Sustainability 2021, 13, 5739 20 of 25

Concerning the shading control setpoint (x12), a stochastic relationship is also found when analyzing the optimization variables and the objectives outputs. Nonetheless, the variables interval among the solutions remains within a smaller dimension (490–590 W/m2) than the initial range (400–600 W/m2). Thus, the search space is limited, easing local parameter improvement. As a final comment, the optimized configurations of Figure 11 could be replicable in similar buildings under the same climatic conditions or used as a starting point when performing analogous studies. In this way, local improvements can be implemented by restricting the variables number with reference values, thus preoptimizing the solutions. Lastly, designing on a parametric platform makes it easier to handle the numerous geometric variables of a project, which is one of the challenges when proposing high- performance solutions. Therefore, the approach is an uncomplicated way to deal mainly with the building shape and experiment with various alternatives to find the one that best fits the proposed objectives.

7. Conclusions This study uses parameterization, simulation, sensitivity analyses, and optimization tools applied to a residential building, set as a reference case. An optimization framework is introduced, employing a parametric 3D modeling platform and a radial-based algorithm. Moreover, the paper presents a brief review of performance-based design combined with building simulation and optimization. It evidenced the use of the same program in project development as a user-friendly alternative to integrate the concept of Multiobjective Optimization (MOO) into the design process. Sensitivity Analysis (SA) was performed before the optimization step in an addendum to the one-software approach, given the variables under investigation. Thus, the algorithm performance could be improved, enhancing the search for the optimal solutions to build. Among the main conclusions concerning the SA and optimization outcomes, it is highlighted that: • The influential variables identified in SA analyses depended on the objective consid- ered, showing different ranks among the three established metrics: Natural Ventilation Effectiveness (NVE), Total Heating Loads (THL), and Total Coaling Loads (TCL). How- ever, an overall perspective identified those with the most impact as the setpoint temperatures that regulated natural ventilation or mechanical systems activation. On the other hand, although considered relevant for openings design, the parameter about the ventilation area provided smaller contributions. Therefore, together with the less influential variables, it was locally improved; • MOO results showed a direct relationship between the size of the windows, NVE, and TCL, which does not apply to THL. The building envelope’s thermal transmittance showed a more significant impact for the heating loads (THL), and all optimized solutions had low U-values for both opaque and transparent surfaces. Given these dif- ferences, the complexity of multiobjective problems is evidenced, and the optimization stage can be considered an ally when developing high-performance buildings; • The model-based algorithm (RBFMOpt) used at the optimization step showed per- formance consistent with that presented in the benchmark studies, converging with a low number of interactions. Therefore, its application in time-intense simulation investigations is endorsed; • Findings concerning the physical and geometric variables range could be applied in similar studies, limiting the parameters related to material properties and increasing those about geometry. The optimization results showed that the geometric aspects provided a greater solution diversity among the variables investigated in this work. • Regarding the framework adopted in this research, the following aspects can be stressed. • Modeling through a 3D parametric platform allows for the manipulating of numerous variables, being especially effective when dealing with geometric parameters; Sustainability 2021, 13, 5739 21 of 25

• Performing all processes through a single software reduces uncertainties and provides a more straightforward workflow, which facilitates control and implementation; • The approach is suitable for early project stages because architects and designers would be more receptive and better instrumented to apply MOO, encouraging passive strategies implementation when using such tools. Finally, future research could include testing different algorithms to evaluate their performance and differences between the optimized solutions. Such investigations can sup- port studies and applications related to performance-based design, helping to consolidate the approach.

Author Contributions: Conceptualization, N.R.M.S. and J.C.C.; Data curation, N.R.M.S.; Formal analysis, N.R.M.S.; Investigation, N.R.M.S.; Methodology, N.R.M.S.; Project administration, H.G.; Supervision, J.C.C.; Visualization, N.R.M.S.; Writing—original draft, N.R.M.S.; Writing—review & editing, J.C.C. and L.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Supplementary material associated with the reference [93] can be found in the online version at doi: 10.1016/j.dib.2021.106753. The data presented in this study are available on request from the corresponding author. Acknowledgments: This research was possible thanks to the contributions of the Federal Univer- sity of the Jequitinhonha and Mucuri Valleys (UFVJM, Brazil), and the Materials Testing Institute University of Stuttgart (MPA, Germany), which collectively supported this work. A special acknowl- edgment goes to Mario Alves da Silva, who provided valuable information and assistance on the optimization phase. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations AFN, Airflow Network; BBCOMP, Black Box Optimization Competition; BIM, Building Information Modelling; BSO, Building Simulation Optimization; EMS, Energy Management System; E+, Ener- gyPlus; HB, Honeybee; HVAC, Heating, Ventilating, and Air Conditioning; INES, French National Institute for Solar Energy; MOO, multiobjective optimization; NVE, Natural Ventilation Effectiveness; PCM’s, Phase Change Materials; PRC, Partial Ranked Correlation; RBFMOpt, Radial Basis Function Multiobjective Optimization; SA, Sensitivity Analysis; SHGC, Solar Heat Gain Coefficient; TCL, Total Cooling Loads; THL, Total Heating Loads; VWR, Ventilation area x Window Ratio; WWR, Window-to-Wall Ratio.

References 1. European Commission. Communication from the Commission to the European Parliament, the Council, the European Economic and Social Committee and the Committee of the Regions: A Policy Framework for Climate and Energy in the Period from 2020 Up to 2030, Brussels. 2014. Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX: 52014DC0015&from=EN (accessed on 13 September 2020). 2. Yu, W.; Li, B.; Jia, H.; Zhang, M.; Wang, D. Application of multi-objective genetic algorithm to optimize energy efficiency and thermal comfort in building design. Energy Build. 2015, 88, 135–143. [CrossRef] 3. Gou, S.; Nik, V.M.; Scartezzini, J.-L.; Zhao, Q.; Li, Z. Passive design optimization of newly-built residential buildings in Shanghai for improving indoor thermal comfort while reducing building energy demand. Energy Build. 2018, 169, 484–506. [CrossRef] 4.M éndez Echenagucia, T.; Capozzoli, A.; Cascone, Y.; Sassone, M. The early design stage of a building envelope: Multi-objective search through heating, cooling and lighting energy performance analysis. Appl. Energy 2015, 154, 577–591. [CrossRef] 5. Huang, K.-T.; Hwang, R.-L. Parametric study on energy and thermal performance of school buildings with natural ventilation, hybrid ventilation and air conditioning. Indoor Built Environ. 2016, 25, 1148–1162. [CrossRef] 6. Nguyen, A.-T.; Reiter, S.; Rigo, P. A review on simulation-based optimization methods applied to building performance analysis. Appl. Energy 2014, 113, 1043–1058. [CrossRef] Sustainability 2021, 13, 5739 22 of 25

7. Westermann, P.; Evins, R. Surrogate modelling for sustainable building design—A review. Energy Build. 2019, 198, 170–186. [CrossRef] 8. Chen, X.; Yang, H.; Zhang, W. Simulation-based approach to optimize passively designed buildings: A case study on a typical architectural form in hot and humid climates. Renew. Sustain. Energy Rev. 2018, 82, 1712–1725. [CrossRef] 9. Bradner, E.; Iorio, F.; Davis, M. Parameters tell the design story: Ideation and abstraction in design optimization. In Proceedings of the SimAUD 2014, Symposium on Simulation for Architecture and Urban Design, Tampa, FL, USA, 13–16 April 2014. 10. Shi, X.; Tian, Z.; Chen, W.; Si, B.; Jin, X. A review on building energy efficient design optimization rom the perspective of architects. Renew. Sustain. Energy Rev. 2016, 65, 872–884. [CrossRef] 11. Hamdy, M.; Nguyen, A.-T.; Hensen, J.L.M. A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems. Energy Build. 2016, 121, 57–71. [CrossRef] 12. Bre, F.; Silva, A.S.; Ghisi, E.; Fachinotti, V.D. Residential building design optimisation using sensitivity analysis and genetic algorithm. Energy Build. 2016, 133, 853–866. [CrossRef] 13. Yang, M.-D.; Lin, M.-D.; Lin, Y.-H.; Tsai, K.-T. Multiobjective optimization design of green building envelope material using a non-dominated sorting genetic algorithm. Appl. Therm. Eng. 2017, 111, 1255–1264. [CrossRef] 14. Augenbroe, G. Trends in building simulation. Build. Environ. 2002, 37, 891–902. [CrossRef] 15. Law, A.M. How to build valid and credible simulation models. In Proceedings of the Winter Simulation Conference, Austin, TX, USA, 13–16 December 2019; Rossetti, M.D., Hill, R.R., Johansson, B., Dunkin, A., Ingalls, R.G., Eds.; IEEE: Piscataway, NJ, USA, 2009. 16. Tian, Z.; Zhang, X.; Jin, X.; Zhou, X.; Si, B.; Shi, X. Towards adoption of building energy simulation and optimization for passive building design: A survey and a review. Energy Build. 2018, 158, 1306–1316. [CrossRef] 17. Konak, A.; Coit, D.W.; Smith, A.E. Multi-objective optimization using genetic algorithms: A tutorial. Reliab. Eng. Syst. Saf. 2006, 91, 992–1007. [CrossRef] 18. Evins, R. A review of computational optimisation methods applied to sustainable building design. Renew. Sustain. Energy Rev. 2013, 22, 230–245. [CrossRef] 19. Machairas, V.; Tsangrassoulis, A.; Axarli, K. Algorithms for optimization of building design: A review. Renew. Sustain. Energy Rev. 2014, 31, 101–112. [CrossRef] 20. Tuhus-Dubrow, D.; Krarti, M. Genetic-algorithm based approach to optimize building envelope design for residential buildings. Build. Environ. 2010, 45, 1574–1581. [CrossRef] 21. Gossard, D.; Lartigue, B.; Thellier, F. Multi-objective optimization of a building envelope for thermal performance using genetic algorithms and artificial neural network. Energy Build. 2013, 67, 253–260. [CrossRef] 22. Ascione, F.; de Masi, R.F.; de Rossi, F.; Ruggiero, S.; Vanoli, G.P. Optimization of building envelope design for nZEBs in Mediterranean climate: Performance analysis of residential case study. Appl. Energy 2016, 183, 938–957. [CrossRef] 23. Zhai, D.; Soh, Y.C. Balancing indoor thermal comfort and energy consumption of ACMV systems via sparse swarm algorithms in optimizations. Energy Build. 2017, 149, 1–15. [CrossRef] 24. Marini, D. Optimization of HVAC systems for distributed generation as a function of different types of heat sources and climatic conditions. Appl. Energy 2013, 102, 813–826. [CrossRef] 25. Stavrakakis, G.M.; Zervas, P.L.; Sarimveis, H.; Markatos, N.C. Optimization of window-openings design for thermal comfort in naturally ventilated buildings. Appl. Math. Model. 2012, 36, 193–211. [CrossRef] 26. Grygierek, K.; Ferdyn-Grygierek, J. Multi-Objective Optimization of the Envelope of Building with Natural Ventilation. Energies 2018, 11, 1383. [CrossRef] 27. Lapisa, R.; Bozonnet, E.; Salagnac, P.; Abadie, M.O. Optimized design of low-rise commercial buildings under various climates—Energy performance and passive cooling strategies. Build. Environ. 2018, 132, 83–95. [CrossRef] 28. Ibrahim, S.H.; Roslan, Q.; Affandi, R.; Razali, A.W.; Samat, Y.S.; Nawi, M.N.M. Study on the Optimum Roof Type with 30◦ Roof Angle to Enhance Natural Ventilation and Air Circulation of a Passive Design. IJTech 2018, 9, 1692. [CrossRef] 29. Piselli, C.; Prabhakar, M.; de Gracia, A.; Saffari, M.; Pisello, A.L.; Cabeza, L.F. Optimal control of natural ventilation as passive cooling strategy for improving the energy performance of building envelope with PCM integration. Renew. Energy 2020, 162, 171–181. [CrossRef] 30. Prabhakar, M.; Saffari, M.; de Gracia, A.; Cabeza, L.F. Improving the energy efficiency of passive PCM system using controlled natural ventilation. Energy Build. 2020, 228, 110483. [CrossRef] 31. Craig, S. The optimal tuning, within carbon limits, of thermal mass in naturally ventilated buildings. Build. Environ. 2019, 165, 106373. [CrossRef] 32. Lawrence Berkeley National Laboratory. GenOpt—Generic Optimization Program; Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 2004. 33. MathWorks. Simulation and Model-Based Design. Available online: https://de.mathworks.com/products/matlab.html (accessed on 23 November 2020). 34. Utkucu, D.; Sözer, H. An evaluation process for natural ventilation using a scenario-based multi-criteria and multi-interaction analysis. Energy Rep. 2020, 6, 644–661. [CrossRef] 35. Amoruso, F.; Dietrich, U.; Schuetze, T. Development of a Building Information Modeling-Parametric Workflow Based Renovation Strategy for an Exemplary Apartment Building in Seoul, Korea. Sustainability 2018, 10, 4494. [CrossRef] Sustainability 2021, 13, 5739 23 of 25

36. Derazgisou, S.; Bausys, R.; Fayaz, R. Computational optimization of housing complexes forms to enhance energy efficiency. J. Civ. Eng. Manag. 2018, 24, 193–205. [CrossRef] 37. Xu, X.; Yin, C.; Wang, W.; Xu, N.; Hong, T.; Li, Q. Revealing Urban Morphology and Outdoor Comfort through Genetic Algorithm-Driven Urban Block Design in Dry and Hot Regions of China. Sustainability 2019, 11, 3683. [CrossRef] 38. Lucarelli, C.D.C.; Carlo, J.C. Parametric modeling simulation for an origami shaped canopy. Front. Archit. Res. 2020, 9, 67–81. [CrossRef] 39. Díaz, H.; Alarcón, L.F.; Mourgues, C.; García, S. Multidisciplinary Design Optimization through process integration in the AEC industry: Strategies and challenges. Autom. Constr. 2017, 73, 102–119. [CrossRef] 40. Touloupaki, E.; Theodosiou, T. Performance Simulation Integrated in Parametric 3D Modeling as a Method for Early Stage Design Optimization—A Review. Energies 2017, 10, 637. [CrossRef] 41. Robert McNeel & Associates. Rhinoceros. Available online: https://www.rhino3d.com (accessed on 23 November 2020). 42. Autodesk. Dynamo. Available online: https://dynamobim.org/ (accessed on 23 November 2020). 43. Bentley. Generative Components. Available online: https://www.bentley.com/en/products/product-line/modeling-and- visualization-software/generativecomponents (accessed on 23 November 2020). 44. Scott Davison. Grasshopper-Algorithmic Modeling for Rhino. Available online: https://www.grasshopper3d.com/ (accessed on 23 November 2020). 45. Konis, K.; Gamas, A.; Kensek, K. Passive performance and building form: An optimization framework for early-stage design support. Sol. Energy 2016, 125, 161–179. [CrossRef] 46. Trubiano, F.; Roudsari, M.S.; Ozkan, A. Building simulation and evolutionary optimization in the conceptual design of a high- performance office building. In Proceedings of the Building Simulation—BS 2013, 13th Conference of International Building Performance Simulation Association, Chambéry, France, 26–28 August 2013; pp. 1306–1314. 47. Zhang, L.; Zhang, L.; Wang, Y. Shape optimization of free-form buildings based on solar radiation gain and space efficiency using a multi-objective genetic algorithm in the severe cold zones of China. Sol. Energy 2016, 132, 38–50. [CrossRef] 48. Lucarelli, C.D.C.; Carlo, J.C.; Martínez, A.C.P. Parameterization and solar radiation simulation for optimization of a modular canopy. PARC Pesq. Arquit. Constr. 2019, 10, e019017. [CrossRef] 49. Wang, B.; Malkawi, A. Genetic algorithm based building form optimization study for natural ventilation potential. In Proceedings of the Building Simulation—BS 2015, 14th Conference of International Building Performance Simulation Association, Hyderabad, India, 7–9 December 2015; pp. 640–647. 50. Yoon, N.; Piette, M.A.; Han, J.M.; Wu, W.; Malkawi, A. Optimization of Window Positions for Wind-Driven Natural Ventilation Performance. Energies 2020, 13, 2464. [CrossRef] 51. Chi, D.A.; Moreno, D.; Navarro, J. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance. Build. Environ. 2017, 125, 383–400. [CrossRef] 52. Eltaweel, A.; Su, Y. Controlling venetian blinds based on parametric design; via implementing Grasshopper’s plugins: A case study of an office building in Cairo. Energy Build. 2017, 139, 31–43. [CrossRef] 53. Touloupaki, E.; Theodosiou, T. Optimization of Building form to Minimize Energy Consumption through Parametric Modelling. Procedia Environ. Sci. 2017, 38, 509–514. [CrossRef] 54. Da Silva, M.A.; Carlo, J.C.; e Silva, L.B. Modelagem paramétrica e desempenho da edificação: Otimização baseada em simulação luminosa e energética através de algorismos genéticos. Cadernos PROARQ 30 2018, 126, 150–176. 55. Hou, D.; Liu, G.; Zhang, Q.; Wang, L.; Dang, R. Integrated building envelope design process combining parametric modelling and multi-objective optimization. Trans. Tianjin Univ. 2017, 23, 138–146. [CrossRef] 56. Yoon, N.; Malkawi, A. Predicting the efectiveness of wind-driven natural ventilation strategy for interactive building design. In Proceedings of the 15th International Building Simulation Conference, San Francisco, CA, USA, 7–9 August 2017; pp. 2163–2170. 57. ASHRAE. ASHRAE Standard 55. Thermal Environmental Conditions for Human Occupancy; ASHRAE: Peachtree Corners, GA, USA, 2013. 58. ASHRAE. ANSI/ASHRAE Standard 62.1-2019 Ventilation for Acceptable Indoor Air; ASHRAE: Peachtree Corners, GA, USA, 2019. 59. Ibrahim, M.; Biwole, P.H.; Achard, P.; Wurtz, E.; Ansart, G. Building envelope with a new aerogel-based insulating rendering: Experimental and numerical study, cost analysis, and thickness optimization. Appl. Energy 2015, 159, 490–501. [CrossRef] 60. Chu, C.R.; Chiu, Y.-H.; Chen, Y.-J.; Wang, Y.-W.; Chou, C.-P. Turbulence effects on the discharge coefficient and mean flow rate of wind-driven cross-ventilation. Build. Environ. 2009, 44, 2064–2072. [CrossRef] 61. Chu, C.-R.; Wang, Y.-W. The loss factors of building openings for wind-driven ventilation. Build. Environ. 2010, 45, 2273–2279. [CrossRef] 62. Flourentzou, F.; Van der Maas, J.; Roulet, C.-A. Natural ventilation for passive cooling measurement of discharge coefficients. Energy Build. 1998, 27, 283–292. [CrossRef] 63. Karava, P.; Stathopoulos, T.; Athienitis, A.K. Wind Driven Flow through Openings—A Review of Discharge Coefficients. Int. J. Vent. 2004, 3, 255–266. [CrossRef] 64. Swami, M.V.; Chandra, S. Procedures for Calculating Natural Ventilation Airflow Rates in Buildings; Florida Solar Energy Center: Cape Canaveral, FL, USA, 1987. 65. Cruz, H.; Viegas, J.C. On-site assessment of the discharge coefficient of open windows. Energy Build. 2016, 126, 463–476. [CrossRef] Sustainability 2021, 13, 5739 24 of 25

66. Fernandes, L.; Friedrich, M.; Cóstola, D.; Matsumoto, E.; Labaki, L.; Wellershoff, F. Evaluation of discharge coefficients of large openable windows using full-scale samples in wind tunnel tests. Rev. Ing. de Construcción 2020, 35, 203–2014. [CrossRef] 67. Tian, W. A review of sensitivity analysis methods in building energy analysis. Renew. Sustain. Energy Rev. 2013, 20, 411–419. [CrossRef] 68. Cipriano, J.; Mor, G.; Chemisana, D.; Pérez, D.; Gamboa, G.; Cipriano, X. Evaluation of a multi-stage guided search approach for the calibration of building energy simulation models. Energy Build. 2015, 87, 370–385. [CrossRef] 69. Burhenne, S.; Jacob, D.; Henze, G.P. Sampling based on Sobol’ sequences for Monte Carlo techniques applied to building simulation. In Proceedings of the Building Simulation—BS 2011, 12th Conference of International Building Performance Simulation Association, Sydney, Australia, 14–16 November 2011; pp. 1816–1823. 70. CORE Studio at Thornton Tomasetti. TT ToolBox. 2017. Available online: https://www.food4rhino.com/app/tt-toolbox (accessed on 23 November 2020). 71. Bader, J.; Zitzler, E. HypE: An algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 2011, 19, 45–76. [CrossRef] 72. Zitzler, E.; Laumanns, M.; Thiele, L. SPEA2: Improving the Strength Pareto Evolutionary Algorithm; Swiss Federal Institute of Technology: Zurich, Switzerland, 2001. 73. Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 2002, 6, 182–197. [CrossRef] 74. Loshchilov, I.; Glasmachers, T. Black Box Optimization Competition. Available online: https://www.ini.rub.de/PEOPLE/ glasmtbl/projects/bbcomp/results/BBComp2019-2OBJ-expensive/summary.html (accessed on 17 March 2021). 75. Wortmann, T.; Natanian, J. Multi-Objective Optimization for Zero- Energy Urban Design in China: A Benchmark. In Proceedings of the SimAUD 2020, Symposium on Simulation in Architecture + Urban Design, online, 25–27 May 2020; pp. 203–210. 76. Wortmann, T. Model-based Optimization for Architectural Design: Optimizing Daylight and Glare in Grasshopper. Technol. Archit. Design 2017, 1, 176–185. [CrossRef] 77. Wortmann, T. Genetic evolution vs. function approximation: Benchmarking algorithms for architectural design optimization. J. Comput. Des. Eng. 2019, 6, 414–428. [CrossRef] 78. Radford, A.D.; Gero, J.S. On optimization in computer aided architectural design. Build. Environ. 1980, 15, 73–80. [CrossRef] 79. Costa, A.; Nannicini, G. RBFOpt: An open-source library for black-box optimization with costly function evaluations. Math. Program. Comput. 2018, 10, 597–629. [CrossRef] 80. Halton, J.H. Algorithm 247: Radical-inverse quasi-random point sequence. Commun. ACM 1964, 7, 701–702. [CrossRef] 81. Wortmann, T.; Costa, A.; Nannicini, G.; Schroepfer, T. Advantages of surrogate models for architectural design optimization. AIEDAM 2015, 29, 471–481. [CrossRef] 82. Holmström, K. An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization. J. Glob. Optim. 2008, 41, 447–464. [CrossRef] 83. Wortmann, T. Opossum—Optimization Solver with Surrogate Models. Available online: https://www.food4rhino.com/app/ opossum-optimization-solver-surrogate-models (accessed on 23 November 2020). 84. Spitz, C.; Mora, L.; Wurtz, E.; Jay, A. Practical application of uncertainty analysis and sensitivity analysis on an experimental house. Energy Build. 2012, 55, 459–470. [CrossRef] 85. Janssens, A. International Energy Agency, EBC Annex 58 Reliable Building Energy Performance Characterisation Based on Full Scale Dynamic Measurements: Report of Subtask 1a: Inventory of Full Scale Test Facilities for Evaluation of Building Energy Performance; KU Leuven: Leuven, Belgium, 2016. 86. Peel, M.C.; Finlayson, B.L.; McMahon, T.A. Updated world map of the Koppen-Geiger climate classification. Hydrol. Earth Syst. Sci. 2007, 11, 1633–1644. [CrossRef] 87. Feist, W.; Schnieders, J.; Dorer, V.; Haas, A. Re-inventing air heating: Convenient and comfortable within the frame of the Passive House concept. Energy Build. 2005, 37, 1186–1203. [CrossRef] 88. Leardini, P.; Manfredini, M.; Callau, M. Energy upgrade to Passive House standard for historic public housing in New Zealand. Energy Build. 2015, 95, 211–218. [CrossRef] 89. Müller, L.; Berker, T. Passive House at the crossroads: The past and the present of a voluntary standard that managed to bridge the energy efficiency gap. Energy Policy 2013, 60, 586–593. [CrossRef] 90. Piccardo, C.; Dodoo, A.; Gustavsson, L. Retrofitting a building to passive house level: A life cycle carbon balance. Energy Build. 2020, 223, 110135. [CrossRef] 91. Sakiyama, N.R.M.; Mazzaferro, L.; Carlo, J.C.; Bejat, T.; Garrecht, H. Natural ventilation potential from weather analyses and building simulation. Energy Build. 2021, 231, 110596. [CrossRef] 92. Sakiyama, R.M.N.; Frick, J.; Bejat, T.; Garrecht, H. Using CFD to Evaluate Natural Ventilation through a 3D Parametric Modeling Approach. Energies 2021, 14, 2197. [CrossRef] 93. Sakiyama, N.R.M.; Mazzaferro, L.; Carlo, J.C.; Bejat, T.; Garrecht, H. Dataset of the EnergyPlus model used in the assessment of natural ventilation potential through building simulation. Data Brief. 2021, 34, 106753. [CrossRef][PubMed] 94. U.S. Department of Energy. Application Guide for EMS; U.S. Department of Energy: Washington, DC, USA, 2019. Sustainability 2021, 13, 5739 25 of 25

95. Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C.M.; da Fonseca, V.G. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans. Evol. Computat. 2003, 7, 117–132. [CrossRef] 96. Bayoumi, M. Improving Natural Ventilation Conditions on Semi-Outdoor and Indoor Levels in Warm–Humid Climates. Buildings 2018, 8, 75. [CrossRef] 97. Huang, L.; Ouyang, Q.; Zhu, Y.; Jiang, L. A study about the demand for air movement in warm environment. Build. Environ. 2013, 61, 27–33. [CrossRef] 98. Cândido, C.; de Dear, R.; Lamberts, R. Combined thermal acceptability and air movement assessments in a hot humid climate. Build. Environ. 2011, 46, 379–385. [CrossRef]