Pushing the Boundaries of Modular-Integrated Construction: A Symmetric Skeleton GrammarBased Multi-objective Optimization of Passive Design for Energy Savings and Daylight Autonomy
Qianyun Zhou 1, Fan Xue 2*
This is the peer-reviewed post-print version of the paper:
Zhou, Q., & Xue, F. (2023). Pushing the boundaries of modular-integrated
construction: A symmetric skeleton grammar-based multi-objective optimization of
passive design for energy savings and daylight autonomy. Energy and Buildings, 296,
113417. Doi: 10.1016/j.enbuild.2023.113417
The final version of this paper is available at: https://doi.org/10.1016/j.enbuild.2023.113417.
The use of this file must follow the Creative Commons Attribution Non-Commercial No
Derivatives License, as required by Elsevier’s policy.
Highlights
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Automatic MiC envelopes and layout generation by a novel SSG-MOO method.

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Multi-objective optimization formulation for passive MiC design.

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A pilot MiC study in Hong Kong produced 5 selected Pareto optima out of 625.
Up to 0.42% energy savings and 9.71% spatial daylight autonomy improvement
against the baseline.

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A multi-level analysis of results and design strategies for practitioners.

Abstract

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Modular-integrated Construction (MiC) is an emerging construction technique promoted in the
building sector for high productivity and low waste emission in the construction phase; yet, the
standardized modules also bring new challenges, such as balancing passive energy efficiency
and spatial daylight autonomy, to the operational phase. This paper proposes a Symmetric
Skeleton Grammar-based Multi-Objective Optimization (SSG-MOO) method to formulate
parametric MiC envelopes and detailed layout, with the two objective functions being energy
efficiency and interior daylight performance in the operational phase. Pareto optima of the
SSG-MOO, computed by the Non-dominated Sorting Genetic Algorithm II, are generally
verified and analyzed in three levels, i.e., MOO’s solution space, SSG layout, and MiC design
parameters. A case study of MiC residential building in Hong Kong demonstrated the SSGMOO method through five new passive MiC designs (i.e., spatial reorganization of three
architectural modules, and parameter tuning of the envelops and corridors), achieving up to
0.42% energy savings and 9.71% spatial daylight autonomy improvement compared to the
baseline design. The contribution of this paper is two-fold, including a novel and sound SSG-

1 Qianyun Zhou, MArch,
Research Assistant, Department of Real Estate and Construction, The university of Hong Kong, Pokfulam, Hong Kong, China
E-mail: qianyunz@hku.hk ORCiD: https://orcid.org/0000-0002-5466-6225
2 Fan Xue, PhD
Assistant Professor, Department of Real Estate and Construction, The university of Hong Kong, Pokfulam, Hong Kong, China
E-mail: xuef@hku.hk ORCiD: https://orcid.org/0000-0003-2217-3693
* Corresponding author, Tel: +852 3917 4174, Fax: +852 2559 9457, Email: xuef@hku.hk

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MOO formulation for parametric MiC designs, and offering time-efficient and evidence-based
design tactics for MiC designers and industrial practitioners to push boundaries of MiC.
Keywords
Modular-integrated Construction; Multi-objective Optimization; Symmetric Skeleton
Grammar; Energy Efficiency; Daylight Performance; Passive Generative Design

1 Introduction

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Worldwide, over 34% of final energy is consumed by the building and construction sector,
emitting a third of green gas emissions (UNEP 2022). As a high-rise high-density city, Hong
Kong receives roughly 60% of greenhouse gas emissions from the building sector, and the
energy consumption has risen by 13.7% from 2010 to 66416 TJ in 2020 in the residential sector
(EMSD 2022). The high energy consumption necessitates the development of novel sustainable
construction technologies. Recently, a list of innovative sustainable construction technologies,
such as modular construction and 3D printing, offer more advantages of enhancing productivity,
reusability, and occupational safety than energy savings over the construction life cycle (Wang
et al. 2020; Li et al. 2022).
Modular-integrated Construction (MiC) is a novel construction technology best-known
in the construction phase. MiC assembles free-standing integrated and volumetric modules
before on-site installation (Pan & Hon 2020). According to Abdelmageed & Zayed (2020),
MiC outperforms many construction technologies, including prefabrication, panelized
construction, and hybrid construction, with higher productivity and safety, maintaining lower
energy consumption and wastage in the construction phase. MiC also facilitates manufacturing,
assembly, supply chain, and logistics management (Li et al. 2022). Therefore, MiC is highly
promoted in Hong Kong, where around 20,000 new units of public housing projects are
expected to use MiC technology for the 10-year period from 2022/23 to 2031/32 (HKHA 2022).
However, the standard modularization also brings new challenges, such as constrained building
designs and exponential combinations of modules.
However, few studies have addressed optimum MiC designs in the operational phase,
which involves up to 80%–90% of the total energy consumption (Habash 2022). Echenagucia
et al. (2015) demonstrated that the optimal design of buildings could successfully improve
indoor environmental comfort. Appropriate natural illumination and thermal comfort, for
example, can save energy from lighting, cooling, and heating throughout the operational phase.
Furthermore, MiC is a new technology without detailed written standards. Therefore, it is
urgent and vital to study the optimal design for energy-efficient MiC buildings for the
operational phase.
Generally, energy-efficient MiC building designs are highly related to passive design
strategies, such as proper building layouts, windows, and insulation materials in the walls and
roof (Baños et al. 2011; Fang & Cho 2019). Building layouts, different from other architectural
components (such as windows), are infeasible to reconstruct by variables only, due to the
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topological properties. Some state-of-the-art research has suggested the connection patterns
between multiple modules, but the lack of a generic rule has made widespread implementation
challenging. Previous studies suggested shape grammar as a transferable formulation for
automatic layout generation in computer-aided design systems, which was operated through
replacement rules on finite shapes (Haakonsen et al. 2023). Over the past fifty years, shape
grammar has evolved to encode the design language of classic architectural projects and has
been applied to generalize design guidelines to represent and generate a diverse range of
architectural layouts. However, the existing shape grammars are subject to specific building
types and require to be redefined manually in each design situation. Applying traditional shape
grammars to guide the replacement rules thus is a labor-intensive procedure. Additionally, MiC
layouts exhibit symmetry and standardization, notably in high-density Hong Kong. Thus, a
generic and symmetric generation grammar is required for efficiently creating MiC layouts. In
addition to energy efficiency, there are additional objectives such as visual comfort and health
(Echenagucia et al. 2015). In the literature, multi-objective optimization (MOO) is often
adopted to guide designers in generating optimal passive design with complex objectives
(Hamdy et al. 2016).
This paper proposes a symmetric skeleton grammar-based Multi-objective
Optimization (SSG-MOO), a computer-aided passive design method, for energy-efficient MiC
designs. First, a symmetric skeleton grammar is defined to formulate the layout and envelope
of a standard MiC story using a set of design variables, including window-to-wall ratios,
window heights, corridor axis, corridor lengths, and module distribution. Two objective
formulations are then defined, with numerical simulations of energy use intensity (EUI) and
spatial daylight autonomy (sDA), for evaluating the building performance of MiC design. MOO
algorithms can optimize the SSG formulation against the two objectives by perturbating the
passive MiC designs, with two hard constraints on the total modules and total floor area. Indepth analysis of the Pareto front are presented for validation and insights, with comparisons
between the SSG-MOO’s optima and the baseline design. A pioneering 19-story MiC housing
project was studied in Hong Kong to demonstrate the proposed method. The contribution of
this paper is thus twofold: (i) A novel SSG-MOO formulation of energy-efficient and ambientdaylighting MiC designs and (ii) a time-efficient method and evidence-based design principles
for planners and designers to push the boundaries of MiC.
The remainder of the paper is structured as follows: Section 2 reviews previous research
for building layout grammars and passive design optimization. Section 3 elaborately presents
the research method in four parts and proposes an SSG-MOO method, emphasizing the
symmetric skeleton grammar, for energy-efficient MiC designs. Then, Section 4 explains the
experimental settings and analyzes the results in three levels. Finally, Sections 5 and 6 discuss
the main findings and summarize the conclusions.

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2 Literature review
2.1 Modular building design rules and grammars

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In prefabricated and modular construction, layout rules and grammars have been studied with
prefabricated modules. Gan et al. (2019) parameterized the modular building layouts by
measuring one core area and multiple wings; each wing consisted of a corridor and adjacent
household modules. Gan (2022) later extended the parameterized modular layouts with a graph
model representing the topological, geometric, and semantic information. Zhang et al. (2021)
then explored the connection patterns of multiple-shaped architectural modules to generate
layout rules. Nevertheless, for MiC typologies, which are highly efficient and standardized, a
systematic and scalable grammar for generating standard floor layouts is still lacking.
Shape grammar has been developed as a systematic formalization of recursive rules to
represent and generate floor layouts of various building types since the 1970s in the literature,
as illustrated in Figure 1 (Stiny & Gips 1972; Ning & Peiman 2018; Haakonsen et al. 2023).
For example, Stiny and Mitchell (1978) employed a parametric shape grammar to generate the
ground plans of Palladio’s villas. Koning and Eizenberg (1981) encoded the design language
of Frank Lloyd Wright’s prairie house with a shape grammar derivation. Similarly, Gülen
(1996) and Duarte (2005) created varied architectural layouts for different types of residential
houses by defining the connection rules of the shape grammar. Ruiz-Montiel et al. (2013)
studied proximity relationships of architectural spaces with given design requirements using
shape grammars and reinforcement learning, presenting diverse design solutions for singlefamily housing. Moreover, Paulino et al. (2023) developed the Reviver shape grammar for
converting historic buildings into social housing; the Reviver grammar helped to generate
various types of housing layouts, i.e., studios, one-bedroom, and two-bedroom apartments.

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Figure 1. The timeline review of shape grammars and modular building design rules in the
literature

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The benefits of shape grammar include encoding the topological variations and
presenting universal properties for building layouts by summarizing the architectural design
guidelines. However, the existing shape grammars often need to be manually redefined by
designers regarding different built objects; and the generated building footprints are commonly
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non-standardized. MiC with mass construction and standardized manufacturing properties
cannot be fully adapted to existing shape grammars. Thus, a concise and scalable generative
grammar is urgently needed for the represent the standardized modules of MiC.
2.2 Multi-objective optimization for passive building design

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Passive building design promotes solutions with comfortable indoor environments that
effectively reduce energy consumption during the operational phase (Sadineni et al. 2011).
Later, computer-aided passive design optimization relieved designers from manually
modifying numerous architectural parameters (Stevanović 2013). The optimization is often an
iterative procedure coupled with numerical simulation tools. The popular tools for building
performance simulation in optimization studies are EnergyPlus and TRNSYS (Nguyen et al.
2014). Usually, designers are required to address multiple – and sometimes conflictive –
objectives simultaneously for achieving a comfortable indoor environment, such as proper
illumination and thermal comfort (Liu et al. 2020; Zheng et al. 2023). Therefore, the MOO
method has been widely adopted to find the optimal solutions for comfortable and low-energy
passive building design (Clarke & Hensen 2015; Hamdy et al. 2016).
Existing MOO techniques can be classified into two categories: aggregate weight
functions and Pareto-based optimization methods (Baños et al. 2011). Aggregating functions
transform all the objectives into a single weighted-sum function to optimize the objectives.
However, aggregating functions have several limitations, such as constant weights and linear
summation, that oversimplify complex objectives and return only a single solution after the
lengthy search process (Hajela & Lin 1992). In contrast, Pareto-based MOO examines a set of
trade-off optimal solutions (a Pareto set) between each objective and determines appropriate
solutions (Nguyen et al. 2014). Pareto-based MOO can overcome the major drawbacks of
aggregating functions. The common algorithms for Pareto-based MOO are metaheuristics,
including Genetic Algorithm (GA), Covariance Matrix Adaptation Evolutionary Strategy
(CMA-ES), Harmony Search (HS), Particle Swarm Optimization (PSO), and Ant Colony
Optimization (ACO). GA, in particular the Non-dominated Sorting Genetic Algorithm (NSGAII) (Hamdy et al. 2016), was the most prominent Pareto-based MMO algorithm for building
performance problems in the literature (Evins 2013; Ascione et al. 2017; Ciardiello et al. 2020).
Popular optimization environments for NSGA-II include Matlab (Ljung & Singh 2012),
modeFRONTIER (Clarich et al. 2011), and Grasshopper (Wallacei, Galapagos, Octopus) on
Rhinoceros (Makki et al. 2015).
Existing MOO studies of passive designs using NSGA-II in the literature were
primarily conducted from three perspectives, i.e., the building envelopes, floor layout, and
building form-finding. For example, with NSGA-II, Didier et al. (2013) studied the optimal
thermophysical properties of the dwelling’s envelope in two French climates, targeting reduced
annual energy consumption and improved summer comfort. Echenagucia et al. (2015) further
explored the optimal envelope variables to minimize energy consumption for heating, cooling,
and lighting in four urban contexts (i.e., Palermo, Torino, Frankfurt, and Oslo). The research
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was conducted on an office building by optimizing the number, position, shape, and type of
windows and the thickness of masonry walls. Moreover, the study developed by Zhang et al.
(2021) showed the effectiveness of optimizing floor layouts to enhance energy efficiency in
the early design stage for a residence case in Beijing. Based on four different climate zones, an
MOO study by Konis et al. (2016) concluded that the optimum building form and orientation
could considerably improve the performance of daylighting and energy efficiency.
Therefore, it can be concluded that passive design optimization based on MOO can
effectively achieve energy reductions in heating, ventilation, air conditioning (HVAC) and
artificial lighting by modifying architectural properties (Tian et al. 2018). This paper thus aims
to design energy-efficient and daylight-autonomous MiC that rely the least on heating, cooling,
and lighting, using an MiC design grammar and optimum modular fenestration and layouts.
3 Research methods

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This paper presents a bi-objective passive design optimization method focusing on MiC
envelope and layout. As shown in Figure 2, the method contains four parts: (1) A symmetric
skeleton grammar of combinatorial MiC design variables; (2) Definition of the SSG-MOO
problem of energy-efficient and ambient-daylighting MiC with constrains; (3) MiC design
generation by solving SSG-MOO; (4) Pareto optima selection and multi-level verification and
analysis.

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Figure 2. The proposed SSG-MMO method for energy-efficient and ambient-daylighting
MiC design.
3.1 Definition of symmetric skeleton grammar and design variables

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This section defines a symmetric skeleton grammar deriving from the basic features of shape
grammar and aesthetics to represent the spatial topology between MiC modules. The grammar
first indicates the core point from which the axis of symmetry is subsequently defined. Later,
the skeletons of the main corridors (Sci) are defined, where i denotes the number of circulation
corridors. By rotating Sci through the angle θ (clockwise rotation from Y-axis), the spatial
topology of the corridor skeletons to the core point is obtained, which is saved as Sci’. The
grammar constructs sub-skeletons for sub-corridors (Ssi) and locations for modules by
determining the placement of sub-skeleton nodes (Snj) or module nodes (Mnj). Then, the
modules are arranged by vectors (Mvj). Here j represents the total number of modules in relation
to the number of occupants. The entire layout is horizontally symmetrical. Therefore, for
symmetrical wings, the computed decision is only required once to generate the mirrored wing;
this setting can considerably increase the computational speed. The derivation tree diagram for
this grammar is illustrated in Figure 3. The grammar well represents the majority layouts of
new residential buildings in Hong Kong; for example, Figure 4 shows the standard layouts for
public housing in Hong Kong (HKHA 2020).

Figure 3. The derivation tree diagram for the proposed symmetric skeleton grammar.

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Figure 4. Examples of symmetric skeleton grammar representation of public housing layouts
in Hong Kong.
With the symmetric skeleton grammar, a MiC model can be decoded and parameterized
in Rhinoceros3D (Ver.7.0) with Grasshopper. The former is the professional 3D CAD software
with high compatibility, whereas the latter is a graphical algorithm editor interacting 3D
modeling with numerical simulations (McNeel 2023). As shown in Figure 2, a MiC layout
consists of symmetric and asymmetric parts. The symmetric parts include three main corridors
(Sc1’, Sc2’, Sc3’) with two nodes (Sn1, Sn1’) generating sub-corridors (Ss1, Ss2, Ss1’, Ss2’), where
θ1, θ2, and θ3 are 0°, 270°, and 90°, respectively. The midpoint of the corridor axis (Sc2’, Sc3’)
can be altered within the vertical range (Pc). Three parameters of corridors’ lengths (L1, L2, L3)
are variable, while L4 is a constant value when the number of modules per floor is determined.
Different modules (e.g., MA, MB, MC) are arrangeable for the layout according to Mvj, while
each module has a parametric window with the WWR and height variables on the north (WWRN,
WHN) or south (WWRS, WHS) side of the module. The asymmetric part is usually much smaller
than the symmetric ones in size, which differs between projects. The three fixed-location
modules (Cw, Ct, Bw) are arranged in the bottom of the south, also with parametric windows.
3.2 Definition of SSG-MOO problem of energy-efficient and ambient-daylighting MiC

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We formulate the MOO of passive MiC envelope and layout design as a bi-objective problem:
arg minx∈X EUI(SSG(x)), sDA−1(SSG(x))
subject to GFA(SSG(x)) = TGFA,
(1)
Σ Mnj = Constant
Where SSG maps input design parameters to an MiC layout, EUI is the energy use intensity
(kWh/(m2·yr)) that is calculated by dividing the total energy used per year by the gross floor
area (Konis et al. 2016), sDA−1 refers to the inversed spatial daylight autonomy (to minimize)
that expresses the annual deficiency of ambient daylight levels for the interior environment,
quantifying the percentage of minimum received brightness during daytime working hours in
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the target space (Heschong et al. 2012), the first constraint is that the SSG’s gross floor area is
equal to the expected value (TGFA), x stands for a combination of the n design variables (x1,
x2, ..., xn), and X means the set of all possible combinations. And the second constraint is the
constant number of total modules.
The EUI computation is based on an integrated energy model of multi-feature data,
including local climate data, construction materials, construction type, and HVAC. The energy
model (.osm) can be translated into the .idf file via the OpenStudio component in Honeybee
(Ver.1.5) and run on the built-in EnergyPlus program (Roudsari & Pak 2013). The target
meteorological data can be downloaded from the EnergyPlus weather website through
the Ladybug (Ver.1.5) EPWmap component (ASHRAE 2021). As a result, the EUI and related
end-use value (i.e., heating, cooling, interior lighting, and the other end-uses) can be calculated.
The sDA−1 is the reciprocal of sDA. In general, sDA assesses whether the floor area
receives a minimum target illuminance of 300lx for at least 50% of the year during standard
occupied hours (sDA300/50%) on the horizontal work plane. According to the LEED V4.1
standard (standard for green building design, construction, operations, and performance), the
average sDA300/50% value for the regularly occupied floor area should be reached 40% to earn
one point of standard daylight evaluation, and 50% for two points (Pilechiha et al. 2020;
USGBC 2022). The formula for sDA can be defined as (Pilechiha et al. 2020): sDA = Σρ =1…N
ST(ρ) / N, where ST(ρ) = 1 if stρ ≥ 𝜏𝜏 ty, and ST(ρ) = 0 if stρ ≤ 𝜏𝜏 ty. stρ is the occurrence count

above the sDA illuminance threshold at point ρ; ty is the annual timestamp count, and 𝜏𝜏 denotes
the temporal fraction threshold. Assuming an N-point grid with function ST(ρ), the value turns
to one when point ρ in the grid has a minimum required illuminance that exceeds a given
percentage of the total occupied time, and zero vice versa. Later, the Honeybee-Radiance
components launch the annual daylight simulation for each sensor based on the preset grid size
(Gs). Since sDA takes probability between zero and one, the interval of sDA−1 is one to ∞. By

minimizing the sDA−1, the SSG-MMO in Eq. (1) tends to improve MiC layouts toward less
deficiency of ambient daylighting.
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3.3 MiC design generation with SSG-MOO
Many MOO algorithms can solve the SSG-MOO problem in Eq. (1). For simplicity and clarity,
the NSGA-II algorithm implemented in Wallacei (Ver. 2.7), an add-on that interacts with
simulation data with Honeybee and Ladybug in Grasshopper (Makki et al. 2018), is adopted in
the remainder of this paper. The design variables described in Section 3.1 are transferred as
genes, while EUI and sDA−1 values in Eq. (1) are then positioned and sorted among the
objective space. The major algorithmic parameters of NSGA-II are population size and
crossover/mutation index.
The output of NSGA-II is the Pareto optima that is the set of non-dominated solutions.
A dominated solution indicates all its objective values are inferior than another (or more)
solutions (Deb et al. 2002; Li et al. 2023). However, it can be time-consuming and
computationally challenging for decision-makers to analyze the entire Pareto optima or quickly
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select a unique ‘best solution’. Proper selection, verification, and analysis are thus essential for
prioritizing the most promising solutions for MiC practitioners.
3.4 Multi-level verification and analysis of selected Pareto front
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This paper employs verification and analysis in three levels for validating the selected solutions
on the Pareto front. The three levels are MOO solution space, SSG modular layout, and MiC
design parameters.
Firstly, the bi-objective ranking of the Pareto optimal solutions is sorted, compared, and
analyzed. The overall density and trending curves of Pareto front are summarized for the
alternative. Then, we extend the ‘Utopia’ point method with the baseline MiC layout as the
second reference solution in the solution space. The ‘Utopia’ point is the virtual position of the
ideal solution in the objective space, obtained by minimizing each objective function without
regard for other objective function (Showkatbakhsh & Makki 2022). A rectangular-shaded area
can be drawn between the ‘Utopia’ point and the baseline MiC reference point. Pareto optimal
solutions in the rectangular are most desirable for decision-makers, due to all the objectives are
superior than the baseline. This screening approach can effectively save time and effort for
practitioners to select multiple Pareto optimal solution(s) while keeping the variation and
diversity of the selected subsets.
Secondly, the modular layouts of the selected Pareto optima are generated by SSG for
visualization and assessment. The selection and arrangement of multiple modules can be
assessed and compared together with the baseline MiC layout. The layouts’ improvement
effects on the target performance are analyzable accordingly.
Finally, passive design variables are explored, and general design trends for energyefficient MiC design are presented. The data sample is based on the selected Pareto optimal
solutions. This paper applies Spearman’s correlation to testing the correlations between the two
optimization objectives and the eleven design variables. The Spearman’s correlation
coefficient (r) is a value between −1 and 1. And the significant (e.g., p < 0.001) correlations
often indicate interesting relations to investigate and interpret further with domain knowledge.
4 Experimental tests

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4.1 Experimental settings

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A pioneering 19-story MiC residential building was the test case in this paper. The building is
a university student hostel located at 142 Pokfulam Road, Hong Kong, Latitude 22°15’51.76”
N, Longitude 114°8’7.72” E, and to be completed by the second quarter of 2024 (HKSAR
2021). Figure 5 (a) depicts the climatic indicators for the building, explicitly showing the meanminimum-maximum dry bulb temperature and global horizontal radiation values for each
month. As shown in Figure 5 (a), the dry-bulb temperatures reach more than 30 °C in summer
in Hong Kong, with average winter levels around 10 °C; and the summer lasts approximately
six months. Figure 5 (b) shows the baseline MiC layout, which was designed by a professional
architect consultant, consisting of a core tube with six different types of modules. Modules Bw,
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Cw, and Ct remain spatially constant in this study, and the corresponding window features were
added to the optimization calculation. The spatial layouts for the three modules, MA, MB, and
MC, were then reorganized in the optimization. The width and height of each module type are
fixed at 2.5 m and 3.15 m, respectively. Those modules differ primarily in terms of length and
windows’ features.

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Figure 5. (a) Annual climate indicators for Hong Kong SAR. (b) The baseline MiC layout.
Table 1 lists the design variables considered in the SSG-MOO experiments, along with
data units and ranges. The design variables were divided into two types: corridors and windows.
L1 was based on Sc1’, varied from 0 to 2 m, and controlled the corridor length on the north; L2
and L3, which were based on Ss1 and Ss2, respectively, modified the length of the northern and
southern sub-corridors, with values ranging from 1m to 6m. Pc guided the vertical movement
(0% to 100%) of the horizontal corridors along the axis of symmetry. WWRN and WWRS varied
between 20% and 70% for the south and north facades, respectively. Moreover, WHN and WHS
were optimized in the range of 1.0m to 2.5m. The TGFA in this experiment was 531.34 m2, and
the modules number (C) was 31. To fulfill the requirement for the number of occupants on
each floor, modular amount and L4 were fixed values of 31 and 13.75 m, respectively.
Table 1. Independent variables in MiC parametric design excluding selection of modules.
Type
Corridor

Component
Corridor length (L1, L2, L3)

Unit
m

Window

Vertical range for the corridor %
axis (Pc)
Window-to-Wall
Ratio %
(WWRN, WWRS)
Window height (WHN, WHS)
m

Variable’s value range
0 ≤ L1≤ 2.00; 1.00 ≤ L2, L3 ≤
6.00
0 ≤ Pc ≤ 100
20 ≤ WWRN, WWRS ≤ 70
1.0 ≤ WHN, WHS ≤ 2.5

Table 2 lists the material settings for MiC envelopes. In this case, the single clear glass
had a thickness of 0.006m, where the U-value was 5.78 W/m2K, the Solar Heat Gain
Coefficient (SHGC) value was 0.775, and the visible transmittance value was 0.881. The wall
and floor slab thicknesses were set as 0.14 m and 0.1 m, respectively, with U-values as 3.72
W/m2K and 2.89 W/m2K. The above parameters referred to the energy modeling
recommendations for residential buildings specified in the Hong Kong environmental
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evaluation (Qin & Pan 2020). According to Honeybee Heat Cool Templates, the HVAC system
was configured as a “Window AC with baseboard electric” for high-rise apartments. In addition,
the construction set applied “ASHRAE 90.1 2019” for building vintages and “2-Hot” for the
climate zone. The numerical simulations were then conducted with a resolution grid size (Gs =
0.5m).
Table 2. Material parameter settings for MiC envelopes.
Envelopes
Single clear glass
Wall
Floor

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Thickness
(m)
0.006
0.140
0.100

k
(W/mK)
0.900
2.160
2.160

U_ Factor
(W/m2K)
5.78
3.72
2.89

SHGC
0.775
−
−

Visible
Transmittance
0.881
−
−

For the NSGA-II algorithm settings, both the generation size and generation count were
chosen as 25, producing a total population of 625. And the index for crossover and mutation
distribution was set as 20 in Wallacei. The rest parameters of NSGA-II algorithm were set
according to the existing literature expertise (Chantrelle et al. 2011; Makki et al. 2015;
Showkatbakhsh & Makki 2022).
4.2 Experimental results and analysis
The experiments were conducted on a desktop computer with an Intel (R) Core i7-10700 CPU
@ 2.90 GHz processor and 32 GB memory. The total time cost was 15.56 hours to solve the
SSG-MOO problem by the NSGA-II algorithm and the simulations. A total of 39 Pareto optima
were returned. Within the Pareto-Utopia shaded area, as shown in Figure 6 (a), the five selected
MiC Pareto optima decreased the EUI values and increased daylight performance for the same
floor area and units as the baseline case. The visualization analysis of daylight and energy enduse for each of these five options is shown in Figures 6(b) and (c). In Figure 6(b), the closer
the color is to red, the more daylight can be received, and the closer it is to blue, the less. In
particular, the energy end use (in heating, cooling, lighting, equipment, and water) of these five
options is presented in detail in Figure 6(c).

Figure 6. The selection and comparative analysis of the five MiC Pareto optima. (a) 39 Pareto
optima solution space; (b) Modular layouts of the five selected MiC Pareto optima with
daylighting visualization; (c) End use intensity of the selected.
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4.2.1 On the MOO solution space level
Every dot in Figure 6 indicates a Pareto optimum, i.e., a Pareto optimal solution, and they
depict the Pareto front collectively. In Figure 6 (a), the purple square symbol represents the
‘Utopia’ point, the blue diamond symbol shows the location of the baseline MiC scheme, and
the magenta triangular symbol highlights the five selected MiC Pareto optima. The closer a
point is to the square “Utopia” point, the superior the behavior of the specific solution in
relation to that objective. The rectangular shading area bounded by the ‘Utopia’ point and the
baseline case suggests the most promising Pareto optimal solutions, which were superior than
both objective values – or dominate over – the input baseline case.
In addition to the five options located in the Pareto-Utopia shaded area, Figure 6(a)
shows five more Pareto optimal solutions between the baseline point and the horizontal dash
line sDA−1 = 2.5. The threshold sDA−1 = 2.5 (or sDA = 40%) will grant at least one point based
on LEED V4.1 standard. These five options might also be available for the project team to
consider, if they would like to emphasize on the EUI. In the remainder of this section, we
mainly focus on the five MiC designs in Figure 6 (b) without loss of generality.
4.2.2 On SSG modular layout level
Figure 6(b), (c) and Table 3 comprehensively compare the layouts of the five selected MiC
Pareto solutions and the baseline project concerning the improvement magnitude in energy and
daylighting performance. In Table 3, the improvement magnitude [% Imp.*] is the percentage
increase or decrease, where v0 is the EUI value of the baseline scheme, and v1 is the EUI value
of the calculated option; w0 represents baseline scheme’s sDA, and w1 represents the sDA value
of the calculated option. For the MOO process, modules Bw, Cw, and Ct (three modules arranged
horizontally below) remain spatially constant in this paper. The baseline MiC design solution
consists of 12 MA, 2 MB, and 14 MC. And the baseline scheme simulated the EUI as 133.259
kWh/m2·yr and the sDA as 56.05%.
Option 1 reduces annual energy consumption by 0.42% per square meter compared to
the baseline scheme. In terms of modular layout, Option 1 arranges more MB than the baseline
one and tends to be essentially flat at the northern boundary. Similarly, Options 2 and 3 are
close to the horizontal line in the layout of the modules on the north side. Option 2 has a higher
energy efficiency than Option 3, with close indoor daylighting performance. Option 4, which
arranges the three modules evenly on the north and south sides, computed the EUI as 133.151
kWh/m2·yr, a reduction of 0.08% compared to the baseline one, while the sDA improves by
7.78%. Option 5 significantly improves the performance of daylighting with an increase of
9.71%, while its building energy consumption is reduced by only 0.05%. It can also be noticed
that from Option 1 to Option 5, as the value of sDA increases from 57% to 61.49%, the energy
consumption of cooling increases from 38.913 kWh/m2·yr to 39.357 kWh/m2·yr, while the
energy use of lighting gradually decreases.

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Table 3. Objective values and improvements of the five Pareto optimal solutions of MiC
designs in Figure 6 (b).
EUI
EUI [% Imp.*]
sDA (%)
sDA [% Imp.*]
2
(kWh/m ·yr)
1
132.693
0.42
57.00
1.69
2
132.799
0.35
57.47
2.53
3
132.878
0.29
57.71
2.96
4
133.151
0.08
60.41
7.78
5
133.192
0.05
61.49
9.71
Baseline
133.259
56.05
*
: Improvement by percentage, (v0 − v1)/v0 × 100% for EUI, (w1 – w0)/w0 × 100% for sDA.
Option

410

415

Overall, from Option 1 to Option 5, the annual energy consumption per square meter
of the MiC designs gradually increases, while the daylight performance shows an opposite
trend. Compared with the baseline scheme, the five Pareto optimal schemes all meet the
requirements of the LEED V4.1 standard to obtain two points for daylight assessment, and all
have improved the energy efficiency for MiC design.
4.2.3 On MiC design parameters level
Figure 7 shows the Spearman’s rank correlations between the design variables and the two
objectives. Figure 7 contains histograms at diagonal subfigures, and the lower half involves
scatter plots and trend lines, where the color and size of the circle in the upper triangle indicate
the sign and value of the correlation coefficient (r). Note that six insignificant variables (Pc, L1,
L2, L3, WHN, WHS) in this case are hidden in Figure 7. Specifically, the findings reveal
significant and very strong correlations (r = ± 0.91, p ≤ 0.001, N = 39) between WWRS and
the two objectives.

420

Figure 7. Results of Spearman’s correlation analysis based on 39 Pareto optima, with
histograms, scatter plots, and the correlation coefficient r (cool color indicates positive, size
stands for strength) and significance (*** p ≤ 0.001, ** p ≤ 0.01, * p ≤ 0.05, two-tailed).
14

Similarly, WWRN shows strong correlations (r = ± 0.70, p ≤ 0.001, N = 39) with EUI

425

and sDA−1. For the three types of modules, the number of MB has a moderate positive
correlation (r = 0.47, p ≤ 0.01, N = 39) with EUI, whereas the number of MA and MC has a
moderate negative correlation (r = –0.47) with EUI. It can be found an opposite result in
correlation coefficients of MB and MA, MC calculated by sDA−1. Moreover, the results show
that the number of MB has a robust negative correlation with the number of MA and MC, with
a coefficient of –1.0 (p ≤ 0.001), while the number of MA has a robust positive correlation

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435

440

445

450

(1.0) with the number of MC. However, the values of WHN and WHS did not show significant
correlations with EUI or sDA−1.

Figure 8. Comparison of 11 design parameters and the layout perimeter between 39 MiC
Pareto optimal solutions and the baseline project.
Figure 8 compares the statistics of optimized design variables in the 39 MiC Pareto
optima against the baseline design parameters. In the baseline solution, Pc is assigned as 50%,
which means that the axis of the horizontal corridors is located in the middle of the core tube.
As shown by the red bolded short line in the box plot, the median value of the optimized Pc
was 30%, which means that the axis of the horizontal corridors is shifted towards south. The
optimized values of L2 are mainly distributed between 3.75m and 5.25m, which are slightly
larger than the baseline parameters (3.66m). L2 is utilized to modify the length of the subcorridor on the north side, and a smaller Pc value would also mean an increase in L2. The
optimized values of L3 are slightly smaller than the baseline parameters (3.66m), with the
median of 2.26m. In contrast, the difference between the median value of optimized L1 and the
baseline solution is tiny, at 0.17m.
Meanwhile, the three types of modules are distributed in distinct ways. Figure 8 shows
that the data spread of three types of modules is relatively concentrated. The number of MB is
significantly higher than the baseline scheme, with a median of 26. The total number for MA is
slightly lower than that of MC, with median values of 2 and 0, respectively.
The optimized window design parameters vary considerably from the baseline
parameters, especially for the WWRN, and WWRS. In the baseline scheme, the WWRN and
WWRS were designed with an equal value of 35%, while the WHN and WHS were both in 1.2m.
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However, the optimized WWRN shows higher values, predominantly between 47% and 64%.
The values for the optimized WWRS, on the other hand, are mainly distributed between 21%
and 40%. With regard to the height of the windows, the optimal solutions emphasize the almost
same height of the windows on the north side (WHN) and the south side (WHS). The median
value of the window’s height on the north is 2.0m, while the value is 2.1m for the south side.
Moreover, the optimized schemes’ median perimeter value is roughly 137m, which is
substantially less than the baseline project’s perimeter value of 167.7m, indicating that the
optimized schemes were more compact.
4.3 Sensitivity analysis

465

470

475

A sensitivity analysis was conducted to identify a cost-effective MOO setting from the aspects
of daylighting simulation grid size and total population size. The grid size substantially
influences the quantity of sensors utilized in daylight simulations, which subsequently affects
the sDA computation outcomes and the simulation time frame. In the preliminary study, six
grid sizes (i.e., 0.1 m, 0.2 m, 0.5m, 1m, 1.5m, and 2m) were selected for daylighting simulation
of the baseline model, and the corresponding simulation times required for each case were
documented, as illustrated in Figure 9. The computing time exhibited a substantial increase
when the grid size was reduced to less than 0.5 m. E.g., a 0.2 m grid necessitated 135 seconds
for computation, whereas a 0.1 m grid demanded 454 seconds. For the case in this paper, Figure
9 suggests that there was an ‘elbow point’ around time = 60s. Thus, a grid size of 0.5 m was
selected to maintain a reasonable trade-off between computation time (i.e., 48 seconds per
simulation on average) and accuracy.

Figure 9. Sensitivity testing results of grid size for daylighting simulation. (a) The sDA
values and time required for each simulation against grid size (dashed line indicates 60s); (b)
Daylighting simulation results.
Figure 10 compares the number and location of the Pareto optimal solutions in three
situations: total population size in 100 (10 chromosomes times by 10 generations), 625, and
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485

490

2500. The experiments led to 14, 39, and 90 Pareto optima in 2.28 h, 15.56 h, and 72.48 h,
respectively. In Figure 10 (a), there was only one Pareto optimum in the Pareto-Utopia shaded
area when the population was 100. In contrast, the number of the most promising Pareto optima
reached 16 after examining the population of 2,500, as shown in Figure 10 (c). In Figure 10 (c),
the new Pareto optima in the shaded area progressed the five options in Figure 10 (b) to a
limited extent, but it required a significant amount of time and effort for the decision-makers
to compute and compare the final optimal solutions. Therefore, increasing the population size
can generate slightly more promising solutions, at the costs of computer time for computation
and experts’ time for narrowing down the candidate MiC schemes for decision-makers.

Figure 10. Scatter plot of Pareto optima against the population size of NSGA-II. (a)
Population size as 100; (b) Population size as 625; (c) Population size as 2,500.
5 Discussion

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500

505

510

The SSG-MMO method presented in this paper shows promising experimental results in
improving ambient daylighting and reducing operational energy costs in the early design phase
of MiC projects. The three-level comparative analysis provides an efficient and elaborate way
of analyzing the information in the MiC Pareto optima. By subject to the target gross floor area,
the decision-makers have the flexibility to compare multiple Pareto optimal solutions under a
defined number of occupants. In terms of modular layout, the optimized MiC designs arrange
more MB than the baseline one and tends to be essentially flat at the northern boundary.
According to Spearman’s correlation analysis, the value of WWRN, and WWRS have a robust
correlation with optimizing the energy efficiency and daylight performance in the Hong Kong
region.
Therefore, the optimized parameters for MiC window and corridor design can also be
summarized into valuable suggestions for energy-efficient design strategies. Specifically, the
optimized window design parameters indicate that the window ratio should be distinguished
for the north and south sides, while the values of WWR should be increased on the north side.
Meanwhile, the optimized Pc suggests that the corridors’ layout becomes more passive energy
efficient as it is shifted southward. The optimization results for the window and corridor
parameters are consistent with the geographical location and climatic conditions of Hong Kong.
Therefore, for Hong Kong in a subtropical climate, the energy-efficient MiC designs (with a
due north orientation) should increase the ratio of windows on the north side of the building

17

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520

525

530

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540

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550

and design the axis of the horizontal corridor towards the southern part of the core, as well as
reduce the concavity of the northern boundary.
However, there are three groups of limitations in this paper. Firstly, there are limitations
in the SSG-MOO formulation. This paper mainly conducts optimization from energy
consumption and daylighting aspects, without other operational performance indicators for
MiC design, such as target wind load, ventilation, personalized thermal comfort, and carbon
emissions. Also, the envelope optimization in this paper concerns the size of the windows
regardless of the influence of different materials and coating on energy efficiency. Therefore,
the conclusive design tactics may be overridden by other design needs in practice. Secondly,
this paper is limited in applying NSGA-II as the only algorithm. In the future, other MOO
algorithms, such as CMA-ES and PSO, are also potential to solve the SSG-MOO problem for
MiC. Lastly, the numerical computational results need further validation and comments by
field experts.
6 Conclusion
Novel construction technologies are required with lifecycle passive designs to address energy
crises and comfort concerns. This paper presents a symmetric skeleton grammar to handle the
constrained MiC designs and MOO to cope with the exponential combinations of various
modules for energy efficiency and daylight autonomy in the operational phase. A pilot MiC
project was studied in Hong Kong to evaluate the proposed method. By optimizing 11 design
variables regarding windows, corridors, and layouts of MiC modules, five optimized options
were selected from 39 Pareto optima using the Pareto-Utopia shaded screening method.
Meanwhile, the optimal design tactics can be summarized to passive MiC designs for energy
efficiency and daylight autonomy: (i) the ratio of north-facing windows (WWRN) should be
increased, and (ii) the axis of the horizontal corridor should move southward, while maintaining
flatness at the northern boundary.
The main contribution of this paper can be concluded in two aspects. From the MiC
researchers’ perspective, the method presents a symmetric skeleton grammar of MiC designs.
Moreover, the proposed bi-objective formulation optimizes the parametric MiC designs in an
energy-efficient and sufficient daylighting manner. From the industrial practitioners’
perspective, the SSG-MOO with Pareto-Utopia-shaded screening method can efficiently assist
designers in selecting the optimized solution(s) with multi-level evidence-based information.
And valuable energy-efficient design strategies can be suggested for MiC designers in Hong
Kong.
In the future, researchers can broaden the goals of MiC design optimization for wind
load, thermal comfort, and carbon emissions, and taking into account the impact of different
envelope materials on building performance. Furthermore, advanced MOO algorithms can be
studied and applied to address the complex SSG-MOO problems. In addition, human experts
can be included in the loop to verify and guide the Pareto optima selection for multi-level
evidence-based decision making.
18

Acknowledgment
The study was supported by Hong Kong Research Grants Council (RGC) (Nos. 27200520,
C7080-22GF, T22-504/21-R).
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