Automatic information gain-guided convergence for refining building design parameters:
Enhancing effectiveness and interpretability in simulation-based optimization
Qianyun Zhou 1, Fan Xue 2*
This is the peer-reviewed post-print version of the paper:
Zhou, Q., & Xue, F. (2025). Automatic information gain-guided convergence for
refining building design parameters: Enhancing effectiveness and interpretability in
simulation-based optimization. Building and Environment, 275, 112788.
Doi: 10.1016/j.buildenv.2025.112788
The final version of this paper is available at: https://doi.org/10.1016/j.buildenv.2025.112788.
The use of this file must follow the Creative Commons Attribution NonCommercial No Derivatives License, as required by Elsevier’s policy.
Abstract
5

10

15

20

Simulation-based optimization (SBO) is widely applied to building designs by iteratively
tuning design parameters towards sustainable goals. However, numerous design parameters in
exploratory stages lead to design uncertainty and exponentially increase optimization search
space’s dimensionality. The non-linear, non-derivative nature of objective functions
determines SBO tasks a black box, which lacks interpretability for design decisions or
optimization strategies. This study introduces an Automatic Information Gain-guided
Convergence (AIGGC) method for refining critical design parameters in building performance
SBO. The AIGGC method extends the generic SBO process with interpretable information
gain analysis for each design parameter and component, to converge to the most promising
domain sub-intervals prior to traditional SBOs. Experimental results evaluated the robustness
and scalability of AIGGC across two design scales. Under the same iteration budgets, AIGGC
significantly enhanced three SBO algorithms, i.e., RBFOpt, CMAES, and GA, by 0.62~0.67%
less energy use intensity and 2.14~4.74% more direct sunlight hours against the baseline
solutions, respectively. The contribution of this study involves two aspects, including
introducing a novel information-theory-based method for optimizing design parameters in
high-dimensional SBO tasks of sustainable building designs, and a novel perspective in guiding
stakeholders with interpretable analysis of building design parameters.
Keywords: Information gain; Simulation-based optimization; Sustainable building design;
Interpretability analysis

1 Qianyun Zhou, MArch, PhD student
Department of Real Estate and Construction, The University of Hong Kong, Pokfulam, Hong Kong, China
E-mail: qianyun8@connect.hku.hk ORCiD: https://orcid.org/0000-0002-5466-6225
2 Fan Xue, PhD, Associate Professor

Department of Real Estate and Construction, The University of Hong Kong, Pokfulam, Hong Kong, China
National Center of Technology Innovation for Digital Construction Hong Kong Branch, 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

1

25

30

Highlights
•

A novel Information Gain-guided parameter convergence for complex sustainable designs

•

A sound information-theory-based method to enhance generic simulation-based
optimization (SBO)

•

Automatic converging design parameters to most promising domain sub-intervals

•

Improved 3 SBO algorithms in 2 cases, by 0.62~0.67% less energy cost and 2.14~4.74%
more sunlight hours

•

Interpretable guidance for stakeholders in sustainable design decision-making

1 Introduction
35

40

45

50

55

60

The building and construction sector significantly contributes to global climate change,
accounting for 34 percent of global energy demand and 37 percent of greenhouse gas emissions
(UNEP 2024). Nowadays, the sector follows sustainable planning guidelines and standards
among countries, focusing on reducing building energy consumption and enhancing occupant
well-being to create environmentally friendly buildings and urban neighborhoods (Luca et al.
2024; He et al. 2024). The environmental performance analysis of buildings includes various
aspects, such as energy consumption, thermal comfort, and daylighting (Zhan et al. 2024).
Extensive research has shown that early-stage building design is critical to effectively
enhancing these performance outcomes (Wang et al. 2024). By integrating simulation engines
into visual programming environments, parametric modeling techniques can couple with
simulation data to deliver instant performance feedback during design generation (Hinkle et al.
2024).
Simulation-based optimization (SBO) automates the design exploration process
through iterative algorithms, enabling the identification of optimal or near-optimal solutions
with less time and labor (Nguyen et al. 2014). Typically, an SBO process begins with defining
the target design parameters and objective function, followed by an optimizer iteratively
updating the design parameters to converge towards the optimal solution. Early-stage building
design often involves a vast range of parameters that control the building’s physical
components, materials, and systems (Wang et al. 2024; Zhan et al. 2024; Es-sakali et al. 2025).
A large number of design parameters results in the uncertainty of potential designs and the
exponential growth of the design search space, known as the ‘curse of dimensionality’ (Nguyen
et al. 2014; Chen et al. 2015; Han et al. 2023). The high dimensionality of the search space
complicates SBO convergence; furthermore, time-intensive simulations plus limited iteration
budgets confine the efficiency in SBO. On the other hand, the non-linear, non-derivative nature
of objective functions makes SBO a black box (Waibel et al. 2019), which limits
interpretability for decision-makers and provides little insight into guiding the convergence of
the design search space.
Current frontier research employed sensitivity analysis techniques to quantify the
importance of design parameters (Østergård et al. 2017; Brown & Mueller 2019; Hinkle et al.
2

65

70

75

80

85

90

95

100

2024). Some studies have incorporated surrogate models to replace simulation engines in SBO,
enabling real-time interactive optimization (Lin et al. 2021; Han et al. 2023; Li et al. 2024).
Others have explored visual analytics to enhance the interpretability of SBO results
(Showkatbakhsh & Makki 2022). However, both sensitivity-based techniques and surrogate
models rely on extensive simulation datasets for analysis and often need rerunning for different
optimization tasks, requiring considerable time and labor. Additionally, while visualizing
optimization results improves interpretability, it does not enhance optimization efficiency,
leaving a research gap in improving the interpretability of the optimization convergence
process.
The uncertainty and lack of interpretability in high-dimensional SBO search spaces
make it challenging for stakeholders to fully understand the SBO process. In this context,
information entropy, a classical concept in information theory (Shannon 1948), provides the
fundamental measure of uncertainty within a variable or dataset. The entropy reflects the
amount of information gained when observing the outcome of a potential state. Information
gain (IG), that quantifies changes in information entropy, is a classic descriptor for assessing
feature importance during data partitioning (Zhang et al. 2022). IG is, therefore, widely applied
in many fields, such as machine learning and data mining, to address the curse of
dimensionality while enhancing model interpretability and decision-making capability (Omuya
et al. 2021; Son & Hyun 2022). However, in the building and construction sector, few studies
have conducted IG-based methods or analyses for SBO tasks.
Our research aims to enhance the generic SBO process by incorporating IG-guided
analysis for each design parameter and component, optimizing the initial parameter set to those
most promising for improving building performance and thereby reducing the dimensionality
of the search space. Additionally, the visualized results of IG-guided analysis provide
interpretable insights for stakeholders, enabling them to independently navigate optimization
convergence, and enhancing their understanding of the process.
Therefore, this paper presents an Automatic IG-guided Convergence (AIGGC) method
for refining design parameters in sustainable building designs. This method allocates a small
portion of the iteration budget for first-phase optimization, using its results to conduct IGguided analysis of sub-intervals within each design parameter. This analysis aids stakeholders
in automatically converging design parameters and identifying high-quality interval domains.
The remaining iteration budget is then applied to re-optimize the converged parameters, further
improving the solution. This paper tested the robustness and scalability of the proposed method
on two prominent optimization objectives: minimizing the annual energy consumption of a
typical modular flat in Hong Kong and maximizing sunlight hours on the ground floor of a
south-facing urban block in Jianhu City. The contribution of this paper is thus twofold: (i) a
novel information-theory-based method for optimizing design parameters in high-dimensional
SBO tasks of sustainable building designs, and (ii) a novel perspective in guiding stakeholders
with interpretable analysis of building design parameters.

3

2 Literature review
2.1 Simulation-based optimization for buildings and construction
105

110

115

120

125

130

135

140

SBO is recognized as a commonly used strategy for satisfying the sustainable requirements of
high-performance building designs, both in research and practice. Since the late 2000s, the
workflow of iteratively coupling optimization algorithms with simulation programs to
approximate sub-optimal solutions has gained popularity (Evins 2013; Nguyen et al. 2014;
Javanroodi et al. 2019). The generic SBO process can be divided in three phases: the first phase
is the definition of the optimization task, including setting independent design parameters,
objective functions, and constraints; then it follows by running optimization algorithms while
monitoring convergence; and finally, the optimized data is transformed into visualized charts
(Nguyen et al. 2014; Zhan et al. 2024).
Optimization is the process of discovering the minimum or maximum of a function by
selecting certain variables under given constraints (Machairas et al. 2014; Yu et al. 2023). In
SBO, the objective function is typically a “black box” computed by third-party simulation
engines, relying on complex physical models and climate data, making direct mathematical
formulation infeasible (Evins 2013; Cruz et al. 2024). The highly non-linear, non-derivative
mapping of multi-dimensional inputs defines SBO as a black-box optimization problem
(Wortmann 2019; Waibel et al. 2019). Consequently, derivative-free algorithms, including
Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA),
Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and RBFOpt, are widely
employed in architectural design exploration (Machairas et al. 2014; Waibel et al. 2019).
Statistics show that GA is the most frequently used among these algorithms (Evins 2013;
Nguyen et al. 2014), while comparative studies have found that CMA-ES and RBFOpt
outperform in black-box optimization for building design (Kämpf et al. 2010; Xue et al. 2019;
Wortmann 2019; Rehbach et al. 2022).
Energy performance optimization has been extensively studied in SBO tasks to mitigate
buildings’ environmental impact (Evins 2013; Luca et al. 2024). By integrating energy
simulation engines such as EnergyPlus, TRNSYS, and DOE-2, key metrics like cooling and
heating loads and Energy Use Intensity (EUI) can be evaluated (Nguyen et al. 2014). Among
building components, optimizing orientation, layouts, HVAC systems, envelope design, and
openings play a crucial role in passively reducing energy consumption (Konis et al. 2016;
Javanroodi et al. 2019; Mousavi et al. 2022; Gupta & Deb 2023; Zhou & Xue 2023). Notably,
envelope optimization is essential for substantial energy savings, with studies showing
reductions of up to 50% (Es-sakali et al. 2025). Optimizing the building envelope involves
multiple factors, including wall materials, window-to-wall ratio (WWR), window shape,
glazing, and shading (Hinkle et al. 2022; Wortmann et al. 2022). Among these, studies identify
WWR as a major factor influencing building energy consumption (Wang et al. 2024).
Daylight quality is also a crucial aspect of sustainable design exploration, serving as a
critical indicator of livability and well-being (Fang & Cho 2019; Bushra 2022; Luca et al. 2024).
4

145

150

155

160

165

170

175

In the built environment, daylight accessibility is influenced by inter-building overshadowing,
and numerous studies have shown that optimizing block morphology and layout can
significantly enhance regional daylight quality (Javanroodi et al. 2019; Liu et al. 2023; Liu et
al. 2024).
Nowadays, researchers have developed a range of tools on Grasshopper and Dynamo
platforms to integrate the whole generic SBO process, enabling architects to seamlessly
transition from parametric modeling to simulation engines (e.g., Diva, Radiance, Honeybee,
and Ladybug), and finally to optimizers and visualization tools such as Galapagos, Octopus,
Wallacei, and Opossum (Javanroodi et al. 2019; Wortmann et al. 2022; Luca et al. 2024).
However, given the high-dimensional design search space generated by numerous design
parameters in early design stages, combined with the black-box nature of SBO, the generic
SBO process still faces limitations in search efficiency and the interpretable guidance for
optimization convergence.
2.2 Design parameter analysis for convergence of search space
The memory and computational cost may rise exponentially and become difficult to navigate
as more design parameters are brought into the SBO task (Nguyen et al. 2014). In practice, the
convergence of design parameters is heavily influenced by the designer’s prior knowledge
(Brown & Mueller 2019; Wang et al. 2024). However, this process can be particularly
challenging for other stakeholders with little design experience. Therefore, implementing a
systematic converging and analysis approach in the early design stages is essential to maintain
a manageable and effective set of design parameters.
Previous studies have conducted design parameters analysis through literature reviews
(Zhou et al. 2023), sensitivity analysis (Tian 2013; Østergård et al. 2017), or machine learningbased feature selection method (Olu-Ajayi et al. 2022; Liu et al. 2022; Hinkle et al. 2024).
Zhou et al. (2023), for instance, reviewed 50 papers published between 2010 and 2022,
summarizing eight types of design parameters that significantly impact building environmental
performance. This review helps to focus on the categories of design parameters in SBO.
Sensitivity analysis is commonly divided into local and global approaches (Tian 2013), with
global sensitivity analysis being more widely used in building analysis due to the non-linear,
multi-modal, and discontinuous character of building simulation results (Nguyen et al. 2014).
Global sensitivity analysis methods include regression techniques (e.g., Standardized
Regression Coefficients and Standardized Rank Regression Coefficients), screening-based
methods (e.g., the Morris method), variance-based methods (e.g., Fourier Amplitude
Sensitivity Test and Sobol method), and meta-modeling approaches (e.g., Multivariate
Adaptive Regression Splines and Support Vector Machines). Machine learning-based feature
selection methods, such as Random Forest (RF) or Extra Trees classifiers, apply recursive
assessment of feature importance by evaluating the effect of adding or removing individual
features (Olu-Ajayi et al. 2022; Liu et al. 2022; Tian et al. 2024).

5

180

185

190

While Zhou et al. (2023) emphasize the categories of design parameters in SBO, it has
a limited impact on reducing the dimensionality of the optimization search space. In contrast,
most global sensitivity analyses require extensive large-scale sampling techniques, such as
Monte Carlo or Latin Hypercube Sampling, which is impractical for SBO tasks with timeintensive simulations, as each simulation can take several minutes or even hours (Tian 2013;
Nguyen et al. 2014; Østergård et al. 2017). Additionally, machine learning-based feature
selection methods provide important metrics through training; however, if variables or their
value boundaries change, retraining becomes necessary to maintain accuracy, which increases
computational costs (Hinkle et al. 2024). Therefore, effectively screening design parameters
without increasing computational burden and seamlessly integrating this process into the SBO
workflow remains a research challenge in SBO tasks.
2.3 Information gain and applications

195

200

205

210

Given the uncertainty and lack of interpretability in high-dimensional SBO, information theory
provides a possible approach to addressing these challenges. In information theory, information
entropy is proposed as the metric for uncertainty or randomness within a dataset (Shannon
1948). And information gain (IG) is an entropy-based feature evaluation method widely used
in machine learning (Zhang et al. 2022). In decision trees, it helps to choose the feature that
best splits the data, with higher IG indicating more effective sample separation and improved
classification (Kotsiantis 2013). Chen and Hao (2017) applied IG to rank feature importance
in stock market indices prediction, providing a basis for computing feature weights in weighted
Support Vector Machines. Besides, Omuya et al. (2021) utilized an IG-based feature selection
technique to address the curse of dimensionality, improving the accuracy and overall
performance of machine learning algorithms.
In the building design sector, limited research has integrated information entropy or
information gain. Hester et al. (2018) were the first to apply information entropy in early-stage
building design optimization, quantifying the flexibility of uncertain or probabilistic designs
during iterative refinement and optimization. Son et al. (2022) developed a proactive design
exploration system incorporating Bayesian information gain and information entropy to
provide designers with guidance feedback during the design exploration process. Additionally,
other researchers employed information gain to determine criterion weights in multi-criteria
decision-making (Weerasuriya et al. 2021; Zhang et al. 2022). However, information gainguided methods remain scarce in high-dimensional SBO tasks, revealing a gap in the research.
3 Research methods

215

This paper demonstrates the effectiveness of the Automatic Information Gain-guided
Convergence (AIGGC) method in early-stage building design through two sustainable design
case studies. The overall workflow is illustrated in Figure 1.

6

220

225

230

Figure 1. The proposed workflow for Automatic IG-guided Convergence of design
parameters.
Distinct from the generic SBO process, which optimizes the program by running the
total iteration budget once, this method allocates a small portion of the total budget for firstphase optimization. The optimized results from first-phase optimization, comprising objective
function values and corresponding design parameter sets, are then utilized as a dataset for IGguided analysis. Second, the dataset is pre-processed, and the initial domain intervals of the
design parameters are partitioned. IG is then calculated for each sub-interval, enabling
automatic convergence by prioritizing high-information design parameters based on the total
IG score. The IG-guided visual analysis provides stakeholders with interpretable insights from
both design parameters and components, allowing them to converge design parameters and
gain a deeper understanding of influential components. Finally, the converged design
parameters are adopted for the second phase of optimization.
3.1 Information gain-guided approach for automatic convergence
3.1.1 Design the allocation of iteration budget
As shown in Figure 1, the AIGGC method consists of two optimization phases. First, building
designers set the total iteration budget (N) and determine the distribution ratio (rd) between the
7

235

240

245

two phases, resulting in the pre-convergence budget (N1 = N × rd) and the post-convergence
budget (N2 = N − N1). In the second phase, the converged design parameters based on IGguided visual analysis are re-inputted into the optimizer to finally find the optimal solution.
The optimization settings and algorithm remain the same across both phases.
3.1.2 Dataset preprocessing
The first-phase optimization generates a dataset of optimized design solutions (S) and
corresponding objective function values f(S), organized as a matrix. The first row lists the
names of design parameters and the objective function, while each subsequent row represents
an optimized solution. The matrix is then sorted by the optimization objective in ascending
order (for minimizing f(x)) or descending order (for maximizing f(x)). Subsequently, inspired
by the elitism strategy in GA, the dataset is categorized into ‘elite’ and ‘non-elite’ groups based
on a designer-defined elite ratio (re), as shown in Figure 2.

Figure 2. Detailed procedures of IG-guided automatic convergence.

250

255

3.1.3 Decomposing the domain of design parameters
The initial design parameter domains (R) are divided into multiple sub-interval bins using the
partitioning method (BinM), and the number of bins (Nb) determines the analytical granularity.
This partitioning process helps to analyze the distribution of pre-optimized solutions within
each sub-interval bin after the first-phase optimization and to calculate the probability of
solutions belonging to the ‘elite’ group. In addition, it aids in targeting promising regions of
design parameters for further optimization.
This study proposes three approaches for the partitioning method (BinM ∈ Ζ): (1) BinM
= 10, dividing each design parameter domain into 10 bins; (2) BinM = N1 /10, with the number
of bins set to the integer value of the pre-convergence budget (N1) divided by 10; (3) BinM =
�𝑁𝑁1 , with the number of bins set to the integer value of the square root of the pre-convergence
budget (N1).

260

3.1.4 IG-guided Automatic Convergence
The information gain (γ) for each design parameter can be computed automatically according
to Algorithm 1. The algorithm takes as input a set of solutions (S) with their objective function
values f(S), the design parameter’s initial domain range (R), the elite ratio (re), and the number
of bins (Nb).

8

265

270

275

280

285

Algorithm 1 first computes the baseline entropy (e0), assuming an equal distribution of
elite solutions across the parameter range. The algorithm determines the threshold value of f
for elite solutions to identify the elite solutions (SE). The initial range R is then decomposed
into Nb equally spaced sub-intervals I. For each sub-interval i, the entropy of elites in i is
calculated by the probability p of elite solutions. The algorithm also computes the probability
r of input solutions S in each sub-interval, and accumulates the weighted entropy (ew) by
weighting the elite entropy with probability r before summing across sub-intervals. Finally, the
information gain (γ) is computed as the difference between the baseline entropy (e0) and the
accumulated weighted entropy (ew). A higher IG value for a design parameter indicates greater
importance in reducing the uncertainty of finding the optimal solution within the search space.
Algorithm 2 and Figure 2 show the following steps, which converge design parameter
intervals based on IG values, improving optimization efficiency by either converging interval
ranges or fixing parameters as constants. Algorithm 2 takes as input the number of design
parameters (n), corresponding initial domain range (R), corresponding information gains (Γ),
and the corresponding sub-intervals (I). Additionally, it requires a set of elite solutions (SE) and
two ratios: rconv, associated with the highest IG, which determines the subsets of parameters
that should converge; and rconst, associated with the lowest IG, which defines the subsets of
parameters that should be fixed to constants. Specifically, the lower threshold (γconv) of gain to
converge is set at the (1 - rconv) percentile of the information gains, while the upper threshold
(γconst) of gain to constant is set at the rconst percentile.

9

290

295

300

305

For each design parameter, the algorithm applies a three-way decision rule based on its
information gain (γi). If the gain γi is greater than or equal to γconv, the parameter range is
converged by removing sub-intervals that do not appear in elite solutions. If the gain γi is less
than or equal to γconst, the parameter is converted to a constant value, which is determined as
the design value observed in the optimum of elite solutions. Otherwise, the parameter range
remains unchanged. Finally, the converged set of parameter ranges R* is returned. This process
effectively reduces the design search space by eliminating irrelevant or highly stable parameter
variations, thereby improving the efficiency of the second-phase optimization.
3.1.5 Interpretable analysis of building design parameters and components
The IG-guided interpretable analysis starts with information from design parameters, traces
their association with different design components, and finally provides stakeholders with
guidance on overall design strategies. As shown in the Sankey diagram in Figure 3(a), design
parameters originally belonging to various design components are ranked based on their IG
values and subsequently categorized into three subsets, corresponding to different modes of
domain interval convergence. Figure 3(b) further explains and visually presents the
convergence modes within three IG-guided subsets. Furthermore, the IG values of individual
design parameters can be aggregated to evaluate their associated design components,
highlighting the most impactful components for design optimization within the given SBO task.
The IG-guided interpretable analysis explicitly demonstrates the convergence to effective subintervals during the SBO process while effectively supporting designers and stakeholders in
making informed design decisions.

10

310

Figure 3. An example visualization for interpretable analysis in AIGGC. (a) Flow of design
parameters information: from design components to IG-guided subsets. (b) Visual
transformation from initial to converged domain intervals. (c) Illustration of IG ranking for
design components.
3.2 Case study

315

320

325

330

335

To evaluate the robustness and scalability of the proposed method, we applied AIGGC to
enhance three optimization algorithms to SBO tasks in two scales. The first conducted
sustainable design optimization for energy efficiency at the building scale, while the other
optimized daylight quality at the urban scale. Residential energy consumption has steadily risen
in recent years, highlighting the need for sustainable building technologies (Qin & Pan 2020;
Zhou & Xue 2023). Modular construction, known for its productivity, reusability, and pollution
reduction, is extensively studied and particularly vital in Hong Kong due to its dense population
and limited land resources (Zhou & Xue 2023). This paper optimizes the design of modular
flats based on the building dimensions published by the Hong Kong Housing Authority (HKHA
2015). Given the floor layout of a one-bedroom modular flat, the building envelope was
optimized to minimize energy consumption. Additionally, daylight quality, which significantly
impacts residents’ quality of life, is affected by mutual shading among urban buildings (Liu et
al. 2023). Therefore, optimizing building forms during the early stages of urban block
development is also essential for enhancing daylight accessibility and improving living
conditions.
3.2.1 Definition of initial design parameters
The first design case focuses on optimizing the building envelope of a modular flat in Hong
Kong, designed for 1-2 occupants, with an internal floor area rationalized to 14.1~14.5 m2.
Hong Kong has a subtropical climate, with warm and humid conditions year-round. Summers
are long and hot, with dry-bulb temperatures exceeding 30°C, leading to a high energy demand
for cooling (Zhou & Xue 2023). To enhance passive energy efficiency, we further optimize the
envelope components. Numerous studies have identified the window-to-wall ratio (WWR) as
a significant factor influencing building energy consumption (Wang et al. 2024). Besides, we
consider details such as window shape (where variations in window height, given a fixed WWR,
determine the window’s width), sill height, and the angle and number of louvers used for
11

340

345

shading, as illustrated in Figure 4(a). The design scheme includes four façades to be optimized,
comprising 11 continuous variables, 7 discrete variables, and 4 binary variables. The specific
design parameters and their domain intervals are shown in Table 1.

Figure 4. Design cases to be optimized. (a) Case 1: Envelope design optimization for onebedroom modular flat; (b) Case 2: Urban block forms design optimization.
Table 1. Description of envelope design parameters for one-bedroom modular flat.
Design parameters

350

355

Unit

Parameter domain intervals

Precision

Window-to-Wall Ratio (WWR1, WWR2)

Parameter
type
Continuous

-

0.1 ≤ WWR1, WWR2 ≤ 0.6

0.01

Window-to-Wall Ratio (WWR3, WWR4)
Window height (WH1&2)

Continuous
Discrete

m

0.1 ≤ WWR3, WWR4 ≤ 0.3
1.0 ≤ WH1&2 ≤ 2.0

0.01
0.1

Window height (WH3, WH4)
Window sill height (WSH1&2, WSH3, WSH4)
Window louvers count (LC1, LC2, LC3, LC4)
Window louvers angle (LA1, LA2, LA3, LA4)
Window louvers direction (LVH1, LVH2,
LVH3, LVH4)

Discrete
Continuous
Discrete
Continuous
Binary

m
m
°
-

1.0 ≤ WH3, WH4 ≤ 1.5
0.80 ≤ WSH1&2, WSH3, WSH4 ≤ 1.20
1 ≤ LC1, LC2, LC3, LC4 ≤ 6
-45 ≤ LA1, LA2, LA3, LA4 ≤ 45
Horizontal = 0; Vertical = 1

0.1
0.01
1
1
-

The second design case focuses on optimizing the building forms of urban blocks in
Jianhu City, located in Jiangsu Province, China. The selection of initial design parameters is
based on the findings of Liu et al. (2023). As shown in Figure 4(b), the urban block consists of
nine zones, numbered from 0 to 8. According to the generative rules by Liu et al., one of these
zones is designated as open space, while the remaining eight plots are selected from nine typical
building combinations. These building combinations are derived from actual residential
clusters in Jianhu City and are categorized into three major types: point-type buildings
(including P-1, P-2, P-3, and P-4), slab-type buildings (including S-1, S-2, S-3), and courtyardtype buildings (including C-1 and C-2). Specifically, P-1, S-1, and C-1 are low-rise buildings;
P-2, S-2, and C-2 are mid-rise buildings; P-3, P-4, and S-3 are high-rise buildings; with their
respective floor number counts detailed in Table 2. Each block is uniformly south-facing, with
a floor area ratio (FAR) of approximately 2.5. There are 1 discrete variable, 9 continuous
variables, and 8 categorical variables.

12

360

Table 2. Description of urban block form design parameters.
Design parameters
Open space location (OPos)
Building type of remaining plots (Pos1,
Pos2, Pos3, Pos4, Pos5, Pos6, Pos7, Pos8)
Number of floors (NFP1, NFS1, NFC1, NFP2,
NFS2, NFC2, NFP3, NFP4, NFS3)

Parameter
type
Discrete
Categorical

Unit

Continuous

-

-

Parameter domain intervals

Precision

[0, 1, 2, 3, 4, 5, 6, 7, 8]
[P-1, S-1, C-1, P-2, S-2, C-2, P-3, P-4,
S-3]
1 ≤ NFP1, NFS1, NFC1≤ 3
4 ≤ NFP2, NFS2, NFC2≤ 12
13 ≤ NFP3, NFP4, NFS3≤ 30

1
1

3.2.2 Definition of objective functions
In the first design case, we aim to minimize energy use intensity and the objective function can
be concluded as:
(1)
arg minx∈X EUI(x)

365

370

375

380

Where EUI is the energy use intensity (kWh/m2·yr) that can be calculated by dividing
the total annual energy consumption over the gross floor area (Konis et al. 2016), x represents
a combination of the n design parameters (x1, x2, ..., xn), and X indicates the set of all potential
design combinations. The optimization problem’s dimensionality is defined by n, determining
the search space complexity and computational effort. The numerical computing of EUI is
performed using the Honeybee components in the Grasshopper platform (Zhou & Xue 2023).
First, the Honeybee-Radiance (Ver.1.5) component integrates context data (Qin & Pan 2020),
including local climate, construction materials, construction type, and HVAC systems, to
simulate annual daylight based on a predefined grid size (Gs1). The results are then utilized to
set up the daylight control schedule for the target model. Next, the context data and the
generated schedule are passed to the Honeybee-OpenStudio (Ver.1.5) component, which
translates this information to create an energy model (.osm) and convert it into a .idf file for
total EUI calculation via the built-in EnergyPlus program (Roudsari & Pak 2013). According
to Qin and Pan (2020), the EUI of local modular flats in Hong Kong is generally 153.8
kWh/m2·yr.
In contrast, the second design case focuses on an opposing optimization objective:
maximizing the average direct sunlight hours on the south-facing ground floors of urban blocks
in Jianhu City. Jianhu City is situated in the hot summer and cold winter (HSCW) climate zone.
According to mainland China’s building code (MOHURD 2018), residential buildings in this
zone must receive at least two hours of sunlight on the south-facing ground floor on the coldest
day of the year, i.e., January 20th (Liu et al. 2023). We formulate the function as follows:
1
(2)
arg maxy∈Y ∑𝑚𝑚
𝑖𝑖=1 𝐷𝐷𝐷𝐷𝐷𝐷𝑖𝑖 (𝑦𝑦)
𝑚𝑚

subject to | FARori – FARopt |≤ 0.05

385

Where DSHi(y) is the direct sunlight hours for the i-th sampling point as a function of
the design parameter y, m means the total number of sampling points determined by the
simulation grid size (Gs2), and Y denotes the set of all design parameters. The constraint is that
the absolute difference between the optimized block’s floor area ratio (FARopt) and the original
block’s FAR (FARori = 2.5) must be less than 0.05. The DSHi(y) can be simulated through
13

390

395

400

405

410

the Ladybug-Direct Sun Hours (Ver.1.5) component, which calculates direct sunlight hours on
geometry using sun vectors and ray intersection methods (Roudsari & Pak 2013).
3.2.3 Optimization algorithms selection
In this study, both design cases are single-objective optimization tasks. To evaluate the
robustness of the proposed method, we compared three optimization algorithms with distinct
search strategies, GA, CMA-ES, and RBFOpt, which are integrated into Grasshopper and
interact smoothly with the design parameters and simulation engines. Statistical data indicates
that GA has been the most frequently used algorithm in single-objective SBO tasks over
decades (Evins 2013; Nguyen et al. 2014). Moreover, CMA-ES and RBFOpt have
demonstrated efficiency advantages in black-box optimization for sustainable building design
(Kämpf et al. 2010; Xue et al. 2019; Wortmann 2019; Rehbach et al. 2022).
GA is a population-based metaheuristic algorithm inspired by natural selection,
iteratively generating new populations through selection, mutation, and crossover (Katoch et
al. 2021). CMA-ES aims to reduce the stochastic nature of evolutionary strategies by using the
Covariance Matrix (CM) in each iteration, which has been shown to be an efficient method in
building design optimization, especially for small population sizes (Hansen et al. 2003;
Ramallo-González & Coley 2014). RBFOpt is a model-based algorithm that applies sampling
points to refine an approximation model for the unknown objective function (Waibel et al.
2019). GA can be implemented in the Galapagos plugin, while CMA-ES and RBFOpt can be
operated in the Opossum plugin.
4 Experimental tests
4.1 Experimental settings

415

420

425

The experiments were conducted on a desktop computer with an Intel (R) Core i7-10700 CPU
@ 2.90 GHz processor and 32 GB memory. In this study, both design cases were parametrically
reconstructed in Rhinoceros3D (Ver.7.0) and the visual programming platform Grasshopper,
based on the detailed dimensions provided by the Hong Kong Housing Authority (HKHA 2015)
and the published work of Liu et al. (2023), respectively.
The first sustainable design case utilized the Ladybug-EPWmap (Ver.1.5) component
to obtain meteorological data for Hong Kong (ASHRAE 2021). The Honeybee plugin assigned
physical properties of construction materials to the parametric model, including thickness,
conductivity, density, specific heat capacity, and U-value, following (Qin & Pan 2020). The
EUI value was then calculated via the Honeybee-Radiance (Ver.1.5) and HoneybeeOpenStudio (Ver.1.5) components, with a sensor grid size (Gs1) of 0.2 meters. The original onebedroom modular flat served as the baseline, with its design parameters used as initial
optimization inputs, resulting in an EUI value of 159.599 kWh/m2·yr, as detailed in Table 1 in
the Appendix.
Similarly, in the second sustainable design case, climate data for Jianhu City was
collected using the Ladybug-EPWmap (Ver.1.5) component and processed through the
Ladybug-SunPath (Ver.1.5) component to obtain the sun position between 8:00 a.m. and 5:00
14

430

435

440

445

p.m. on January 20th (i.e., the coldest day). The resulting sunlight vector data was then fed into
the Ladybug-Direct Sun Hours (Ver.1.5) component to calculate the direct sunlight duration on
the ground floor of a south-facing urban block. The sensor grid size (Gs2) was set to 1 meter
for this urban-scale optimization. The baseline urban model’s parameters are listed in Table 2
of the Appendix, with a corresponding DSH value of 6.081 hours.
This experiment evaluated the robustness and advantages of the AIGGC method across
two design cases using different SBO algorithms, i.e., RBFOpt, CMA-ES, and GA. Since many
algorithms contain randomized factors during the optimization process (Waibel et al. 2019),
each algorithm was rerun 5 times for Case 1 (as a single set of runs required 36 hours) and 20
times for Case 2 to ensure reliable results.
For the three SBO algorithms, this experiment included an experimental group with
AIGGC and a control group without AIGGC under the same iteration budget. The detailed
hyperparameter settings for the single-objective algorithms are described in Appendix Table 3,
referring to previous literature (Waibel et al. 2019). For both design cases, the total iteration
budget (N) was set to 300 with a distribution ratio (rd) of 1:2, resulting in the pre-convergence
budget (N1) as 100 and the post-convergence budget (N2) as 200. The elite ratio (re) was set to
20% to classify the solutions into ‘elite’ and ‘non-elite’ groups. The partitioning method for
sub-interval bins was chosen as BinM (Nb) = 10, which divided each design parameter domain
into 10 bins. For design parameters convergence, rconv and rconst were both set to one-third.
4.2 Experimental results and analysis

450

455

4.2.1 Optimized results with AIGGC
The experimental results compare the best of optimized design solutions from multiple runs of
the three SBO algorithms (i.e., RBFOpt, CMAES, and GA), using the AIGGC method, against
the baseline design solution, as detailed in Table 3. RBFOpt, after five reruns of three SBO
algorithms, provided the best optimization result in Case 1, resulting in a minimum EUI value
of 149.149 kWh/m2·yr. Compared to the baseline design solution, all four window façades
showed a significant increase in the number of louvers. Notably, except for the first window,
the remaining three featured a vertical louver design.
Table 3. Comparison between the best of optimized solutions with AIGGC and the baseline
solution.

Case 1

EUI
(kWh/m2·yr)
Algorithm

Best optimized
solution based on
AIGGC

Baseline design
solution

149.149

159.599
RBFOpt

Case 2

DSH
(hours)
Algorithm

15

Best optimized
solution based on
AIGGC

Baseline design
solution

9.000

6.081
RBFOpt

460

465

470

In Case 2, RBFOpt still stands out among the other algorithms across 20 reruns,
achieving the optimal DSH value of 9 hours under the constraints of a given floor area ratio.
The P-1 building cluster most frequently appeared in the best solution from multiple runs, with
a noticeable trend of locating lower-rise blocks in the southern plots and higher-rise buildings
in the northern plots.
4.2.2 Robustness and significance across different optimization algorithms
Table 4 compares the average and best objective performance values among three SBO
algorithms between the experimental group (With AIGGC) and the control group (NO AIGGC),
as well as the magnitude and significance of performance improvements achieved by AIGGC.
The result demonstrates that incorporating AIGGC into SBO algorithms consistently improves
optimization performance across multiple runs, with statistically significant enhancements in
average results. Notably, RBFOpt shows the best overall performance among all algorithms,
achieving the best solution in both cases.
Table 4. The magnitude and significance of AIGGC’s performance in improving SBO
algorithms in multiple runs.
Average SBO results
NO
With
†
Sig.#
% Imp.
Δ
AIGGC AIGGC
150.289 149.301 -0.988
0.62 0.008
RBFOpt
min EUI
1
CMA-ES
151.961
150.935
-1.026
0.64 0.019
(159.599 kWh/m2·yr)
GA
155.305 154.241 -1.064
0.67 0.018
RBFOpt
8.449
8.579 0.130
2.14 0.036
max DSH
2
CMA-ES
7.997
8.202 0.205
3.37 0.037
(6.081 hours)
GA
7.977
8.265 0.288
4.74 0.000
*: Smaller values are better for Case 1 and larger values are preferred for Case 2.
†: Improvement by percentage, | Δ |/v0 × 100%, v0 for baseline value.
#: Two-tailed p-value of independent t-test, bold when p-value < 0.05.
Case

475

480

485

Objective function f*
(Baseline value v0)

SBO
algorithm

Best solution
NO
With
AIGGC AIGGC
149.719 149.149
151.429 150.099
154.469 153.709
9.000
8.764
8.554
8.708
8.329
8.680

Δ
-0.57
-1.33
-0.76
0.236
0.154
0.351

In Case 1, where a lower EUI value is preferred, AIGGC leads to a reduction in the
average EUI across all algorithms, with the improvement percentage ranging from 0.62% to
0.67%. With the incorporation of AIGGC, RBFOpt reduced the average EUI from 150.289
kWh/m2·yr (NO AIGGC) to 149.301 kWh/m2·yr. CMA-ES and GA also showed
improvements with AIGGC, achieving average EUI reductions of 0.64% (from 151.961 to
150.935 kWh/m2·yr) and 0.67% (from 155.305 to 154.241 kWh/m2·yr), respectively.
Moreover, RBFOpt achieved the best performance value of 149.149 kWh/m2·yr after five
reruns, representing a 3.024% improvement compared to the general EUI of local modular flats,
which is 153.8 kWh/m2·yr.
In Case 2, where higher DSH values are desirable, AIGGC similarly enhances the
performance of all three algorithms, with the improvement percentage ranging from 2.14% to
4.74% across 20 repeated runs. When combined with AIGGC, RBFOpt achieved an average
DSH of 8.579 hours, which is 0.13 hours higher than without AIGGC. Similarly, CMA-ES and
GA showed notable enhancements with AIGGC, achieving average sunlight hours
improvements of 3.37% (from 7.997 to 8.202 hours) and 4.74% (from 7.977 to 8.265 hours),
respectively. The best DSH value obtained with AIGGC was 9.000 hours, followed by 8.708
16

490

495

500

505

hours identified by CMA-ES and 8.680 hours identified by GA, all significantly exceeding the
two-hour requirement specified in the local residential building code.
The statistical significance of the performance improvements was evaluated using the
independent two-tailed t-test. For both cases, RBFOpt consistently showed significant
improvements when AIGGC was applied (two-tailed p = 0.008 < 0.05 for Case 1 and p = 0.036
< 0.05 for Case 2). The significant p-values across all algorithms validate the robustness and
reliability of the AIGGC method, demonstrating its ability to improve optimization
performance under different objectives and scenarios.
Figure 5 (a) and (b) apply violin plots to compare the deviations of best performance
values achieved by three SBO algorithms under two conditions. The ‘NO AIGGC’ control
group is represented in blue, the ‘AIGGC’ experimental group is in red, and the baseline is
indicated by a red dashed line. In both cases, the median values of the ‘AIGGC’ group
consistently outperform those of the ‘NO AIGGC’ group, with the ‘AIGGC’ group showing a
larger overall deviation from the baseline, indicating a more significant improvement. Overall,
the RBFOpt algorithm with the AIGGC method exhibits the most concentrated distribution and
is more efficient in finding the minimum solution for EUI and the maximum solution for DSH.

Figure 5. Comparison of optimal performance deviations of three optimization algorithms
with and without AIGGC. (a) Case 1: Minimize EUI; (b) Case 2: Maximize DSH.

17

510

515

520

525

530

535

Figure 6. Convergence trend of optimization with and without AIGGC. (a) Case 1: Minimize
EUI; (b) Case 2: Maximize DSH.
Figure 6 (a) and (b) illustrate the optimization line graphs of RBFOpt achieving the best
performance in two cases, i.e., 149.149 kWh/m2·yr for Case 1 and 9.000 hours for Case 2. The
convergence trends highlight the performance improvements achieved by integrating the
AIGGC method. The blue lines represent the control group without AIGGC, while the red lines
represent the experimental group with AIGGC. The thin solid lines depict the iterative solution
values during the optimization process, and the thick solid lines indicate the best objective
values achieved so far. It can be observed that in high-dimensional optimization problems,
algorithms without AIGGC struggle to converge in the later stages and often get trapped near
sub-optimal solutions. In contrast, optimization algorithms incorporating AIGGC can apply
IG-guided information to identify superior solutions. According to the experimental settings,
the group with AIGGC first used 100 iterations to compute a dataset, followed by IG-guided
analysis and refining of the design parameters. The results demonstrate that the experimental
group, with converged design parameters, quickly surpassed the control group within the 50
iterations in the second phase, while the control group ran for 150 iterations. Statistically,
AIGGC performed a faster descent/ascent in Figure 6. The fast descent/ascent confirms the
hypothesis that reducing the dimensionality of the design search space enhances the efficiency
of the RBFOpt algorithm.
4.2.3 Design parameters and components analysis
Figures 7 and 8 illustrate the reduction in the number of design parameters and the size of the
potential solution space before and after IG-guided analysis for both cases. In Case 1, the initial
four design components included 22 design parameters, with a fine-grained division of the total
domain intervals revealing 4.45×1025 possible solutions. After applying the AIGGC method to
calculate, rank, and group the IG value for each design parameter, the number of design
parameters was reduced to 16, with 8 partially converged and 8 remaining unchanged.
Consequently, the design solution space size decreased sharply to 6.30×1018, by seven orders
of magnitude. Similarly, in Case 2, the design parameters were reduced from 18 to 12, with 6
18

partially converged and 6 unchanged, while the solution space shrank from 4.45×1016 to
2.21×109 by seven orders of magnitude.

540

Figure 7. Detailed visualization of the design parameter convergence process for RBFOpt’s
best performance solution in Case 1.

19

545

550

555

560

565

Figure 8. Detailed visualization of the design parameter convergence process for RBFOpt’s
best performance solution in Case 2.
Figure 9 presents a series of heatmaps visualizing the average probability associated
with the sub-interval bins of each design parameter. The probability indicates the likelihood of
solutions within a given bin belonging to the ‘elite’ group. The color intensity of the heatmap
reflects the probability magnitude, with darker colors corresponding to higher probabilities.
Blank regions denote that there are no design solutions within those sub-interval bins. The bin
sequence is arranged from 1 to 10, representing the full domain range of each design parameter
from smallest to largest. On the right side, a bar chart illustrates the average IG value of each
design parameter observed in this experiment.

Figure 9. Visualization of design parameters’ average IG values and probabilities of subinterval bin contributions to the ‘elite’ group.
In Case 1, the window-to-wall ratio (WWR) and window louvers’ angle (LA) exhibit
relatively high IG values overall, with WWR1 showing the highest average IG value. The results
suggest that decision-makers may focus on adjusting the values of WWR and LA to minimize
energy use intensity efficiently. Moreover, high-probability sub-intervals for WWR are
concentrated in the larger bin indices (i.e., bins 9th and 10th), which means that when the WWR
of façades 1 and 2 approaches 0.5 to 0.6, and that of façades 3 and 4 approaches 0.27 to 0.3,
the likelihood of achieving low-EUI design solutions increases. Similarly, for LA2, the 2nd bin
emerges as a promising sub-interval, suggesting that setting LA2 between -35° and -27° is more
effective for high-performance building design exploration. In contrast, the parameter LVH
contributes minimally to the optimization objective regarding IG value and probability.
In Case 2, OPos shows the highest average IG value, with higher probabilities of
approaching high-DSH solutions concentrated in sub-interval bins 2nd, 5th, and 9th,
20

570

575

580

585

590

corresponding to plots 1st, 4th, and 7th in the urban block design. For building clusters of P-1,
S-1, and C-1, the suggested number of floors is primarily concentrated in the 1st and 2nd bins,
indicating single- or double-story configurations. Moreover, for clusters P-2, S-2, and C-2,
higher probabilities of optimal solutions are found from bins 1st to 3rd, with a preferred range
of four to six floors. And the suggested floor numbers for P-3, P-4, and S-3 building clusters
are 25–26, 27–28, and 17–18, respectively. Regarding plot allocation, S-1 is applicable for
most plots, whereas C-2 presents a lower likelihood of existing good design solutions across
all plots. P-1 and S-3 are recommended for plots 4th and 8th, respectively.
Analyzing the IG values of design components is also meaningful, as it highlights their
importance in reducing the uncertainty of finding optimal solutions within the optimization
search space. Figure 10(a) and (b) compare the average IG values of design components and
parameter categories in Case 1. Specifically, Win_01 demonstrates the highest IG value (0.75),
followed by Win_02 (0.699). Therefore, decision-makers may prioritize the optimization of
Win_01 to effectively reduce building energy consumption. Among the five parameter
categories, WWR ranks the highest with an IG value of 0.624, while LVH ranks the lowest with
an IG value of 0.118. The result means that WWR is the most significant factor in the Case 1
optimization task, whereas LVH can be given less emphasis.

Figure 10. Visualization of average IG values for design components and parameter
categories in Case 1. (a) Average IG values for design components; (b) Average IG values for
design parameter categories.
Similarly, in Case 2, the placement of the ‘Open Space’ plot significantly impacts the
average direct sunlight hours on the south-facing ground floors of urban blocks. Combining
Figures 9 and 11, the three plots with the highest average IG values also correspond to the plots
with the highest probabilities, i.e., plot 1st (IG of 0.327), plot 4th (IG of 0.371), and plot 7th (IG
21

595

of 0.349). This observation suggests that positioning the ‘Open Space’ plot along the central
axis of the urban block is most conducive to achieving the optimal solutions.

Figure 11. Visualization of average IG values for positioning ‘Open Space’ plot in Case 2.
4.3 Sensitivity analysis

600

605

610

A sensitivity analysis was conducted to determine the trade-off between time cost and optimal
results, identifying the most effective experimental settings for the experimental and control
groups. This experiment involved three key parameters: (i) the total iteration budget (N), with
comparisons made between 100, 300, 500, 1000, 3000, and 5000; (ii) the distribution ratio (rd)
between the two optimization phases, tested with ratios of 1:1, 1:2, and 1:4; and (iii) the
partitioning method for sub-interval bins (BinM), which was evaluated using three scenarios:
BinM = 10, BinM = N1 /10, and BinM = �𝑁𝑁1. Due to the computational expense of energy
consumption simulations in Case 1, Case 2 was selected for comparing experimental
configurations. The experimental and control groups were compared under the same iteration
budget.
Figures 12 and 13 visually compare the impact of different experimental configurations
on the number of sub-interval bins and the maximum DSH values achieved via the AIGGC
method. Where BinM is distinguished by symbols and colors: blue squares represent ‘BinM =
N1 /10’, purple inverted triangles for ‘BinM = �𝑁𝑁1 ’, and red circles for ‘BinM = 10’.

615

Meanwhile, solid symbols indicate that the experimental group outperformed the control group
(i.e., obtained higher DSH values), while hollow symbols indicate the opposite. In addition, the
distribution ratio (rd) is represented by pink circles of varying sizes.

22

Figure 12. Variation in bin counts for BinM methods across iteration budgets.

620

625

Figure 13. Sensitivity analysis of experimental settings.
From Figures 12 and 13, it can be observed that the number of sub-interval bins
increases significantly with higher iteration budgets at ‘BinM = N1 /10’, indicating finer
granularity for IG-guided analysis. When ‘BinM = N1 /10’, the frequency of finding the optimal
solution is also higher under most iteration budgets. Interestingly, with ‘BinM = 10’, the
number of bins remains constant regardless of the iteration budget, yet it consistently ensures
the discovery of optimal solutions (e.g., performing well with budgets of 300, 500, 1000, and
5000). In contrast, ‘BinM = �𝑁𝑁1’ shows relatively average performance. Furthermore, a side-

by-side comparison in Figure 12 reveals that a distribution ratio (rd) of 1:2 is most common
near the top of the stack of points, implying a higher chance of finding the optimal solution.

23

630

635

640

645

650

655

660

The proportion of solid and hollow symbols is also noteworthy. Only hollow symbols
are observed at a total iteration budget of 100, indicating that the generic SBO process is more
suitable for small-budget optimization tasks. In medium-budget tasks (ranging from 300 to
1000 iterations), the AIGGC method demonstrates clear advantages, particularly at 1000
iterations, where it consistently outperforms the generic SBO across all experimental
configurations. For large-budget tasks (e.g., 3000 and 5000 iterations), the AIGGC method
demonstrates a more remarkable ability to find the optimal solution than the generic SBO, as
solid symbols consistently appear at the top.
In this study, considering the balance between the time cost of expensive simulations
(e.g., energy simulation) and overall efficiency, we recommend the experimental configuration
of ‘BinM = 10’, a distribution ratio (rd) of 1:2, and a total iteration budget of 300.
5 Discussion
This study presents the AIGGC method for high-dimensional SBO building designs for the
first time, establishing an information-theory-based method for the automatic convergence of
design parameter domains, thus reducing the dimensionality of the search space. Based on the
dataset from first-phase optimization, the AIGGC method effectively enhances the
performance of existing optimization algorithms under a limited iteration budget. Through IGguided fine-grained visual analysis at the parameter and component levels, Case 1 highlights
the importance of the Win_01 object and the design parameter category WWR, while Case 2
provides applicable insights into the central axis placement of the ‘Open Space’ plot. AIGGC
applies information gain measurement into interpretable guidance, to enable designers and
stakeholders to identify optimization strategies and make informed decisions in early design
exploration. It can also enhance SBO efficiency in real-world sustainable building projects
while improving stakeholders’ understanding of optimization convergence.
Nevertheless, this study still has a few limitations. First, the analysis of design
parameters was conducted independently based on information gain, while potential non-linear
and complex interactions between parameters remain an area for future exploration. Second,
future research will consider more complex real-world projects, incorporating factors such as
practical occupant schedules, energy-efficient building materials, and the shading effects or
microclimate conditions of the built environment to optimize thermal comfort and energy
consumption, further assessing the method’s scalability to multi-objective optimization tasks.
Third, future work will focus on dynamically enhancing search efficiency within the solution
space by integrating advanced machine learning models and extending the applications to highdimensional optimization problems in other fields, such as architectural engineering and
environmental science.
6 Conclusion

665

The proposed Automatic Information Gain-guided Convergence (AIGGC) method in this
paper demonstrates promising experimental results in enhancing effectiveness and
24

670

675

680

685

interpretability for high-dimensional sustainable building designs. The AIGGC method
reallocates a limited budget by utilizing first-phase optimization results as a dataset and
performing IG-guided analysis on sub-intervals of each design parameter. The value of
information gain assists stakeholders in quickly identifying high-information design
parameters and high-quality domain intervals. The interpretable analysis of building design
parameters and components enables stakeholders to converge design parameters by effectively
reducing the number of design parameters as well as the size of the potential solution space.
This study validated the AIGGC method for robustness and scalability in optimizing energy
consumption and daylight quality at both the building and urban scales, while also significantly
improving the convergence efficiency of three SBO algorithms — RBFOpt, CMA-ES, and GA.
The findings in this study contribute to both the theory and application of SBO in highdimensional architectural design involving a large number of design parameters. The AIGGC
method establishes an information-theory-based method for optimizing design parameters in
addressing the challenge of the ‘curse of dimensionality’ in design search spaces. Furthermore,
for non-derivative black-box SBO tasks, this method can enhance optimization efficiency
while integrating interpretability analysis, enabling building designers and stakeholders to
make informed and rational decisions in early architectural design exploration.
Future work directions include multivariate analysis of design parameters, integration
of IG-based metrics with advanced machine learning techniques to uncover non-linear
correlations, and exploration of AIGGC’s applications in broader fields, such as multiobjective optimization in engineering and environmental science.
Acknowledgment

690

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

695

700

705

ASHRAE. (2021). Weather Data Viewer. Peachtree Corners, GA, USA: American Society of
Heating, Refrigerating and Air-Conditioning Engineers. Retrieved 12 8, 2024, from
https://www.ashrae.org/technical-resources/bookstore/weather-data-center#weather
Brown, N. C. & Mueller, C. T. (2019). Design variable analysis and generation for
performance-based parametric modeling in architecture. International Journal of
Architectural Computing, 17(1), 36–52. doi:10.1177/1478077118799491
Bushra, N. (2022). A comprehensive analysis of parametric design approaches for solar
integration with buildings: A literature review. Renewable and Sustainable Energy
Reviews, 168, 112849. doi:10.1016/j.rser.2022.112849
Chen, S., Montgomery, J. & Bolufé-Röhler, A. (2015). Measuring the curse of dimensionality
and its effects on particle swarm optimization and differential evolution. Applied
Intelligence, 42, 514–526. doi:10.1007/s10489-014-0613-2
Chen, Y. & Hao, Y. (2017). A feature weighted support vector machine and K-nearest neighbor
algorithm for stock market indices prediction. Expert Systems with Applications, 80,
340-355. doi:10.1016/j.eswa.2017.02.044

25

710

715

720

725

730

735

740

745

750

Cruz, A., Caldas, L., Mendes, V., Mendes, J. & Bastos, L. (2024). Multi-objective optimization
based on surrogate models for sustainable building design: A systematic literature
review. Building and Environment, 266, 112147. doi:10.1016/j.buildenv.2024.112147
Es-sakali, N., Pfafferott, J., Mghazli, M. O. & Cherkaoui, M. (2025). Towards climateresponsive net zero energy rural schools: A multi-objective passive design optimization
with bio-based insulations, shading, and roof vegetation. Sustainable Cities and Society,
120, 106142. doi:10.1016/j.scs.2025.106142
Evins, R. (2013). A review of computational optimisation methods applied to sustainable
building design. Renewable and Sustainable Energy Reviews, 22, 230-245.
doi:10.1016/j.rser.2013.02.004
Fang, Y. & Cho, S. (2019). Design optimization of building geometry and fenestration for
daylighting
and
energy
performance.
Solar
Energy,
191,
7-18.
doi:10.1016/j.solener.2019.08.039
Gupta, V. & Deb, C. (2023). Envelope design for low-energy buildings in the tropics: A review.
Renewable
and
Sustainable
Energy
Reviews,
186,
113650.
doi:10.1016/j.rser.2023.113650
Han, Z., Li, X., Sun, J., Wang, M. & Liu, G. (2023). An interactive multi-criteria decisionmaking method for building performance design. Energy and Buildings, 282, 112793.
doi:10.1016/j.enbuild.2023.112793
Hansen, N., Müller, S. D. & Koumoutsakos, P. (2003). Reducing the time complexity of the
derandomized evolution strategy with covariance matrix adaptation (CMA-ES).
Evolutionary Computation, 11(1), 1-18. doi:10.1162/106365603321828970
He, Q., Wu, Z. & Chen, X. (2024). An integrated framework for automatic green building
evaluation: A case study of China. Frontiers of Engineering Management, 11, 269–287.
doi:10.1007/s42524-023-0274-0
Hester, J., Gregory, J., Ulm, F.-J. & Kirchain, R. (2018). Building design-space exploration
through quasi-optimization of life cycle impacts and costs. Building and Environment,
144, 34-44. doi:10.1016/j.buildenv.2018.08.003
Hinkle, L. E., Pavlak, G., Curtis, L. & Brown, N. C. (2024). Implementing dynamic subset
sensitivity analysis for early design datasets. Automation in Construction, 158, 105198.
doi:10.1016/j.autcon.2023.105198
Hinkle, L. E., Wang, J. & Brown, N. C. (2022). Quantifying potential dynamic façade energy
savings in early design using constrained optimization. Building and Environment, 221,
109265. doi:10.1016/j.buildenv.2022.109265
HKHA. (2015). Design of the new public housing flats by the Hong Kong Housing Authority.
Transport and Housing Bureau. Hong Kong: Legislative Council Panel on Housing.
Retrieved
12
2,
2024,
from
https://www.legco.gov.hk/yr1415/english/panels/hg/papers/hg20150706cb1-1037-1-e.pdf
Javanroodi, K., Nik, V. M. & Mahdavinejad, M. (2019). A novel design-based optimization
framework for enhancing the energy efficiency of high-rise office buildings in urban
areas. Sustainable Cities and Society, 49, 101597. doi:10.1016/j.scs.2019.101597
Kämpf, J. H., Wetter, M. & Robinson, D. (2010). A comparison of global optimization
algorithms with standard benchmark functions and real-world applications using
EnergyPlus. Journal of Building Performance Simulation, 3(2), 103-120.
doi:10.1080/19401490903494597
Katoch, S., Chauhan, S. S. & Kumar, V. (2021). A review on genetic algorithm: past, present,
and future. Multimedia Tools and Applications, 80, 8091–8126. doi:10.1007/s11042020-10139-6

26

755

760

765

770

775

780

785

790

795

800

Konis, K., Gamas, A. & Kensek, K. (2016). Passive performance and building form: An
optimization framework for early-stage design support. Solar Energy, 125, 161-179.
doi:10.1016/j.solener.2015.12.020
Kotsiantis, S. B. (2013). Decision trees: a recent overview. Artificial Intelligence Review, 39,
261-283. doi:10.1007/s10462-011-9272-4
Li, X., Lu, W., Peng, Z., Zhang, Y. & Huang, J. (2024). Generative design of walkable urban
cool spots using a novel heuristic GAN×GAN approach. Building and Environment,
266, 112027. doi:10.1016/j.buildenv.2024.112027
Lin, B., Chen, H., Yu, Q., Zhou, X., Lv, S., He, Q. & Li, Z. (2021). MOOSAS – A systematic
solution for multiple objective building performance optimization in the early design
stage. Building and Environment, 200, 107929. doi:10.1016/j.buildenv.2021.107929
Liu, K., Xu, X., Huang, W., Zhang, R., Kong, L. & Wang, X. (2023). A multi-objective
optimization framework for designing urban block forms considering daylight, energy
consumption, and photovoltaic energy potential. Building and Environment, 242,
110585. doi:10.1016/j.buildenv.2023.110585
Liu, R., Liu, Z., Xiong, W., Zhang, L., Zhao, C. & Yin, Y. (2024). Performance simulation and
optimization of building façade photovoltaic systems under different urban building
layouts. Energy, 288, 129708. doi:10.1016/j.energy.2023.129708
Liu, X., Tang, H., Ding, Y. & Yan, D. (2022). Investigating the performance of machine
learning models combined with different feature selection methods to estimate the
energy consumption of buildings. Energy and Buildings, 273, 112408.
doi:10.1016/j.enbuild.2022.112408
Luca, F. D., Natanian, J. & Wortmann, T. (2024). Ten questions concerning environmental
architectural design exploration. Building and Environment, 261, 111697.
doi:10.1016/j.buildenv.2024.111697
Machairas, V., Tsangrassoulis, A. & Axarli, K. (2014). Algorithms for optimization of building
design: A review. Renewable and Sustainable Energy Reviews, 31, 101-112.
doi:10.1016/j.rser.2013.11.036
MOHURD. (2018). Standard for urban residential area planning and design. MOHURD
Research Institute of Standards and Norms, Ministry of Housing and Urban-Rural
Development. People's Republic of China: China Architecture & Building Press.
Retrieved 1 2, 2025, from https://www.codeofchina.com/standard/GB50180-2018.html
Mousavi, S., Gijón-Rivera, M., Rivera-Solorio, C. & Rangel, C. G. (2022). Energy, comfort,
and environmental assessment of passive techniques integrated into low-energy
residential buildings in semi-arid climate. Energy and Buildings, 263, 112053.
doi:10.1016/j.enbuild.2022.112053
Nguyen, A.-T., Reiter, S. & Rigo, P. (2014). A review on simulation-based optimization
methods applied to building performance analysis. Applied Energy, 113, 1043-1058.
doi:10.1016/j.apenergy.2013.08.061
Olu-Ajayi, R., Alaka, H., Sulaimon, I., Sunmola, F. & Ajayi, S. (2022). Building energy
consumption prediction for residential buildings using deep learning and other machine
learning techniques. Journal of Building Engineering, 45, 103406.
doi:10.1016/j.jobe.2021.103406
Omuya, E. O., Okeyo, G. O. & Kimwele, M. W. (2021). Feature selection for classification
using principal component analysis and information gain. Expert Systems with
Applications, 174, 114765. doi:10.1016/j.eswa.2021.114765
Østergård, T., Jensen, R. L. & Maagaard, S. E. (2017). Early Building Design: Informed
decision-making by exploring multidimensional design space using sensitivity analysis.
Energy and Buildings, 142, 8-22. doi:10.1016/j.enbuild.2017.02.059
27

805

810

815

820

825

830

835

840

845

850

Qin, H. & Pan, W. (2020). Energy use of subtropical high-rise public residential buildings and
impacts of energy saving measures. Journal of Cleaner Production, 254, 120041.
doi:10.1016/j.jclepro.2020.120041
Ramallo-González, A. & Coley, D. (2014). Using self-adaptive optimisation methods to
perform sequential optimisation for low-energy building design. Energy and Buildings,
81, 18-29. doi:10.1016/j.enbuild.2014.05.037
Rehbach, F., Zaefferer, M., Fischbach, A., Rudolph, G. & Bartz-Beielstein, T. (2022).
Benchmark-driven configuration of a parallel model-based optimization algorithm.
IEEE Transactions on Evolutionary Computation, 26(6), 1365-1379.
doi:10.1109/TEVC.2022.3163843
Roudsari, M. S. & Pak, M. (2013). Ladybug: A parametric environmental plugin for
grasshopper to help designers create an environmentally-conscious design.
Proceedings of the 13th international IBPSA conference (pp. 3128-3135). Lyon, France:
Building Simulation Conference Proceedings. doi:10.26868/25222708.2013.2499
Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical
journal, 27(3), 379 - 423. doi:10.1002/j.1538-7305.1948.tb01338.x
Showkatbakhsh, M. & Makki, M. (2022). Multi-Objective Optimisation of Urban Form: A
Framework for Selecting the Optimal Solution. Buildings, 12(9), 1473.
doi:10.3390/buildings12091473
Son, K. & Hyun, K. H. (2022). Designer-Centric Spatial Design Support. Automation in
Construction, 137, 104195. doi:10.1016/j.autcon.2022.104195
Son, K., Lee, S. W., Yoon, W. & Hyun, K. H. (2022). CreativeSearch: Proactive design
exploration system with Bayesian information gain and information entropy.
Automation in Construction, 142, 104502. doi:10.1016/j.autcon.2022.104502
Tian, L., Hao, T., He, X., Chan, I., Niu, J., Chan, P., Ng, W. & Huang, J. (2024). Examining
the non-linear relationship between urban form and air temperature at street level: A
case of
Hong Kong.
Building
and
Environment,
264,
111884.
doi:10.1016/j.buildenv.2024.111884
Tian, W. (2013). A review of sensitivity analysis methods in building energy analysis.
Renewable
and
Sustainable
Energy
Reviews,
20,
411-419.
doi:10.1016/j.rser.2012.12.014
UNEP. (2024). Global status report for buildings and construction: Beyond foundations:
Mainstreaming sustainable solutions to cut emissions from the buildings sector.
Nairobi: United Nations Environment Programme. Retrieved 11 28, 2024, from
https://www.unep.org/resources/report/global-status-report-buildings-andconstruction
Waibel, C., Wortmann, T., Evins, R. & Carmeliet, J. (2019). Building energy optimization: An
extensive benchmark of global search algorithms. Energy and Buildings, 187, 218-240.
doi:10.1016/j.enbuild.2019.01.048
Wang, X., Teigland, R. & Hollberg, A. (2024). Identifying influential architectural design
variables for early-stage building sustainability optimization. Building and
Environment, 252, 111295. doi:10.1016/j.buildenv.2024.111295
Weerasuriya, A., Zhang, X., Wang, J., Lu, B., Tse, K. & Liu, C.-H. (2021). Performance
evaluation of population-based metaheuristic algorithms and decision-making for
multi-objective optimization of building design. Building and Environment, 198,
107855. doi:10.1016/j.buildenv.2021.107855
Wortmann, T. (2019). Genetic evolution vs. function approximation: Benchmarking
algorithms for architectural design optimization. Journal of Computational Design and
Engineering, 6(3), 414-428. doi:10.1016/j.jcde.2018.09.001
28

855

860

865

870

875

Wortmann, T., Cichocka, J. & Waibel, C. (2022). Simulation-based optimization in
architecture and building engineering—Results from an international user survey in
practice
and
research.
Energy
and
Buildings,
259,
111863.
doi:10.1016/j.enbuild.2022.111863
Xue, F., Lu, W., Chen, K. & Zetkulic, A. (2019). From Semantic Segmentation to Semantic
Registration: Derivative-Free Optimization–Based Approach for Automatic
Generation of Semantically Rich As-Built Building Information Models from 3D Point
Clouds. Journal of Computing in Civil Engineering, 33(4), 04019024.
doi:10.1061/(ASCE)CP.1943-5487.0000839
Yu, S., You, L. & Zhou, S. (2023). A review of optimization modeling and solution methods
in renewable energy systems. Frontiers of Engineering Management, 10, 640–671.
doi:10.1007/s42524-023-0271-3
Zhan, J., He, W. & Huang, J. (2024). Comfort, carbon emissions, and cost of building envelope
and photovoltaic arrangement optimization through a two-stage model. Applied Energy,
356, 122423. doi:10.1016/j.apenergy.2023.122423
Zhang, Z., Geng, Y., Wu, X., Zhou, H. & Lin, B. (2022). A method for determining the weight
of objective indoor environment and subjective response based on information theory.
Building and Environment, 207, 108426. doi:10.1016/j.buildenv.2021.108426
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
Zhou, Y., Ma, M., Tam, V. W. & Le, K. N. (2023). Design variables affecting the
environmental impacts of buildings: A critical review. Journal of Cleaner Production,
387, 135921. doi:10.1016/j.jclepro.2023.135921

879
880
881

29

882

883
884

Appendix A. Supplementary table and figures of experiments
This section shows the detailed settings in experiments.
Table A.1. Baseline settings for the original one-bedroom modular flat (Case 1).
Category
Simulation
setting

Window
parameters
setting

Window
louver
parameters
setting

Items

Values

Unit

Baseline model

Location
Climate zone
Construction set
HVAC system
Grid size (Gs1)
WWR1
WWR2
WWR3
WWR4
WH1&2
WH3
WH4
WSH1&2
WSH3; WSH4
LC1; LC2; LC3; LC4
LA1; LA2; LA3; LA4
LVH1; LVH2; LVH3; LVH4

Hong Kong SAR
2-Hot
ASHRAE 90.1 2019
Window AC with no heat
0.2
0.45
0.35
0.30
0.10
1.5
1.2
1
0.80
1.20
1
0
0

m
m
m
m
m
m
°
-

EUI = 159.599 kWh/m2·yr

885
886

Table A.2. Baseline settings for the urban block forms optimization (Case 2).
Category

Items

Values

Unit

Baseline model

Simulation
setting

Location
Grid size (Gs2)
Date and time
OPos
Pos1
Pos2
Pos3
Pos4
Pos5
Pos6
Pos7
Pos8
NFP1
NFS1
NFC1
NFP2
NFS2
NFC2
NFP3
NFP4; NFS3

Jianhu City, Jiangsu Province
1
Jan. 20th 8:00-16:00
5
C-2
P-4
P-2
S-3
P-2
P-4
P-2
S-2
2
1
3
6
4
6
30
13

m
-

DSH = 6.081 hours

Building
types
position

Window
louver
parameters
setting

887
888

30

889

Table A.3. Hyperparameters settings for single-objective algorithms.
Algorithm

Grasshopper
plugin

Hyperparameters

Description

Value
25
2
50
5%
75%

GA

Galapagos

Population size
Initial boost
Max. Stagnant
Elite rate
Inbreeding rate

CMA-ES

Opossum

Initial sigma

Number of individuals in each generation
Controlling the exploration range in the first generation
Managing convergence efficiency
Preserving best individuals across generations
Controlling genetic diversity by probability of parent solutions’
exchange
Controls the initial step size of the search range

Max. iterations

The maximum number of iterations

10000

Max. evaluations

The maximum number of evaluations

10000

Max. stalled
cycles
Local search box
scaling

The maximum number of consecutive iterations allowed
without significant improvement in the objective function value
Limit the scope of the local search

2000

RBFOpt

Opossum

890

31

0.5

False