# Multi-LOD generative approach for multi-objective sustainability optimization from the early stages of building design

Catherine Bouillon, Benjamin Cohen Boulakia, Karim Beddiar, Yves Jaboin, Fabrice Duval

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Catherine Bouillon, Benjamin Cohen Boulakia, Karim Beddiar, Yves Jaboin, Fabrice Duval. Multi-LOD generative approach for multi-objective sustainability optimization from the early stages of building design. Automation in Construction, 2025, 177, pp.106326. 10.1016/j.autcon.2025.106326. hal-05125651

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# Multi-LOD generative approach for multi-objective sustainability optimization from the early stages of building design

Catherine Bouillon<sup>a,b,c,*</sup>, Benjamin Cohen Boulakia<sup>d</sup>, Karim Beddiar<sup>c</sup>, Yves Jaboin<sup>e</sup>, Fabrice Duval<sup>f</sup>

## ARTICLE INFO

### Keywords:

Sustainability of buildings

Life-cycle

Generative design

Eco-efficiency tools

Early design stage

Design process

Solid voxels

## ABSTRACT

Given the urgency of reducing the buildings' environmental impact, this article focuses on optimizing sustainability from the earliest design phases, when decisions have the greatest influence. To address the challenges posed by the coarse granularity of digital models during the sketching phase and the often-conflicting nature of sustainability criteria, a generative workflow is proposed. This workflow, based on a multi-Level of Detail (LOD) framework, enables the evaluation and tracking of multiple sustainability criteria throughout the design iterations. This systemic methodology integrates automated functional spatial-planning, hierarchical segmentation of construction solutions, and systematic exploration of Pareto-optimal alternatives for bi-objective optimization. The framework is validated during the sketch phase using life-cycle cost and global warming potential, across eight real-world office-building case studies. Feedback from ten construction experts confirms the Proof-of-Concept's effectiveness in supporting both retrospective and prospective decision-making, underscoring its potential to advance sustainable design practices in the Architecture, Engineering, and Construction sector.

## 1. Introduction

Global warming is inherently a natural and vital phenomenon. It is driven by the action of greenhouse gases (GHGs), such as carbon dioxide ($CO_2$), methane ($CH_4$), and nitrous oxide ($N_2O$), which trap heat emitted by the Earth's surface, thus maintaining temperatures conducive to life. However, anthropogenic emissions exacerbate this phenomenon. Human activities amplify its effects to the point of triggering climatic upheavals with unpredictable, complex, and, above all, devastating

consequences [1]. The architecture, engineering, and construction (AEC) industry is recognized as one of the major contributors to these disruptions [2,3]. Given the magnitude of the climate crisis, it is crucial to prioritize sustainability objectives when considering construction projects [4].

Scientific literature from the last decade demonstrates that, in order to meet this ambition, adopted approaches must follow five essential recommendations. First, they must (a) incorporate a comprehensive life-cycle analysis [5], which requires the use of a methodology capable of

<footnote><sup>a</sup> ESSOR Group, 2 rue Pierre Gilles de Gennes, 64140 Lons, France</footnote>

<footnote><sup>b</sup> Arts et Métiers Paris, ENSAM, 151 Boulevard de l'Hôpital, 75013 Paris, France</footnote>

<footnote><sup>c</sup> CESI LINEACT, 1 Avenue Augustin-Louis Cauchy, 44307 Nantes, France</footnote>

<footnote><sup>d</sup> Université Paris-Saclay - Versailles Saint Quentin, DAVID, 78035 Versailles, France</footnote>

<footnote><sup>e</sup> CIR&Dé, 151, Route Nationale 134, 64870 Escout, France</footnote>

<footnote><sup>f</sup> CESI LINEACT, 80, Avenue Edmund Halley Rouen Madrillet Innovation, 76800 Saint-Etienne-du-Rouvray, France</footnote>

<footnote>Abbreviations: ACOAnt, Colony Optimization; AEC, Architecture, Engineering, and Construction; AHP, Analytic Hierarchy Process; BIM, Building Information Modeling; BSP, Baseline Study Period; CAD, Computer-Aided Design; CEDI, Constructive Element Data In; CSDI, Construction Strategy Data In; DAG, Directed Acyclic Graph; DES, Dynamic Energy Simulation; EIS, Environmental Impact Scores; EPL, Estimated Product Life; FDES, Fiche de déclaration environnementale et sanitaire (Environmental and Health Declaration Sheet); FMV, Functional Macro-Voxel; FMVP, Functional Macro-Voxel Primitives; GHG, Greenhouse Gas; gLCC, global Life-Cycle Cost; GWP, Global Warming Potential; HVAC, Heating, Ventilation, and Air Conditioning; INIES, Inventaire National des Impacts Environnementaux et Sanitaires (National Inventory of Environmental and Health Impacts); IPCC, Intergovernmental Panel on Climate Change; LC, Life-Cycle; LCA, Life-Cycle Assessment; LCC, Life-Cycle Cost; LCQ, Life-Cycle Quantity; LCSA, Life-Cycle Sustainability Assessment; LOD, Level of Detail; MDO, Multidisciplinary Design Optimization; ORDI, Owner Requirements Data In; PCA, Principal Component Analysis; POC, Proof of Concept; RF, Renewal Factor; SEDI, Sustainability Evaluation Data In; S-LCA, Social Life-Cycle Assessment.</footnote>

<footnote>* Corresponding author at: ESSOR Group, 2 rue Pierre Gilles de Gennes, 64140 Lons, France.</footnote>

<footnote>E-mail address: cath.bouillon@gmail.com (C. Bouillon).</footnote>
(b) performing dynamic simulations [6]. Second, they must (c) simultaneously consider several dimensions of sustainability [7] and, as such, (d) systematically rely on multi-criteria evaluations of the proposed construction solution [8]. Finally, (e) all these principles must be implemented from the early stages of the design process [9,10], with a particular emphasis on their early integration into architectural design phases [11].

On this last point, Paulson [9] emphasized the strategic importance of the early phases of the design process. In his work, he demonstrated that the earlier decisions are made, the greater their influence on the final quality of the built asset, while their impact on the overall project cost—whether related to engineering, construction, or long-term operation—is significantly reduced. Building upon this perspective, MacLeamy [12] highlighted the critical role of enhanced stakeholder collaboration during the initial engineering phases. This shift results in the design effort peak, traditionally occurring during the middle of the ‘Technical Design’ phase, being moved forward to the end of the ‘Concept Design’ phase, thereby reflecting an improvement in project efficiency (see Fig. 1i).

Holberg (2016) [5] expanded the holistic understanding of the design process by introducing the notion of data availability required for calculating sustainability indicators. The overlay of the various curves, aligned with their respective timelines (see Fig. 1ii), reveals that prior to the ‘Developed Design’ phase, while a qualitative Life Cycle Sustainability Assessment (LCSA) may be envisioned as early as the initial stages of the ‘Concept Design’ phase, a rigorous Life Cycle (Environmental) Assessment (LCA) cannot be reliably conducted—particularly in the context of regulatory compliance. This observation, described as the ‘late availability’ of data, corroborates more recent findings by the same author [13], who emphasized that “the LCA of buildings is commonly conducted at the end of the design process, when the necessary information is available, but it is too late to affect the decision-making process”.

In practice, this uncertainty is most often addressed through the use of simplified Life Cycle (Environmental) Assessment (LCA) methods. However, such approaches inherently rely on incomplete or uncertain assumptions, thereby limiting their relevance when confronted with the demands and realities of subsequent project phases. This misalignment introduces a significant risk of successive revisions, which can complicate the decision-making process and lead to structural inefficiencies throughout the project lifecycle.

The objective of the proposed approach can thus be illustrated within the previously discussed synthesis graph (see Fig. 1iii): it seeks to

explore the potential for shifting the design effort peak toward the ‘Preliminary Studies’ phase, thereby maximizing the positive influence of early-stage architectural decisions [9,12]. Initially, this approach aims to assess the feasibility of an autonomous generative design process based solely on variables expressing the owner’s requirements. This process, operating primarily in a pre-BIM environment, would be capable of generating a model whose components possess near-exact dimensions, achieving a Level of Detail (LOD) of 300 or higher. Such precision would enable the conduct of a LCA from the earliest stages of design [13]. If successful, the secondary objective is to evaluate to what extent such a system could support decision-makers throughout successive choices made during iterative design development. Within this proof of concept (POC), the five fundamental recommendations previously outlined give rise to two major, interdependent challenges: the simultaneous assessment of the various criteria defining the sustainability of a construction project [14].

The first challenge arises from the diversity of granularity levels associated with sustainability criteria [15]. Granularity refers to the size of the smallest component considered in the definition variables of a criterion, which corresponds to the finest qualitative and quantitative decomposition of the construction elements required for evaluating the criterion. For instance, within the Life-cycle scope, estimating life-cycle cost (LCC) can be performed with a coarse definition of structural elements, whereas assessing environmental impact (LCA) demands a detailed decomposition by material. As digital models are progressively refined throughout the iterative design process, the specific challenge of the ‘Preliminary Studies’ phase lies in its particularly low level of detail (LOD) [5]. In practice, construction elements are initially defined in a very rudimentary manner (LOD 100) and gradually gain precision throughout design iterations, eventually reaching a fully detailed characterization of the construction solution (LOD 500). The second challenge relates to the often-antagonistic nature of objectives targeted by the different sustainability criteria [8,16]. In contrast to the concept of orthogonality, which refers to objectives that are independent of each other and lack direct interaction, the concept of antagonism characterizes situations where improving one objective comes at the expense of another. This antagonism manifests both at the specific scale of a single Life-cycle phase and at a broader scale encompassing multiple phases. For instance, the trade-off between land use and building compactness is generally confined to the design phase, whereas managing the balance between embodied carbon and operational carbon impacts spans both the construction and operational phases. This second challenge arises from the principle that “it is generally impossible to address each requirement independently of the others; otherwise, many would result in contradictory solutions” [17]. In practice, global multi-objective optimization approaches consist of analyzing and comparing different feasible constructive solutions.

The widely-accepted definition of sustainability is the one proposed by the World Commission on Environment and Development [18]. It defines sustainable development as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs”. Within this framework, Life-cycle sustainability assessment (LCSA), applicable across all sectors, is based on three pillars: environmental (LCA), economic (LCC), and social aspects (S-LCA) [18].

This approach can be formalized by the equation: LCSA = LCA + LCC + S-LCA [19]. The guiding principles for each of these pillars are respectively outlined in the works of SETAC<fnref n="1" /> for LCA [16], Hunkeler et al. (2008) for LCC [20], and the UNEP/SETAC report (2009) for S-LCA [21]. In the specific field of AEC, the multiplicity of impactful criteria makes the concept of sustainability particularly complex, especially as

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Overlaid presentation of (i) Design effort curves by Paulson [9] and MacLeamy [12], including curves illustrating the impacts of changes to construction elements [5] (dark grey thin dashed lines); (ii) curves indicating the availability of data required for the assessment of sustainability criteria (blue thin solid lines); and (iii) the design effort curve representing the targeted objective (green thick dotted line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<footnote n="1">¹ Society of Environmental Toxicology and Chemistry. In 1993, this organization initiated a standardization process that resulted in the development of the LCA guidelines.</footnote>
its scope is constantly evolving. For example, beyond the identification and prioritization of environmental sustainability factors proposed by Amoozad Mahdiraji et al. [22], recent research highlights the growing importance of low technologies and the potential of vernacular architectural principles [23,24]. These continuous expansions of sustainability criteria amplify the challenges of establishing a standardized, comprehensive, and internationally applicable methodological framework.

This trend likely explains the increasing development of approaches that simplify LCC and LCA concepts, often focusing solely on a broader view of the economic and environmental aspects [25]. Within this framework, global life-cycle cost (gLCC) and life-cycle assessment (LCA) have emerged as reference methods widely recognized by the international community for evaluating the sustainability of a building [26,27]. Moreover, LCA benefits from an established international regulatory framework set by ISO/TC 59/SC 17 and has generated significant scientific interest, as evidenced by numerous recent publications [28,29].

Regarding the late availability of data [30,31] and the heterogeneity of evaluation criteria [15,22], studies have demonstrated that a workflow-structured approach offers significant opportunities to overcome this challenge [30,32]. The workflow framework proposed and validated by these authors is based on the integration of Building Information Modeling (BIM) and LCA, a topic extensively explored in several studies [33,34]. Early in their articles, [30,32] highlight several limitations inherent in the current body of knowledge [35,36].

These limitations primarily concern the mismatch between the data structure of digital models, particularly BIM, and the specific requirements of LCA evaluation methods. They can be divided into two categories, depending on whether their impact remains constant or decreases as the design iterations progress. The first category includes limitations whose impact is independent of the design phase. This is primarily characterized by the lack of an explicit, bidirectional, and proactive data structure between BIM and LCA. This gap hinders the continuous integration of external data, including reference databases, location-specific information, or sustainability-related parameters. It also restricts real-time visualization of results directly within the native design environment. The second category includes limitations whose impact gradually diminishes as the level of detail (LOD) of the digital model approaches the granularity required by LCA. This set of limitations highlights the absence of an integrated BIM-LCA methodology to ensure reliable data exchanges while addressing the late availability of detailed information. All these limitations, in fact, apply to all sustainability criteria [33,36].

Concerning the multi-objective optimization of sustainability criteria, Muthumanickam et al., 2023 [8] reveal that optimization methods in the AEC sector remain siloed into distinct domains, such as structure [37], energy [38], or daylighting [39]. These authors emphasize the need to develop integrated multi-objective approaches capable of overcoming this compartmentalization and deployable from the early design phases. Accordingly, they conclude their study with a call for enhanced collaboration between researchers in Multidisciplinary Design Optimization (MDO) and those in AEC.

Based on the information above, the aim of the research and development efforts described in this article is to demonstrate the applicability of continuous and simultaneous optimization of multiple sustainability objectives from the early design phases. To achieve this, the economic and environmental aspects are considered through the simultaneous implementation of a global life-cycle cost (gLCC) analysis and a comprehensive life-cycle assessment (LCA). This choice is justified by the extensive documentation available on these two criteria and their representation of extreme granularities: a coarse granularity of construction elements for gLCC and a fine-grained component-level analysis for LCA. This disparity tends to maximize the potential for generalizing the process to a broader range of sustainability criteria.

This approach is based on the workflow principle developed by [30,32]. However, rather than adapting the definition of sustainability

criteria to a progressively increasing level of detail in the digital model, its originality lies in the implementation of a generative macroprocess aimed at achieving a high level of detail (minimum LOD 300) from the sketch design phase. To this end, the proposed approach is not directly integrated into a BIM platform. Instead, it is designed as a gateway with a fully BIM-compatible data structure, notably through the use of the UniFormat unified classification system [40]. This choice also aims to enable a clearer and more flexible exploration of various optimization alternatives, both in terms of space planning and in supporting designers in selecting the most suitable construction solutions throughout design iterations.

The developed process is implemented and tested, with all tests focusing on the conceptual design phase. The first series of tests aims to evaluate the representativeness, accuracy, and robustness of the process. This series is conducted on eight real-world office building cases. The second series of tests is designed to assess the process in terms of bi-objective optimization and decision support. It focuses on one of the previously studied cases, exploring various building forms and construction solutions. Finally, the efficiency of the process is evaluated by a panel of ten experts from various fields of the construction industry. A critical discussion of all results, highlighting strengths, limitations, and future research opportunities, concludes this article.

## 2. Methods

This article proposes an iterative workflow designed to enable decision-makers to make informed architectural decisions regarding sustainability from the earliest design phases. Achieving this goal relies on a structured approach consisting of two complementary steps. The first involves automatically translating primarily subjective information from the program, such as owner requirements, into concrete implementation data; in other words, generating a digital model that is representative of the project and compliant with regulatory requirements. This objective, focused on initializing the design framework, presents a major challenge: producing, at the preliminary design stage, a parametric digital model with sufficient detail to define the elements of a construction solution. The minimum required level of detail is set at LOD 300, the threshold beyond which the definition of construction elements is generally recognized as sufficiently detailed to enable meaningful use of data from a digital model [13]. The second step aims to provide decision-makers with a framework to iteratively refine each element of the conceptual model of the proposed structure, allowing for adjustments to the construction methods based on pre-established sustainability objectives. This objective of optimizing the construction solution relies on two aspects: integrating a multi-scale modeling of construction methods and, on the one hand, simultaneously evaluating various sustainability criteria, both for the project under development and for all feasible alternatives; and, on the other hand, presenting decision-makers with the relative efficiency of the solution under development compared to the feasible alternatives. Achieving this last goal requires addressing a problem involving multiple, often conflicting objectives, where improving one comes at the expense of another. This type of conflict precisely characterizes the nature of multi-objective optimization problems. Unlike orthogonal objectives, which do not interact, conflicting objectives require, in the worst case, a thorough exploration of feasible solutions to identify those that best address the set of conflicting criteria. The particularity of this conflictuality lies in the general absence of a single solution that optimally satisfies all objectives. The aim, therefore, consists in identifying a subset of non-dominated solutions, within which no solution exhibits absolute superiority over the others across all considered criteria. In this regard, the implemented method must fulfill two fundamental requirements. First, it must enable an exhaustive exploration of available alternatives—a particularly essential condition in the context of innovative projects, where it is critical to surpass traditional decision-making frameworks. Second, it must preserve the possibility of conducting
rigorous comparative analyses between different strategies, such as the trade-off between a high initial investment versus a lower cost distributed over a period of fifty years. Consequently, these constraints naturally imply that the chosen method must facilitate extensive exploration of possibilities and optimal decision-making flexibility, thereby excluding the integration of restrictive heuristics based on preliminary selection.

These considerations justify employing the so-called “Pareto front” method [41], despite the higher convergence speed and enhanced scalability offered by evolutionary approaches such as NSGA-II or certain variants of Multi-Objective Evolutionary Algorithms (MOEA). In practice, this choice implies structuring the decision-support process into two clearly distinct stages: the first stage, addressed by the present study, aims to allow decision-makers to make informed and unconstrained choices, while the second stage, planned for future investigation, will guide the same decision-makers toward more targeted and optimized solutions. Adopting a Pareto-front approach inherently requires an initial mapping of all feasible trade-offs. The applied methodological framework precisely fulfills this requirement through systematic exploration and rigorous evaluation of each feasible alternative. Four macroprocesses are implemented, as outlined in the schematic presented in Fig. 2.

The first macroprocess, “Generative design”, initializes the workflow by generating a parametric sketch model of LOD greater than 300. The second and third macroprocesses, “Project customization” and “Alternatives exploration”, operate in parallel, evaluating the sustainability criteria vector through a shared procedure. While one focuses on the solution under development, the other explores the entire set of feasible alternatives. Finally, the fourth macroprocess, “Decision support”, compares, in real time, the performance of the solution under development against those of the alternatives, in order to challenge multiple sustainability objectives and to guide decision-makers toward optimal choices.

## 2.1. Generative design macroprocess

This first macroprocess (see Fig. 3) addresses the first challenge identified earlier. Its objective is to counteract the gradual progression of the level of detail in digital models, which remains particularly rudimentary (LOD 100) during the early design phases. In this context, the goal is to develop a module capable of automatically generating a parametric model with a high level of detail (exceeding LOD 300) from the sketching phase. Achieving this objective relies on two key steps:

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Overview of the proposed iterative workflow designed to enable decision-makers to make informed architectural decisions regarding sustainability from the earliest design phases.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Details of the proposed generative macroprocess that characterizes the conversion of the owner's requirements into a Parametric sketch model of LOD greater than 300.</figcaption></figure>

first, generating a digital model that meets the initial project requirements, and second, enhancing this model with a parametric structure.

The needs underpinning a project are primarily functional and are expressed as a functional map, comprising a finite set of volumetric units and their optimal distribution, in terms of both usage and regulatory constraints. However, traditional design methodologies, derived from computer-aided design (CAD), do not support the creation of such a functional map due to their top-down approach. Additionally, in this context (particularly with BIM), design flexibility is often limited by the native structure of software tools, which group construction elements into rigid system families. This rigidity frequently necessitates complex manual adjustments to address the specific needs of a project [42,43].

### 2.1.1. Owner's requirements modeling process

In contrast, the voxel (Volumetric Elements) paradigm offers an intriguing alternative [44]. This paradigm relies on a “sculpting” process that segments the built environment into elementary volumetric units, typically polyhedral in shape [45,46]. It operates at two distinct scales of meshing. The first, microscopic, involves cellular voxels [44] which are often used for solving partial differential equations, such as in the finite volume method [47]. The second scale is mesoscopic and concerns solid voxels, which are parametric, particularly in terms of geometric attributes and specific properties [48]. Although their application in the field of AEC is regularly explored by the scientific community [49,50], it remains largely limited to modeling monolithic construction elements, which are often composite, and typically used to simulate dynamic behaviors [51,52]. In this context, a Functional Macro-Voxel (FMV) principle has been developed using a procedural approach. The first phase of this approach involves predefining unit volumes based on the project's requirements. The corresponding FMV concept is characterized by primitives (FMVP) that correspond to the contents, the bottom face, the four lateral faces, and the upper face of the volumetric units considered. Each FMVP is formatted with a parametric data structure that aligns with BIM data standards. For simplicity and computational efficiency, the elementary units used are parallelepiped in shape. Fig. 4 illustrates a predefined example of an FMV corresponding to a sanitary installation zone.

In the office-building sector, as studied here, it has been observed that only eight classes of FMVs are required to translate the subjective information from a construction program into a concrete digital model. These classes correspond to open-space workstations, offices, meeting rooms, and relaxation areas, as well as restrooms and horizontal and vertical circulation spaces, such as staircases and elevators. The first four classes are defined based on the space requirements for activities expressed by the project owner. The latter four classes address the needs for access and comfort arising from these requirements, as dictated by legislative and regulatory texts related to the protection and well-being
<figure><img src="image_6.png" /></figure>

**Generic attributes:** height, length, and width of the volume unit.

**Additional attributes addressing primitives:**

① Contents \ Sanitary installations, lighting and HVAC,

② Underside \ Slab and floor finishes,

③ Front side \ Partition, wall finishes and interior joinery,

④ Right side \ Facade and exterior joinery,

⑤ Back side \ Zero materiality,

⑥ Left side \ Zero materiality,

⑦ Upper face \ False ceiling and cable trays.

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Extract from the juxtaposition relevance table which characterizes the mutual influence of MVFs according to their class.</figcaption></figure>

of individuals (e.g., the French Labor Code, in the case of office buildings in France). It is noteworthy that the required number of FMVs in each class is also determined, notably by the headcount, either directly (e.g., the number of workstations) or indirectly through standards (e.g., the number of restrooms). The same applies to the dimensions of these FMVs (e.g., the height of steps and the width of staircases). Since the regulations are fixed, the only input variables required to fully define the overall project model are the functional needs specified in the project's requirements document.

### 2.1.2. Space planning process

To automatically generate this model, the second phase of the procedural approach focuses on aggregating the FMVs and proactively adjusting their attributes. In this context, the implantation boundary, defined by the cadastral limits of the site, is first segmented according to the cardinal and intercardinal points and then converted into FMVs. Each previously stated rule is translated into a relevance parameter characterizing the recommended juxtaposition of each FMVP of one FMV class with those of other classes. The resulting coefficients reflect properties of mutual influence, expressed as attraction (positive values) or repulsion (negative values) between pairs of FMVs. Fig. 5 provides an excerpt from the juxtaposition relevance table, illustrating the interpretation of four key rules.

(1) Intra-class attraction: FMVs belonging to the same class exhibit strong mutual attraction, encouraging their aggregation. This complies with space planning principles that recommend functional centralization. (2) Functional proximity: Break rooms, which share a common

characteristic with restrooms (presence of a water source), tend to aggregate. This rule aligns with best practices for optimizing utility networks. (3) Central positioning of staircases: staircases are strongly repelled by the segments of the implantation boundary, positioning them equidistantly from these limits. This layout meets safety requirements by minimizing dead ends and does not conflict with any other rule. (4) Orientation of workstations: workstations are encouraged to group along the south-facing façade, following comfort and well-being guidelines. This ensures optimal natural lighting, good visibility, and contributes to reducing energy consumption.

In this context, an analogy was drawn between FMVs and magnetic particles, allowing the application of behavioral rules similar to those of the generalized Coulomb's Law to determine the balance of magnetic forces, both exerted and experienced, on each FMV.

To minimize the number of computational operations required, given that the height of functional units is nearly constant and cadastral constraints are consistently planar and defined by height slices, the initial 3D problem is decomposed into a series of 2D problems, each addressing a specific floor. This reduces the adjacency of FMVs from 12 edges to 4.

The complexity of the problem lies in calculating the global equilibrium position of all magnetized particles, each with a distinct magnetization, within a fixed boundary that includes specific magnetic poles. In such a system, each particle reaches equilibrium based on its polarity and the nature of the surrounding magnetic field. The exact solution of such a physical system would, for N FMVs, require solving N equations, each characterized by N partial derivatives. In practice, solving this system using its descriptive equations, such as Sobol equations [53,54], is particularly challenging due to the computational load it entails. Moreover, approximate methods based on physical models, such as molecular dynamics simulations or progressive force relaxation techniques, are inherently prone to attraction wells. In the specific context of balancing a potential energy field involving a set of interacting magnetic particles within an irregular environment, this vulnerability is exacerbated by the associated scientific uncertainty, which significantly increases the likelihood of multiple local minima. Given these limitations, a metaheuristic approach is adopted and the problem is formalized as an economic function. The constants of this function are the magnetic moments of each particle ($p_i$) and ($p_j$), as well as each segment of the implantation perimeter ($p_k$). The variables correspond to the distances between each pair of particles ($r_{i,j}$) and between each particle and the perimeter segments ($r_{i,k}$).

$$ \min U = \sum_{i=1}^{N} \sum_{j=i+1}^{N} \frac{P_i P_j}{r_{i,j}} + \sum_{i=1}^{N} \sum_{k=1}^{M} \frac{P_i P_k}{r_{i,k}} \quad (1) $$

Since the system is bounded by a closed implantation perimeter, a simulated annealing method was chosen. This stochastic optimization method is inspired by the thermodynamic process of annealing used in metallurgy, where a material is heated to a high temperature and then slowly cooled to reach a low-energy state. It involves minimizing an objective function, often likened to energy, by exploring the solution space. This algorithm allows escaping local minima by occasionally accepting lower-quality solutions (e.g., higher energy) with a probability that gradually decreases over the course of iterations [55]. This mechanism relies on a probabilistic acceptance criterion applied to each new configuration. If the energy decreases or remains constant, the criterion is set to 1. Otherwise, it is determined using a simplified version of the Boltzmann formula ($k_B = 1$):

$$ P_{\text{accept}}(\Delta U) = \begin{cases} 1 & \text{if } \Delta U \le 0 \\ \exp\left(-\frac{\Delta U}{T}\right) & \text{else} \end{cases} \quad (2) $$
where $\{ \Delta U :$ is the energy gradient between the current iteration and the previous one, $T :$ the current system temperature.

The occasional acceptance of configurations with higher energy is conditioned by comparing this criterion with a randomly generated threshold (cf. Fig. 6).

This mechanism plays a crucial role in significantly reducing the risk of becoming trapped in an energy well (basin), an area corresponding to a local minimum surrounded by higher energy barriers. These instances correspond specifically to collisions between FMVs, represented in Fig. 6 by red ellipses. By enabling the exploration of other regions within the search space, it increases the chances of reaching the global minimum. Furthermore, the formulation of this criterion gradually decreases the probability of accepting higher-energy solutions as the process progresses (at lower temperatures), promoting more precise local exploitation and refining the search around the potential global minimum.

The formal version of the implemented algorithm, presented in Fig. 7, details the nesting of the stopping conditions.

mapping of the spaces (see Fig. 8 - center), resizes circulation areas in compliance with safety and evacuation regulations (including the potential addition of an FMV for an emergency staircase), and adjusts the definitions of other FMV families accordingly. This phase disrupts the distribution of FMVs, requiring their reaggregation. The reaggregation is ensured by the second phase by applying the previously described space planning optimization process.

The third phase aims to align the FMVP, particularly at the façade level (see Fig. 8 - right). This process relies (is based) on an algorithm structured according to an underlying grid. It is based on a criterion for minimizing normalized compactness, defined as follows:

$$C = 1/36\pi S^3/V^2 \quad (3)$$

where S and V are respectively the surface of the envelope and the volume of the building.

The maximum amplitude of this displacement is set to one-tenth of an Exit Width Unit ($\delta = 0.09$ m equivalent). To optimize the trajectory of the metaheuristic, its three initialization parameters are adjusted as follows:

* A high initial temperature ($T_0$) allows the exploration of a wide range of configurations, including those associated with high energy, to avoid being trapped in local minima during the early iterations. $T_0$ is determined based on the maximum variations in the potential energy of a particle, measured during 100 preliminary tests. These tests involved randomly placing a volumetric unit with 2-m sides within a 15-m-square perimeter. The chosen value of $T_0$, 0.39, corresponds to a 50 % acceptance rate for proposed configurations during these preliminary trials. This adjustment resulted in a temporary energy increase of less than 11 % in approximately 7 % of cases.

* A final temperature (Tx) close to zero ensures that the system converges to a local minimum by ceasing to accept higher-energy (and lower-quality) configurations after convergence. Tx is defined based on the desired precision. In the literature, commonly cited values for stable convergence range between $10^{-6}$ and $10^{-4}$. For this application, with a relative positioning precision of 9 cm (10 % of a passage unit), the adopted final temperature is $10^{-4}$.

* The Cooling Factor ($\alpha$) controls the rate of temperature decrease per iteration. A rapid cooling rate (low $\alpha$) limits the exploration of the solution space, while a slow cooling rate (high $\alpha$, close to 1) can excessively slow down the algorithm. Typically, $\alpha$ is chosen in the range [0.80, 0.99]. In this case, the selected value is 0.87. However, a dynamic adjustment procedure is activated during the algorithm's execution to accelerate cooling when energy variations become negligible very quickly.

Finally, this constrained optimization process is terminated when one of the following two criteria is met: either the final temperature is reached, or no significant energy improvement (less than 0.1 %) has been observed over the last seven iterations.

The mechanism for aggregating the project's digital model is carried out in three phases. The first phase generates a maximum occupancy

It should therefore be emphasized that, within the scope of the current proof of concept (POC), envelope compactness constitutes the only optimization criterion applied to spatial planning. Although this criterion indeed represents a significant lever in terms of energy efficiency, a broader exploration might nevertheless be preferable, particularly in the early design phases, to integrate additional sustainability dimensions such as access to external views or natural lighting. This consideration underscores the future necessity to enrich the proposed mechanism by incorporating supplementary constraints. Such an approach would offer the opportunity to transcend solutions strictly oriented toward compactness, thereby placing greater emphasis on complementary criteria. In this regard, it is worth noting that while the inclusion of additional constraints or variables may slow the convergence rate of the metaheuristic, it does not compromise the overall validity of the mechanism—apart from potential effects on the tool's responsiveness in an interactive context.

At the end of this process, an angular constraint relaxation algorithm resolves the misalignment of oblique façades caused by the orthogonality of the parallelepipedic definition of the functional units employed. This relaxation consequently shifts the vertex of each peripheral FMV not aligned with the plane of the considered façade.

### 2.1.3. Multi-LOD modeling process

After completing the first two processes described earlier, the topological aspect of the project's digital model is fully defined, enabling the generation of a manufacturing schedule accompanied by meaningful quantity take-offs. However, its construction elements remain juxtaposed without any connection. This process, therefore, pursues a dual objective: to aggregate the dispersion of building elements and to unify their parametrization. This second objective must be addressed with consideration for the forthcoming goal of evaluating various sustainability criteria, each characterized by a specific level of granularity. The dispersion of building elements arises from the very principle of solid voxels, which discretize built spaces. To overcome this hazard, the FMV concept, while inspired by this principle, is distinguished by a key feature: it is not monolithic. Thus, its native segmentation into FMVPs provides an opportunity to aggregate these primitives into families (see
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Examples of images illustrating the initial position and fives intermediate equilibrium positions associated with local minima: situation that occasionally triggers the metaheuristic acceptance of configurations characterized by a higher energy level.</figcaption></figure>

Adjusting settings: $T_0$, $T_x$ et $\alpha$

Initializing variables:

$S_{current} = S_{best} = \text{Rand}(S_i)$

$U_{current} = U_{best} = U(S_{best})$

$N_{iter} = 100; T = T_0$

Algorithmic core

While $T > T_x$:

For $i=1$ To $N_{iter}$:

$S_{new} = S_{current} + \text{Rand}(S_{current})$

$U_{new} = U(S_{new})$

$\Delta U = U_{new} - U_{current}$

If $\Delta U \le 0$ then

$S_{current} = S_{new}$

$U_{current} = U(S_{new})$

Else

If $\text{Rand}[0,1] \le P_{accept}(\Delta U)$

$S_{current} = S_{new}$

$U_{current} = U(S_{new})$

If $U_{current} < U_{best}$ Then

$S_{best} = S_{current}$

$U_{best} = U_{current}$

$T = T_x$

Random particle positioning;

Calculation of total potential energy (see Eq. 1);

Setting initial variables;

Main loop:

Loop by temperature step;

Slight random disturbance of particle distribution*;

Calculation of new total potential energy (see Eq. 1);

Calculation of total potential energy variation;

If the new distribution improves or maintains energy,

... Systematic validation of this new distribution;

Otherwise,

... Probabilistic validation of this one (see Eq. 2);

Best Distribution Update.

System cooling.

<caption>**Fig. 7.** Formal version of the implemented simulated annealing algorithm.</caption>

*The slight random perturbations to the particle distribution involve selecting a particle at random and applying a bounded random displacement to it ($\Delta x$, $\Delta y \in [-\delta; +\delta]$).

**Fig. 9).**

This ability to group the scattered parameters of FMVs into building elements merges the two initial objectives of this process into a single goal: to associate all FMVPs with a hierarchical decomposition of constructive solutions. The simplest representation of such a decomposition is a tree, where the root represents the constructive solution, and the structure is such that, on the one hand, each evaluation parameter for a given macro component corresponds to a node, and, on the other hand, the links between nodes (or vertices) reflect the genealogy of the material and immaterial elements defining the constructive solution. To

<figure><img src="image_9.png" /><figcaption>**Fig. 9.** Principle of aggregating PMVF into building elements.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Digital model aggregation mechanism (test Case #0).</figcaption></figure>
enable the application of an Analytic Hierarchy Process (AHP) method for exploring and subdividing parent-child dependency relationships, an acyclic structure is adopted; more precisely a directed acyclic graph (DAG). To ensure compatibility with BIM, level 1 and 2 DAG height<fnref n="2" /> nodes are initialized using the categories and subcategories, respectively, of the unified UniFormat system. Additionally, to guarantee the applicability of this model for evaluating sustainability criteria with varying granularities, the leaves of the DAG are defined based on the granularity of the most detailed criteria, specifically components from the French regulatory environmental database INIES. The definition of the intermediate hierarchy was achieved through an AHP following the sequence below:

1. **Creation of initial nodes** based on input data from design tools, such as structural calculations, and simulation tools, notably Dynamic Energy Simulation (DES).

2. **Dependency identification** by consulting various experts.

3. **Formalization of the relationships** in a formal manner whenever possible.

4. **Pairwise comparisons** for node pairs whose relationships could not be defined previously, assigning a ranking on an importance scale from 0 to 9.

5. **Priority vector calculation** based on the previously established scores for each potential link, allowing the identification of the most relevant arcs between undefined nodes.

6. **Validation and refinements** performed by experts, followed by the definition of an approximate calculation for nodes connected by relevant arcs.

7. **Cleaning of unnecessary nodes**, which have no ascendancy.

8. **Deleting cycles** by adding new sheets.

9. **Optimization** of the number of nodes (sub-expressions defining intermediate values) and the data flow (precedence constraints induced by the sub-expressions).

The first dimensionality reduction method implemented is Principal Component Analysis (PCA). This statistical method transforms the variables in a dataset into new, uncorrelated variables, called principal components, which capture most of the variance in the original data. This effectively reduces the number of dimensions while preserving the most significant variances. Less significant variables are replaced by a constant (e.g., the height of levels). The thresholds applied for this method correspond to an absolute Pearson correlation coefficient of 0.9990, a commonly used threshold to define strong interdependence between two pieces of information. After interpreting each principal component as a linear combination of the original variables to update the DAG accordingly, a second method is applied: feature selection using a filter approach with cumulative importance. In this method, variables are ranked according to an importance measure (mutual information and information gain from Step 4, and chi-square statistic). Variables are then progressively selected in this order until the cumulative importance of the chosen variables reaches a predefined global importance ratio. The cumulative contribution threshold is set at 97.0 %, corresponding to an effective error of 3 %, four times lower than the best estimates made online during the design phases [56]. These two phases of structural optimization, performed using the modeFRONTIER® software (developed by ESTECO S.p.A.), reduced the number of leaves by nearly 37 % and the number of internal nodes by approximately 18 %.

The resulting DAG constitutes a multi-scale modeling of construction solutions. It highlights that only five pieces of information, directly related to the project owner's requirements, are sufficient to determine a construction solution. These data are referred to as "Owner's Requirements Data In" (ORDI). The other leaves of the DAG are divided into three specific other data classes: "Construction Strategy Data In"

<figure><img src="image_11.png" /><figcaption>Fig. 10. Synthetic DAG of MVF parameterization from the "Owner Requirements Data In" (ORDI).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 11. Excerpt from the dropdown menu enabling the adjustment of construction modes (CSDI).</figcaption></figure>

(CSDI), which describes the construction methods, "Constructive Element Data In" (CEDI), which characterizes the construction elements, and "Sustainability Evaluation Data In" (SEDI), which handles the information required for evaluating sustainability criteria. The first class, ORDI, is linked to a tabular user interface, enabling decision-makers to initialize basic parameters: the Open-Space Ratio, the Occupancy, the Location, the Usage, and the Number of Underground Parking (see Fig. 10). The second class, CSDI, is associated with a user interface comprising a set of dropdown menus designed for selecting available options (see Fig. 12). The third class, CEDI, is directly connected to the FMVP family parameters, thereby enabling automatic adjustment of all internal model variables (see Fig. 11). Finally, the last class, SEDI, is connected to reference databases, integrating both environmental information (INIES database) and cost data from the specifically developed database.

The CSID user interface integrated into the proposed system is designed to include only the information strictly necessary for selecting the envisaged construction modes. Thus, variable parameters corresponding to specific alternatives, such as the choice of insulation type or waterproofing material, are not provided, as these elements will be systematically considered later during simulations aimed at identifying the feasible solution space.

This DAG integrates the sizing of both structural elements and

<footnote n="2">² Height: distance between a node and its root.</footnote>
<figure><img src="image_13.png" /><figcaption>**Fig. 12.** Synthetic DAG for defining the “Construction Strategy Data In” (CSDI) from the UniFormat unified classification system.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 13.** UML class diagram describing the architecture of an excerpt of the BSM model implemented within the DAG.</figcaption></figure>

technical equipment. The structural design relies on look-up tables based on industry-specific abacuses, enabling the consideration of both superstructures and infrastructures across various construction methods, particularly in terms of materials (concrete, steel, wood).

<figure><img src="image_15.png" /><figcaption>**Fig. 14.** Simplified representation of the data structure implemented for passive mode simulation (left) and overview of the integrated workflow for dynamic simulation (right).</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 15.** Details of the iterative macroprocess proposed to adjust each element of the constructive solution and evaluate each of the latter’s sustainability criteria over the entire Life-cycle of the work.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Fig. 16.** Linearization of regulatory coefficients (RE2020) for temporal weighting applied to dynamic LCA.</figcaption></figure>

The sizing of HVAC components (boiler and heat pump, pump, solar panels) is based on a central energy simulation model: the Building Simulation Model (BSM). This choice is justified by two main reasons: first, it is a well-established and widely recognized model, ensuring the reliability of simulations [57]; second, it follows an adaptive approach that, despite being based on the MVD IFC framework, remains neutral in the sense defined by the Model-Driven Architecture (MDA) for Platform-Independent Models (PIM) [58]. This author provides, in Appendix 2 of his doctoral dissertation [59], a detailed description of the data type and format structuring this model. Furthermore, [60] enhances this methodology, which was initially focused on energy considerations, by
<figure><img src="image_18.png" /><figcaption>**Fig. 17.** Details of the iterative macroprocess proposed to explore each feasible constructive solution and evaluate their sustainability criteria over the entire Life-cycle of the work.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 18.** Details of the proposed decision support macroprocess.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 19.** Evolution of the mean of the eight Procrustes distance measurements performed, according to the superimposition phase.</figcaption></figure>

incorporating aspects derived from emerging environmental concerns. An excerpt of this model, focusing on elements required for the modeling of a boiler and its associated components, is presented in Fig. 13.

The development of the FMV concept and the deployment of the associated DAG model have overcome the limitations of IFC mapping, thereby paving the way for an extension of the functional scope of the BSM. Initially restricted to passive mode simulations [59], the model has been enhanced to incorporate the consideration of usage scenarios and the operational behavior of building systems. This advancement has broadened the range of simulation algorithms integrated into the DAG's

nodes, notably enabling the introduction of time-dependent parameters. These parameters encompass both reference data, such as climate data adapted to the project's location, and calculation variables, particularly those related to occupancy schedules (heating, cooling, lighting, and ventilation hours) (see Fig. 14). The resulting energy consumption estimates are subsequently converted into operational carbon emissions through association with emission factors from the INIES database, depending on the type of energy considered.

In the interest of regulatory compliance, CO₂ emissions associated with the national electricity mix, along with its anticipated evolution through 2050 and beyond, are considered to be intrinsically embedded within the environmental data provided by the Environmental and Health Declaration Sheets (FDES), referenced in the INIES database and established by the French Ministry for the Ecological Transition and the Ministry for Housing. Accordingly, the allocation of these standardized data, specifically tailored to the context of office buildings and the RE2020 French Regulation, is carried out selectively based on a per kilowatt-hour (kWh) unit of electricity and according to the relevant end uses: domestic hot water production (DHW), lighting, heating, air conditioning, and other specific applications. However, this new approach has introduced a divergence from current BIM standards. To restore compatibility, further research and development efforts will be required to adapt the model and ensure its interoperability with existing IFC formats [58].

## 2.2. Project customization and decision support framework

The previous macroprocess generates a parametric conceptual model with a LOD exceeding 300, where the defining criteria are initialized according to a predefined construction solution, particularly derived from the previously studied project. The second macroprocess, dedicated to project customization (see Fig. 15), therefore aims to support decision-makers in the progressive deployment of their sustainability strategy throughout the design iterations.

Its objective is, first, to provide decision-makers with the ability to freely adjust the predefined construction methods, and second, to evaluate the sustainability of the resulting construction solution. Given this framework, the user interface for CSDI is organized into dropdown menus (see Fig. 11), a preferred approach to minimize the risk of taxonomic or syntactic errors when selecting a construction method. The nesting of submenus is directly determined by the structure of the DAG. Each modification triggers an automatic update procedure for the entire system. This procedure consists of two steps. Firstly, all paths containing the node affected by the modification are traversed. Each node thus explored is systematically recalculated, including recalculations for sizing and dynamic simulations. These last two update procedures are performed using simplified calculation codes, based either on FMVP families aggregated in plan or on adjacent FMVs grouped by class, and validated by domain experts.

The structural calculations are systematically applied from the roof to the foundations, floor by floor. Initially, slab loads and loads applied to load-bearing walls are calculated. A preliminary structural sizing is then performed based on the resulting bending moments and deflections. This process is repeated after iteratively subdividing all spans exceeding 7 m and introducing the beam-column systems corresponding to these subdivisions. Finally, each generated beam and column is incorporated into the FMVP of the upper face class and the content or lateral face classes, respectively, based on its placement.

The Dynamic Energy Simulation (DES) code relies on the topological data of the digital model as well as the technical data of the construction elements. Its objective is to determine the heating, cooling, and lighting demands for each day of the year and then to establish an overall energy balance. To achieve this, the code calculates heat losses through transmission and ventilation, as well as solar and internal heat gains. The reference data required for these calculations are extracted from climate databases, notably that of the French meteorological agency, Météo
<figure><img src="image_21.png" /><figcaption>Fig. 20. Digital model and the real building (Case #0).</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 21. Scatter plot showing the estimation error of GHG emissions by lot.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig. 22. Scatter plot showing the estimation error of total costs by lot.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Fig. 23. Point cloud of the solution space and its approximated Pareto Front.</figcaption></figure>

France, and regulatory guidelines, such as functional lighting levels. The technical installations thus defined introduce a notion of lifespan which must be taken into account, particularly in terms of identical replacement. In this context, the Baseline Study Period (BSP) is set at 50 years, in accordance with the conventional building lifespan defined by the current French environmental regulations (RE2020). The Estimated Product Life (EPL) of a product or equipment is determined based on its Environmental and Health Declaration Sheet (FDES). The renewal factor (RF) of each product p encompasses all the sustainability criteria applied

<figure><img src="image_25.png" /><figcaption>Fig. 24. Evolution of the impact of a construction solution based on the footprint shape.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>Fig. 25. Comparison of responses to the “current system” and the “proposed method” according to Van Eldik’s criteria [30].</figcaption></figure>

to the entire Life-cycle (LC); it is therefore systematically applied to quantities.

$$LCQ_p = Q_p \cdot RF_p \text{ with } RF_p = \text{Max} \left( 1, \frac{BSP}{EPL_p} \right) \quad (4)$$

where
$$ \begin{cases} LCQ: \text{ is the Quantity implemented throughout the Life-cycle} \\ Q: \text{ Quantity implemented in the mockup} \\ BSP: \text{ the Baseline Study Period, and} \\ EPL: \text{ the Estimated Product Life of the product p.} \end{cases} $$

The environmental data for each component are formalized into a two-dimensional matrix, aligned with the hierarchy of the INIES database, particularly the Environmental and Health Declaration Sheets (FDES).

The first dimension (lines) addresses three phases of the Life-cycle over five modules, defined according to standard EN 15978:

* Immediate emissions (Year 0):

* Product (A1-A3): Raw material extraction and material production,

* Construction (A4-A5): Transport and implementation;
* Emissions spread over the building's lifetime (50 years for RE2020):
  * Use (B1-B7): Maintenance, operation, and energy consumption;

* Deferred emissions at end-of-life (Years 50–60):
  * End-of-life (C1-C4): Demolition, transport, and waste treatment,
  * Recycling (D): Credit for reusable materials.

The second dimension (columns) addresses twelve environmental indicators, defined in accordance with standards NF EN 15804 + A2 and NF EN 15804/CN, which can be categorized according to the major themes they address as follows:

* Indicators related to GHG emissions and their sources:
  * Total climate change (kg CO₂ eq.);

* Climate change from fossil resources (kg CO₂ eq.);

* Climate change from biogenic resources (kg CO₂ eq.);

* Climate change from land use (kg CO₂ eq.);

* Indicators related to substances affecting the stratospheric ozone layer:
  * Ozone layer depletion (kg CFC-11 eq.);

* Indicators of impacts on aquatic and terrestrial environments:
  * Acidification (mole eq. H⁺);

* Freshwater eutrophication (kg P eq.);

* Marine eutrophication (kg N eq.);

* Terrestrial eutrophication (mole eq. N);

* Indicators of pollutants contributing to tropospheric smog:
  * Photochemical ozone formation (kg NMVOC);

* Indicators of the depletion of materials and fuels:
  * Depletion of abiotic resources – minerals and metals (kg Sb eq.);

* Depletion of abiotic resources – fossil fuels (MJ);

For each product p, the INIES database thus provides a total of sixty indicators I, distributed across five modules m and twelve environmental indicators i.

The first twenty environmental impact scores (EIS) (rows 1 to 5 and columns 1 to 4), related to the impact of GHG emissions on global warming, are evaluated using a dynamic method in accordance with ISO 14067. The subsequent forty scores (rows 1 to 5 and columns 5 to 12) are calculated for each component using a static method, which involves multiplying the corresponding indicator I by the quantity implemented throughout the Life-cycle (LCQ).

The specificity of dynamic methods [61,62] lies in the introduction of temporal weighting. These methods are based on the Dynamic Global Warming Potential (GWP) method developed in alignment with IPCC (Intergovernmental Panel on Climate Change) conventions. In France, legislation—specifically, Article R. 172–6 of the Construction and Housing Code—recommends a simplified dynamic method, with coefficients defined by the Decree of August 4, 2021. This method, inspired by the degradation kinetics of greenhouse gases in the atmosphere, adjusts coefficients so that emissions or capture occurring earlier have a higher impact, and vice versa.

The goal of this adjustment is twofold: to prioritize actions targeting current GHG emissions and to incentivize uncertainty mitigation in end-of-life material scenarios, promoting recycled and reused materials. This approach is simplified since the weighting factors are not applied directly to individual greenhouse gas emissions but to the overall global warming potential indicated in environmental declarations (in kg CO₂ eq.).

Thus, weighting factors, which should theoretically vary based on specific gas degradation rates, are applied uniformly to CO₂, regardless of the emitted gas. Similarly, weighting coefficients for R410A are applied uniformly to all refrigerant emissions not otherwise specified. Additionally, the Life-cycle timeline is simplified: all emissions related to the initial availability of components are assumed to occur at t = 0, while those associated with end-of-life waste management are assumed to occur at t = BSP = 50 years.

To optimize computational efficiency, the simplified model used in

the proposed POC adopts a linear approach defined by W(t) = 1-kt, where k represents the slope of the adjustment line for the RE2020 regulatory coefficients, passing through the point (0;1). The parameter k is set at 0.00826 for general emissions, with a coefficient of determination R² = 0.9990, and at 0.00188 for refrigerant emissions, with R² = 0.9079 (see Fig. 16).

The formulas derived from this simplified linear approach, presented below, are based on a one-year time step, and incorporate the fact that all quantities (LCQ) have been previously multiplied by the renewal factor (RF). Emissions from production and construction, conventionally considered to occur at t = 0, apply only to the original instances. They are thus defined by the equation:

$$ 
\begin{aligned}
\text{EIS}_{\text{p,i}}^{\text{Production}} &= Q_{\text{p}} \cdot \text{I}_{\text{p,i}}^{\text{Production}} \cdot W(0) = \text{LCQ}_{\text{p}} \cdot \frac{\text{I}_{\text{p,i}}^{\text{Production}}}{\text{RF}_{\text{p}}} \\
&= \text{LCQ}_{\text{p}} \cdot \text{J}_{\text{p,i}}^{\text{Production}}
\end{aligned}
\quad (5) $$

$$ 
\begin{aligned}
\text{EIS}_{\text{p,i}}^{\text{Construction}} &= Q_{\text{p}} \cdot \text{I}_{\text{p,i}}^{\text{Construction}} \cdot W(0) = \text{LCQ}_{\text{p}} \cdot \frac{\text{I}_{\text{p,i}}^{\text{Construction}}}{\text{RF}_{\text{p}}} \\
&= \text{LCQ}_{\text{p}} \cdot \text{J}_{\text{p,i}}^{\text{Construction}}
\end{aligned}
\quad (6) $$

The exploitation phase (X) accounts for two types of emissions. The first are the annual emissions related to the regular use of all products, which are considered to be emitted consistently each year and are denoted as I<sup>X</sup><sub>Use</sub>. The second are emissions associated with product replacement, which are considered to be emitted at the effective date of replacement and are denoted as I<sup>X</sup><sub>renewal</sub>. These include emissions generated during the end-of-life phases of replaced products as well as those associated with the production and construction of replacement products. The operational emissions are thus defined by the following formulas:

$$ 
\begin{aligned}
\text{EIS}_{\text{p,i}}^{\text{Use}} &= Q_{\text{p}} \cdot (\text{I}_{\text{p,i}}^{\text{Use}} + \text{I}_{\text{p,i}}^{\text{renewal}}) = \text{LCQ}_{\text{p}} \cdot \frac{\text{I}_{\text{p,i}}^{\text{Use}} + \text{I}_{\text{p,i}}^{\text{renewal}}}{\text{RF}_{\text{p}}} \\
&= \text{LCQ}_{\text{p}} \cdot \text{J}_{\text{p,i}}^{\text{Use}}
\end{aligned}
\quad (7) $$

with:

$$ \text{I}_{\text{p,i}}^{\text{X-Use}} = \frac{\text{I}_{\text{p,i}}^{\text{Use}}}{\text{EPL}_{\text{p}}} \cdot \sum_{j=1}^{\text{BSP}} W(j) $$

$$ \text{I}_{\text{p,i}}^{\text{X.renewal}} = \left( \text{I}_{\text{p,i}}^{\text{Production}} + \text{I}_{\text{p,i}}^{\text{Construction}} + \text{I}_{\text{p,i}}^{\text{End of life}} \right) \cdot \left( \sum_{j=1}^{\alpha-1} W(j \cdot \text{EPL}_{\text{p}}) + \beta \cdot W(\alpha \cdot \text{EPL}_{\text{p}}) \right) $$
where
$$ \begin{cases} \alpha: \text{is the integer part of } \text{BSP}/\text{EPL}_{\text{p}} \text{ and} \\ \beta: \text{the fractional part of this quotient.} \end{cases} $$

End-of-life emissions, conventionally considered to occur at the end of the building's life (t = BSP = 50 years), apply only to the final instances of the product. They are thus defined by the equation:

$$ 
\begin{aligned}
\text{EIS}_{\text{p,i}}^{\text{End of life}} &= Q_{\text{p}} \cdot \text{I}_{\text{p,i}}^{\text{End of life}} \cdot W(\text{BSP}) = \text{LCQ}_{\text{p}} \cdot \frac{(1 - 50 \cdot k) \cdot \text{I}_{\text{p,i}}^{\text{End of life}}}{\text{RF}_{\text{p}}} \\
&= \text{LCQ}_{\text{p}} \cdot \text{J}_{\text{p,i}}^{\text{End of life}}
\end{aligned}
\quad (8) $$

For module D, which relates to recycling (including reuse and recovery) and represents the environmental benefits and burdens that may be generated beyond the boundaries of the considered system, a calculation similar to that of the operational phase is performed, in accordance with Annex D.3.4 of the NF EN 15804 + A2 standard:
The formulations, particularly the variable changes in terms of environmental indicators expressed previously (Eqs. (4) and (5) through (9)), lead to a common expression for all environmental-impact scores that takes product renewals into account.

$$EIS_{p,i} = \sum_{m} EIS_{p,i}^{m} = LCQ_{p} \cdot \sum_{m} K_{p,i}^{m} \qquad (10)$$

where m ranges from A1 to A3 for production, A4 to A5 for construction, B1 to B7 for operation, C1 to C4 for end-of-life, and equals D for benefits and burdens beyond the system boundaries. It is important to note that if, unlike the present case, a specific evaluation of a criterion referring to indicators related to water demand (m³ eq. global scarcity) is included, modules B5 to B7 must be excluded to avoid double counting. This is particularly relevant for the water contribution, such as in non-collective wastewater sanitation, in the calculation of the components' contribution. This expression can be generalized to all sustainability criteria dependent on components. The second step of the automatic

Consequently, these iterative operations are treated as instantaneous processes; therefore, the evaluation of options can be considered as occurring in real time.

In the experiments presented below, the analysis focuses on two criteria: total GHG emissions and total cost. All obtained evaluations can therefore be visualized as a point cloud within an orthonormal coordinate system, where each axis represents one of the aforementioned criteria. However, due to the antagonistic nature of these two criteria, this representation alone is insufficient to effectively guide decision-makers, particularly if they are not experts in the field. To address this, a procedure is implemented to identify optimal solutions, defined as those that cannot be improved in one criterion without worsening the other. This procedure provides decision-makers with two key pieces of information. The first piece of information is graphical and highlights the approximated Pareto front, which characterizes the optimal trade-offs between the criteria.

The determination of this front is based on applying a morphological filter to the point cloud after normalizing the scores (S) to bring both criteria to a common scale. The normalization is performed using the following formula:

$$ 
\begin{aligned}
EIS_{p,i}^{\text{Benefits\&loads}} &= Q_{p,i} \cdot I_{p,i}^{\text{Benefits\&loads}} \cdot \left( \sum_{j=1}^{\alpha-1} W(j.EPL_p) + \beta \cdot W(\alpha.EPL_p) + W(BSP) \right) \\
&= LCQ_p \cdot \frac{I_{p,i}^{\text{Benefits\&loads}}}{RF_p} \cdot \left( \sum_{j=1}^{\alpha-1} W(j.EPL_p) + \beta \cdot W(\alpha.EPL_p) + W(BSP) \right) \\
&= LCQ_p \cdot J_{p,i}^{\text{Benefits\&loads}}
\end{aligned}
\qquad (9) $$

update procedure involves activating the space planning mechanism to adjust the spatial layout accordingly. This update procedure, which concludes macroprocess 2, enables real-time evaluation of the sustainability criteria matrix at the root of the DAG. The third macroprocess, focused on exploring alternatives, resembles the previous one (see Fig. 17) with two key specificities.

First, it does not require human intervention, as this is replaced by an automated mechanism that iteratively explores all possible construction methods. Second, the composition of the simulated construction solu-

$$S_i^* = \frac{S_i - \min_{j=0}^{n-1} (S_j)}{\max_{j=0}^{n-1} (S_j) - \min_{j=0}^{n-1} (S_j)} \qquad (11)$$

The second piece of information is a real-time rating of the solution under development. This Life-Cycle Sustainability Assessment (LCSA) score is defined as the complement to 1 of the Euclidean distance between the point representing the current solution and the interpolation parabola of the previously established approximated Pareto front. It is

$$ \text{with} \quad \begin{cases} K_{p,i}^{m} = J_{p,i}^{m} & \text{if } i \le 4 \text{ (dynamic approach applied to global warming indicators) and} \\ K_{p,i}^{m} = I_{p,i}^{m} & \text{else (static approach).} \end{cases} $$

tion and its corresponding sustainability criteria matrix are systematically saved at each iteration. The fourth and final macroprocess aims to effectively assist decision-makers by providing an overview of possible trade-offs and a quantifiable indicator of the quality of the solution under study (see Fig. 18).

In terms of sustainability criteria, the two previous macroprocesses evaluate both the representative vector of the project under study and the set of vectors associated with all feasible alternatives. As the list of construction options considered in these two cases is unique, the vector characterizing the project necessarily represents one element within the set of feasible alternatives. Given that this set is systematically explored and fully simulated from the outset of the process, any modification of the choices defining the construction mode being adjusted simply consists of indexed referencing of the previously established alternatives database.

expressed as a percentage; thus, a solution located directly on the approximated Pareto front corresponds to an LCSA of 100 %.

## 2.3. Definition of the cost database

As the state-of-the-art review did not reveal any consensus-based source of information, the cost database applied was specifically developed by a construction economics expert from the ESSOR Group. In this regard, it is important to note that replacing this database with any other quantified data source would in no way compromise the validity of the proposed approach. The database was constructed in a deterministic and independent manner, based on two distinct scopes.

The first scope addresses construction costs. It was structured according to the manufacturing nomenclature formalism defined by the DAG, particularly focusing on nodes representing constructive elements,
<table><caption>**Table 1**
Real-world case database for testing the developed process.</caption><thead><tr><th rowspan="2">Cas study</th><th rowspan="2">Sketch phase</th><th rowspan="2">Finale phase</th><th colspan="2">Location</th><th rowspan="2">Shape</th><th rowspan="2">Number of floors</th><th rowspan="2">Number of occupants</th><th rowspan="2">Orientation</th><th rowspan="2">Front opening ratio</th><th rowspan="2">Open space ratio</th></tr><tr><th>Longitude</th><th>Latitude</th></tr></thead><tbody><tr><td>0</td><td>02, 2010</td><td>05, 2012</td><td>43.30175</td><td>-0.40931</td><td>☐</td><td>3</td><td>150</td><td>SO</td><td>45 %</td><td>80 %</td></tr><tr><td>1</td><td>09, 2021</td><td>10, 2023</td><td>43.54520</td><td>1.38614</td><td>☐</td><td>6</td><td>320</td><td>S</td><td>65 %</td><td>80 %</td></tr><tr><td>2</td><td>05, 2018</td><td>03, 2019</td><td>47.22219</td><td>-1.62040</td><td>☐</td><td>8</td><td>590</td><td>S</td><td>40 %</td><td>80 %</td></tr><tr><td>3</td><td>04, 2023</td><td>01, 2024</td><td>43.32857</td><td>-0.35717</td><td>☐</td><td>3</td><td>190</td><td>SW</td><td>35 %</td><td>16 %</td></tr><tr><td>4</td><td>05, 2021</td><td>08, 2023</td><td>43.60079</td><td>1.35044</td><td>☐</td><td>3</td><td>380</td><td>W</td><td>55 %</td><td>85 %</td></tr><tr><td>5</td><td>05, 2019</td><td>02, 2020</td><td>47.03593</td><td>-0.95735</td><td>L</td><td>2</td><td>130</td><td>SE</td><td>30 %</td><td>90 %</td></tr><tr><td>6</td><td>02, 2017</td><td>10, 2017</td><td>43.47098</td><td>-1.59475</td><td>L</td><td>3</td><td>150</td><td>E</td><td>40 %</td><td>70 %</td></tr><tr><td>7</td><td>10, 2021</td><td>09, 2022</td><td>43.58066</td><td>1.51656</td><td>L</td><td>2</td><td>230</td><td>SW</td><td>60 %</td><td>55 %</td></tr></tbody></table>

<table><caption>**Table 2**
Designation of the lots considered within the scope of the completed work.</caption><thead><tr><th>Reference</th><th>Désignation</th></tr></thead><tbody><tr><td>Lot #1</td><td>Roads and Miscellaneous Networks</td></tr><tr><td>Lot #2</td><td>Infrastructure</td></tr><tr><td>Lot #3</td><td>Superstructure</td></tr><tr><td>Lot #4</td><td>Waterproofing, Framework, Zinc Work</td></tr><tr><td>Lot #5</td><td>Partition Walls, Linings, False Ceilings, Interior Joinery</td></tr><tr><td>Lot #6</td><td>Facades and Exterior Joinery</td></tr><tr><td>Lot #7</td><td>Flooring, Wall &amp; Ceiling Finishes, Screeds</td></tr><tr><td>Lot #8</td><td>Heating, Ventilation, and Air Conditioning (HVAC)</td></tr><tr><td>Lot #9</td><td>Sanitary Installations</td></tr><tr><td>Lot #10</td><td>Energy Networks - High Voltage (Power)</td></tr><tr><td>Lot #11</td><td>Communication Networks - Low Voltage (Data)</td></tr><tr><td>Lot #12</td><td>Elevator</td></tr></tbody></table>

macro-components, and technical equipment. This part was subsequently populated based on feedback from similar projects, notably cost analyses derived from unit price schedules of previous projects. It should be noted that labor costs (hourly rates, workforce specialization), implementation costs (machinery, tools, prefabrication), and temporary infrastructure costs (site facilities, storage, protections) are integrated into the analytical pricing data extracted from unit price schedules. The second scope of this database relates to operational costs. This component associates energy quantities, computed within the DAG, with corresponding unit prices classified by type. Costs associated with equipment obsolescence are implicitly accounted for through the renewal factor (RF) (see Eq. (4)) of each product, systematically applied to quantities (see Section 2.2). It is worth emphasizing that the future integration of additional parameters remains entirely feasible. For instance, it would be relevant to include costs associated with dismantling and end-of-life phases of the building, such as demolition expenses, material recycling, recovery or reuse of construction elements, and costs related to regulatory compliance for deconstruction.

Globally, very few instances revealed discrepancies between designations referencing unit price schedules, on one hand, and the internal data derived from the DAG modeling, on the other. This limitation was addressed by inserting ad-hoc intermediate calculations into the hierarchical decomposition. The implementation of predictive algorithms

<table><caption>**Table 3**
Comparison between the model and the constructed building for two significant cases.</caption><thead><tr><th>#</th><th>Digital model</th><th>Constructed building</th></tr></thead><tbody><tr><td>2</td><td></td><td></td></tr><tr><td>4</td><td></td><td></td></tr></tbody></table>

and machine learning models incorporating this cost database—initially created for this experiment and continuously enriched by feedback—is planned to further enhance its accuracy and relevance.

### 3. Validation of the proposed framework

The proof of concept (POC) developed to test the proposed approach aims to efficiently manage two conflicting sustainability criteria within a generative environment, providing a level of detail (LOD) exceeding 300 from the earliest design phases. In this context, a fully autonomous application of the proposed framework was developed within a single Microsoft Excel® workbook. To ensure high performance, the Excel-DNA API was employed to integrate .NET resources into Excel. This choice was based on two main considerations: first, Excel-DNA is free and distributed under an open-source license that permits commercial use; second, it enables the creation of add-ins in C#, offering the flexibility and computational power required for this POC. All automatic update procedures are interfaced through a dedicated sheet within the Excel workbook.

#### 3.1. *Experimentation and testing*

The test database used in this study is the same as previously employed to validate the POC. It consists of eight real office-building projects previously studied and constructed (see Table 1). These eight cases share common characteristics including the absence of functional space in the basement, a concrete construction solution, and flat roofs.

To facilitate a direct comparison of results, the data generated by the POC, initially defined by construction methods in accordance with UniFormat categories, are allocated according to the written specifications of the reference documents (see Table 2).

The same test base was used to evaluate the robustness of the approach, specifically by successively analyzing the quality of the conceptual model generated according to several criteria: its representativeness and the efficiency of its space planning, the accuracy of sustainability criteria assessments, the scope of decision support, and its computation time.

#### 3.1.1. *Representativeness of the generated sketch models*

This experiment was repeated for each of the eight real-world reference cases (see Table 1). Table 3 highlights the two most significant case studies among the eight in terms of the representativeness of the digital model. The first (Case #2) is notable for its large balcony area and cantilever, while the second (Case #4) is distinguished by the oblique orientation of one of its facades.

The similarity between the generated and real envelopes was assessed using the classical Procrustes shape-analysis statistical method, specifically applied in the context of full superimposition [63]. To this end, each model was initially defined by a finite set of landmark points, notably located at its vertices. Subsequently, the shapes underwent a series of successive operations: first, a centering process aimed at positioning their common centroid at the origin; second, a normalization step establishing the root mean square distance (RMSD) between the
points and their new translated origin as equal to 1. Finally, the superimposition procedure was completed by rotating the real model around the origin. Taking the orientation of the generated model as a reference, the optimal rotation angle was determined using a least-squares approach aimed at minimizing the sum of squared distances (SSD) between corresponding points. After each of these three steps, the square root of this sum (SSD), known as the Procrustes distance, provided a relevant statistical measure of shape differences between the examined instances.

The obtained results highlight the fact that while centering and normalization notably influenced the measured values, rotation had no impact whatsoever on the observed outcomes (see Fig. 19). This observation indicates complete adherence to cadastral rules and project orientation constraints.

All statistical measures of shape differences calculated after superimposition ranged from $1 \cdot 10^{-3}$ to $4 \cdot 10^{-3}$. These results thus demonstrate the quality, in terms of representativeness, of the digital models generated compared to the actual building envelope for each of the eight case studies considered. However, it is noteworthy that the angular constraint relaxation algorithm, applied only to peripheral MVFs at the end of the design process in this POC, represents a provisional solution. Consequently, to generalize the applicability of this system to all types of site shapes, it will be necessary to replace the parallelepiped units characterizing the MVFs with prismatic units [64,65].

### 3.1.2. Space planning efficiency

The RMSD value previously calculated using the classical Procrustes method represents a relevant statistical measure for evaluating dimensional discrepancies between the generated and actual envelopes. This measure reveals a significant reduction in building footprint, ranging between 11 % and 23 %, across the eight cases studied, with the scenario designated as “case #0” exhibiting the highest degree of optimization (see Table 1). Furthermore, it was observed that optimized spatial planning, particularly limiting the length of dead-end circulations, allowed the omission of an emergency staircase in two of the eight experimental configurations (see Fig. 20).

Furthermore, the distribution of functional units per floor level, for each of the eight generated envelopes and the eight actual envelopes, was successively represented as a distance matrix and an adjacency matrix. These two matrices were subsequently aggregated into a functional matrix of dimensions $7 \times 7$, corresponding to the number of distinct MVF types considered, excluding horizontal circulations. The comparative analysis of the resulting maps highlights an improvement in spatial efficiency and functional coherence ranging between 3 % and 12 %. Additionally, examination of correlations between these matrices reveals strong spatial consistency, both for the generated and the actual projects.

### 3.1.3. Accuracy of sustainability criteria assessments

To ensure the relevance of the test and to facilitate its analysis within the framework of sustainability criteria evaluation, it is imperative that the footprints of the compared buildings be equivalent. However, the generative process implemented incorporates an optimization of allocated spaces, notably through the spatial planning of functional areas, resulting in dimensional variations. Consequently, normalization is required to ensure comparability of results. Therefore, to meet the specific experimental requirements of this test, this normalization was performed manually through iterative adjustments of circulation widths, until the cumulative slab area of the generated model matched that of the actual reference building. This methodology was applied individually to each simulation corresponding to the eight real reference cases (see Table 1). The criteria selected to evaluate the accuracy of the POC’s estimates are, on the one hand, the GHG footprint, chosen for its particularly fine granularity, and on the other hand, the total cost, chosen for its coarser granularity. These experiments are based on two sources: the INIES regulatory database and a cost database specifically

developed by a construction economics expert from the Essor Group (see Section 2.3).

The results generated by the process based solely on the information available during the sketch phase are compared to actual data obtained at the end of the design phase. The discrepancies between these estimates and the actual data are measured for each lot, as well as globally across all lots. Given that the root mean square error (RMSE) and the mean absolute error (MAE) are consistently close—indicating that the estimates produced by the proposed model are stable—the estimation error considered is defined, for each batch, by a combined error score incorporating both components, specifically the mixed root mean square of the deviations between estimates and actual values.

$$E_{mix} = \sqrt{MAE^2 + (RMSE - MAE)^2} \qquad (12)$$

$$with: MAE = \frac{1}{n} \sum_{i=1}^{n} |\Delta y_i| \quad and \quad RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} \Delta y_i^2}$$

This approach is adopted to capture both the average error and the variability around this mean.

Figs. 21 and 22 present the experimental results from these simulations. The x-axis represents the different analyzed lots, while the y-axis shows the estimation error for each lot.

The small discrepancies observed reflect the accuracy of the manufacturing schedules generated by the model, as the underlying databases used are identical. This precision is attributable to the deterministic method derived from the Analytic Hierarchy Process (AHP), which was employed to define the quantities of each component and macro-component. To better understand the true implications of these deviations, avoid underestimating their impacts, and guide trade-offs toward genuinely critical cost items, it is important to recall that in the AEC sector, the magnitudes of total costs and environmental impacts are particularly high, especially in the context of office buildings.

The results reveal that the dispersion of evaluation deviations by lot converges toward an approximation of $-3 \% \pm 2.5 \%$ for GHG emissions and $-1 \% \pm 1.5 \%$ for total cost. These findings demonstrate that this model, when applied during the conceptual design phase, provides a notable improvement in accuracy compared to the 12 % deviation generally associated with approximate methods [56]. It is also important to note that the error measured for GHG emissions is, in principle, generalizable to all sixty environmental impact scores (EIS). Part of these deviations can be attributed to the dimensionality reduction operations applied to the multi-scale DAG modeling of construction methods (see Section 2.1.3), particularly the cumulative contribution threshold set at 97 % and the simplified models used for structural sizing and dynamic simulations. Therefore, an in-depth analysis of the structure and functions defining this DAG is necessary to further improve result accuracy. Additionally, it is specifically noted that Lot #6, related to façades and external joinery, is consistently underestimated.

A comparative analysis of the manufacturing nomenclature associated with this lot indicates that this underestimation primarily results from the lack of consideration of the symbolic and visual role of façades, which embody the architectural signature and identity of the building. This finding highlights the need to enrich the parameterization of MVFs, particularly by incorporating aesthetic information.

### 3.1.4. Decision support scope

This experiment focuses on the output data from the sketch model generated by the system for the first real-world reference case (see Table 1 - Case #0). It examines the automatic estimates of the GHG footprint and total cost, calculated simultaneously for various construction solutions. These solutions are produced through a systematic exploration of all possible combinations of construction elements (see Section 2.2 - Process 3). In this context, four different building footprints (rectangular, campus-shaped, L-shaped, and H-shaped) are simulated.
All input data from the reference project, particularly those related to the construction program, were rigorously maintained, and the integrity of the generative system was strictly preserved. Thus, the diversity of the shapes obtained, specifically pursued for experimental purposes in the specific context of this test, results from an exceptional manual modification of the cadastral constraints. The system's iterative results are presented as Cartesian coordinates on a plane, with each point representing a potential construction solution (see Fig. 23).

The shape and color of the points vary according to the simulated building footprint forms. The approximated Pareto front, determined by the process and highlighting the optimal trade-offs between the two criteria, is represented by a red broken line. A total of 985,500 different construction solutions were explored. For clarity, these solutions are represented in Fig. 23 as 657 points, each corresponding to the centroid of a cluster of 1500 neighboring solutions with the same footprint shape. Consequently, the approximated Pareto front extracted from these solutions includes 127 points, of which only 42 are visible in this figure. For reference, the point corresponding to the two criteria associated with the model being defined by the decision-makers is indicated within the solution space, as is the 2025 threshold defined by the RE 2020 regulations and the LCSA score. With a constant construction method, it is noteworthy that the variations induced by the footprint form exhibit a characteristic "inverted Z" pattern, with amplitudes that vary depending on the construction solutions considered (see Fig. 24).

The visualization generated by this POC demonstrates that the rectangular form consistently offers the best trade-off between total cost and GHG emissions, owing to its optimal compactness. This characteristic also explains the increasing impact of the “campus,” “L,” and “H” forms, where variations in total cost are primarily driven by differences in façades and slabs. A deeper analysis highlights two significant observations in the current context: at an equal total cost, one construction solution achieves a reduction of over 10 % in GHG emissions (equivalent to 210 tons of CO₂), while at equivalent GHG emissions, another solution enables a 21 % cost saving (equivalent to €420,000).

These findings underscore that, while the costs associated with eco-friendly construction methods are trending downward, compliance with the current French environmental regulation (RE 2020, 2025 target) requires a drastic 15 % reduction in GHG emissions, which translates into a significant 12 % increase in construction costs. These results demonstrate that the proposed system effectively fulfills its role as a decision-support tool, providing insights into possible trade-offs between sustainability and cost.

### 3.1.5. *Calculation time*

The computation times presented below correspond to the complete modeling of the eight real reference cases (see Table 1), involving a number of MVFs ranging from 94 to 163. The manual initialization of the process is limited to entering the five key parameters directly linked to the project owner's requirements (ORDI): Open-Space Ratio, Work-force Size, Location, Usage, and Number of Underground Parking Spaces (see Fig. 10). This step, which triggers the process, is completed in less than two minutes. The base analogon is then generated within a few seconds, corresponding to the convergence time of the functional space planning optimization mechanism. At this stage, the default parameters of this initial model correspond to the previously simulated configuration.

A phase of architectural customization follows, particularly modifying the building envelope (cantilevers, terraces) by adding cadastral constraints that define the implantation perimeter at each level. Some default architectural responses of the base analogon are also adjusted during this phase, such as selecting a pitched roof instead of a flat roof. The time required for this task ranges from 0 min (for a new building similar to the previously studied project) to 7 min.

The next step involves the automatic activation of the macro-process for exploring the feasible solution space, which lasts between 14 and 25 min. In this test, since the project morphology is fixed from this phase

onward, this macro-process is no longer reactivated, as all potential alternatives are considered simulated. During this period, the decision-support macro-process remains inactive, while manual adjustment of the model parameters remains accessible. Notably, between one-third and half of the exploration time was systematically used by the operator to begin refining certain parameters, such as flooring materials based on zone allocation. This refinement work was then continued based on the computed scores until a constructive solution compliant with the RE2020 threshold 2025 at minimal cost was obtained. This final phase required an additional 21 to 48 min. Thus, the total duration for creating the final analogon ranges from 47 to 72 min, including over 7 min of passive waiting time corresponding to the completion of the macro-process for exploring feasible solutions.

Finally, it has been observed that the configuration duration tends to decrease as operators gain experience, demonstrating a progressive learning effect across different processed projects.

### 3.2. User feedbacks

The proposed process and the developed POC underwent an extensive evaluation during a workshop involving ten experts from the ESSOR group,<fnref n="3" /> selected due to the particular sensitivity of their professional activities to sustainability issues. Among these specialists were three experts in numerical modeling, three project review specialists, three architectural project designers, and one architect. To ensure the reliability and relevance of the collected feedback, the experts were rigorously selected according to three specific criteria: possession of an engineering degree, more than ten years of professional experience in their respective fields, and holding, for at least three years, a recognized reference role within their respective sectors.

The workshop was conducted in three distinct phases. The first phase consisted of an introductory presentation of the developed POC. This was followed by an individual experimentation phase, during which each participant employed the tool to generate the practical scenario previously designated as "case #0" (see Table 1). Finally, the third phase involved gathering participant feedback through a questionnaire initially structured by Van Eldik in 2020 [30] and subsequently validated by Berges-Alvarez in 2022 [32] (see Table 4).

The scope of the first two questions of this questionnaire was explicitly limited to the intermediate step referred to as "mid-project". The questionnaire's first seven questions are grouped into four assessment categories: functionality and applicability, ease of use, scalability, and consideration of sustainability. Each question (successively) addresses both the methodology typically employed by the participants (Revit environment, referred to as "CS" in accordance with Van-Eldik's "Current System" designation) and the proposed method (referred to as "PM"), in order to elicit comparative responses. The final questions eight and nine focus exclusively on the newly developed approach and address its deployment potential. Additionally, the experts provided an overall evaluation of the tool by assigning a score from 1 (poor) to 10 (excellent) (see Table 4).

Responses to the first nine questions were collected using a graduated scale ranging from 1 (strongly disagree) to 5 (strongly agree). The overall evaluation provided in the tenth and final question was assessed using a scale from 1 (poor) to 10 (excellent).

The responses were analyzed using the method described by Van Eldik (2020) [30]. Although the survey strictly adhered to the original questionnaire, the analysis of expert feedback differed slightly on two points. First, to capture an overview of expressed trends, the median was

<footnote n="3">³ These questionnaires and interviews were conducted in compliance with French norms and standards for research Ethics: ANR (French Research Agency) Charter, OFIS (French Charter of Ethics for Research Professions) Charter, CESI LINEACT Laboratory Ethics Committee Rules, and ethical rules of the ESSOR group works council.</footnote>
<table><caption>**Table 4**
List of questions and summary of responses from Essor Group experts.</caption><thead><tr><th rowspan="2">Van Eldik criteria [30]</th><th rowspan="2">CS</th><th rowspan="2">PM</th><th rowspan="2">Questions</th><th rowspan="2">Notes</th><th colspan="5">Score count</th><th rowspan="2">Median</th><th rowspan="2">Standard deviation</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><td rowspan="3">Functionality applicability<br>(4,3 vs 1,5)</td><td>Q1</td><td>X</td><td>X</td><td>helps effectively in evaluating the sustainability of a design at mid-<br>project</td><td></td><td>6</td><td>3</td><td>1</td><td>0</td><td>0</td><td>1.0</td><td>0.7</td></tr><tr><td>Q2</td><td>X</td><td>X</td><td>helps effectively in improving the sustainability of a design</td><td></td><td>4</td><td>4</td><td>2</td><td>0</td><td>0</td><td>2.0</td><td><strong>0.4</strong></td></tr><tr><td>Q3</td><td>X</td><td>X</td><td>is easy to use</td><td></td><td>4</td><td>4</td><td>1</td><td>1</td><td>0</td><td>2.0</td><td>0.9</td></tr><tr><td rowspan="2">Ease of use (4,3 vs 2,0)</td><td>Q4</td><td>X</td><td>X</td><td>is fast and yields results that are easy to interpret and understand.</td><td></td><td>0</td><td>0</td><td>2</td><td>5</td><td>3</td><td>4.0</td><td>0.7</td></tr><tr><td>Q5</td><td>X</td><td>X</td><td>can, without large changes, be used in other fields of expertise</td><td></td><td>1</td><td>6</td><td>3</td><td>0</td><td>0</td><td>2.0</td><td>0.6</td></tr><tr><td rowspan="2">Scalability (4,5 vs 2,5)</td><td>Q6</td><td>X</td><td>X</td><td>could / can easily be adjusted / expanded to cover more<br>(sustainability) aspects than just the EIS</td><td></td><td>0</td><td>3</td><td>4</td><td>2</td><td>1</td><td>3.0</td><td>0.9</td></tr><tr><td>Q7</td><td>X</td><td>X</td><td>fosters sustainability consciousness of designers</td><td></td><td>0</td><td>1</td><td>4</td><td>3</td><td>2</td><td>3.5</td><td>0.9</td></tr><tr><td rowspan="2">Sustainability consciousness<br>(4,5 vs 1,0)</td><td>Q8</td><td>X</td><td>X</td><td>The proposed method can easily be implemented in the workflow of design projects<br>within the organization</td><td></td><td>0</td><td>0</td><td>0</td><td>4</td><td>6</td><td>5.0</td><td>0.5</td></tr><tr><td>Q9</td><td>X</td><td>X</td><td>The proposed method makes it easier to include sustainability aspects in more projects<br>within the organization</td><td></td><td>6</td><td>2</td><td>2</td><td>0</td><td>0</td><td>1.0</td><td>0.8</td></tr><tr><td>Specific to PM</td><td>Q9</td><td>X</td><td>X</td><td></td><td></td><td>0</td><td>0</td><td>0</td><td>5</td><td>5</td><td>4.5</td><td>0.5</td></tr><tr><td colspan="6"><strong>Median score</strong></td><td><strong>0</strong></td><td><strong>0</strong></td><td><strong>0</strong></td><td><strong>3</strong></td><td><strong>7</strong></td><td><strong>5.0</strong></td><td><strong>0.5</strong></td></tr></tbody></table>

used instead of the mean, given the ordinal nature of the Likert scale. Second, the standard deviation of responses to each question was used as a measure of the consistency of opinions. This choice is justified by the participants' expertise and the standard deviation's ability to reflect the dispersion of responses.

The analysis results are presented in a radar chart (see Fig. 25). The responses are distinguished based on whether they pertain to the “current system” (questions 1, 3, 6, 7, 10, 11, and 15, shown in orange) or the “proposed method” (questions 2, 4, 5, 8, 9, 12–14, and 16, shown in blue).

According to feedback from the ten experts in their respective fields of expertise, most criteria related to the “proposed method” received median scores of 4 out of 5 or higher. These results reflect a generally favorable, or even highly favorable, reception toward the deployment of this process, particularly regarding functionality, applicability, ease of use, scalability, and sustainability integration. However, responses to questions 5 and 12, which focused on the ease of integrating the system into traditional design project workflows, either within their specific domain or others, showed lower scores of 3 and 3.5, respectively. These results corroborate unanimous expert feedback, reflected in an average score of 8 out of 10 with a standard deviation of 0.77, emphasizing the current absence of a gateway enabling the direct integration of the developed process into a collaborative design and execution environment, such as BIM.

## 4. Discussion and recommendations

The results highlight a key strength of the proposed approach: a framework that ensures precise material and energy assessments from the conceptual design phase, maintaining consistency throughout design iterations, for both the project under study and all feasible alternatives. These contributions are significant, particularly in avoiding the inaccuracies inherent to approximate methods [5,13], often implemented using three main approaches. The first approach, focused on embodied impacts, limits designers to a predefined list of materials [66] or a restricted set of standardized construction elements, such as those used in modular, prefabricated, or industrial buildings [67,68]. The second, centered on operational impacts, relies on automatic extraction of surface models, a method commonly employed for many years in building performance simulation (BPS) [69,70] or to approximate life-cycle assessments [5]. The third approximate method, broader in scope but generally limited to early design phases, uses the geometric model and applies assumptions to materials based on typical reference values defined according to the national construction market and the design

stage [71,72]. Furthermore, the systematic evaluation of sustainability criteria within the explicit workflow proposed, performed simultaneously and continuously, proves particularly relevant and timely for the building and infrastructure sectors [30,73]. Moreover, it is noteworthy that the proposed framework exhibits intrinsic properties facilitating the integration of certain sustainability criteria, such as those addressing spatial efficiency and functional coherence—both directly related to spatial ergonomics [74]—as well as the reduction of building footprints, leading to a significant decrease in soil sealing (see Fig. 8, right panel). However, for broader generalization to the civil-engineering domain, the relevance of the proposed approach requires an in-depth examination of two key aspects. First, its adaptability to regulatory, normative, and environmental information beyond those currently applicable in France. Second, the alignment between the developed workflow and the unique characteristics of the infrastructure sector, both in terms of products and processes [32].

The approach tested within this proof of concept (POC) demonstrates both the feasibility and potential of shifting the design effort peak toward the ‘Preliminary Studies’ phase, with the aim of amplifying the influence of architectural decisions made during the initial iterations of the design process. This initiative seeks to provide a foundation for the architectural community to engage in deeper reflection on the development of automatic generative tools capable of initiating a BIM environment as early as the sketching phase. However, at this stage of development, the disruption introduced by this approach with respect to current BIM standards—particularly regarding IFC format mapping—remains unresolved. This challenge is primarily linked to the integration, from the outset, of usage scenarios and operational behaviors of building systems. To restore compatibility with prevailing data exchange formats, further development efforts appear necessary to ensure effective interoperability with IFC standards. Nevertheless, such an evolution seems achievable, given that the proposed allotment mechanism for construction elements (see Fig. 9), based on the aggregation of FMVPs, produces a plan-type family structure of data, closely aligned with those employed in BIM environments. This framework also has the following limitations:

(1) The systematic exploration of all construction solutions encounters a combinatorial explosion, making the process particularly demanding in terms of computational resources. To address this challenge, a more selective approach could be considered. This would rely, for instance, on the characteristic ‘inverted Z’ signature observed in the evolution of criteria as a function of form (see Fig. 24), thereby enabling the exploration to focus on
the most promising configurations from the earliest iterations. In this context, investigating the NSGA-II method, along with other algorithms for approximating the Pareto front, also represents a promising research direction.

(2) the development of a more user-friendly interface, specifically designed to simplify decision support and, more importantly, decision-making, appears essential. This need is particularly pronounced for decision-makers who lack expertise in design and sustainability, as well as for scientists whose knowledge does not extend to architectural domains.

(3) Finally, the experiments conducted to adjust the parameters of the optimization metaheuristic used for functional space planning, particularly the simulated annealing method integrated into the FMV aggregation engine, highlighted the value of a more in-depth analysis of the solution landscape based on varying levels of attraction.

Furthermore, it is recalled that the cost function of this metaheuristic focuses on the compactness of the envelope, while other criteria, particularly social factors such as access to exterior views or natural lighting, may influence the spatial distribution of functional units. Such developments could enhance the precision of solutions defining the approximated Pareto front. This presents promising opportunities for future research, aiming at improving both the quality of the results and the understanding of optimization mechanisms. Similarly, exploring alternative heuristics, such as Ant Colony Optimization (ACO) algorithms, could provide a more efficient and faster method for functional space planning. It is noteworthy that such developments should also help overcome the current limitations related to the efficiency of this approach, particularly regarding the time required to generate the native conceptual model and define the feasible solution space. These improvements could ultimately lead to a system that is fully operational in real-time.

## 5. Conclusions

Faced with the urgency of global warming, sustainability has become a crucial global concern, impacting all manufacturing sectors, particularly during the design phase of new products. In civil engineering, this concern is further heightened by the long life-cycles and significant scale of structures.

By focusing on the multi-objective optimization of sustainability in construction project studies, the proposed approach aligns seamlessly with this context, particularly within the AEC sector. It respects the principles established in scientific literature over the past decade, systematically incorporating sustainability analysis from the early design stage through a multi-criteria framework that spans the entire lifecycle of the structure.

To achieve this goal, two complementary methodologies were implemented to address the challenge posed by the mismatch between, on the one hand, the gradual progression of detail levels in digital models, which are rudimentary (e.g., LOD 100) during the sketch phase, and, on the other hand, the heterogeneous granularity of different sustainability criteria. The first methodology adopts a generative design approach, leveraging a concept of topological optimization of the functional and regulatory requirements underlying the project. The second focuses on multi-scale modeling of construction methods, structured according to the standardized UniFormat classification system. This second methodology is also employed to explore the space of feasible solutions, thus enabling enhancement of the system the integration of a macroprocess for decision support.

The effectiveness of this approach is demonstrated through the development of a proof of concept (POC), validated through a design process centered on two sustainability criteria: GHG emissions and global cost. This experimentation is based on eight real-world office building projects that were previously studied and constructed. After

validating the robustness and accuracy of the POC, the proposed workflow was evaluated by a panel of ten experts. They confirmed the relevance of this approach, which can automatically generate a model with an LOD exceeding 300 from the early design stages. The experts also highlighted the significant potential of this integrated approach to support informed decision-making on sustainable development, even for decision-makers with limited expertise in the field.

The proposed approach enables a highly flexible and transparent exploration of the interactions between subsystems, inherent to the design process, as well as the associated decisions, whether individual, such as the selection of constructive modes, or collective, such as regulatory clauses. This approach paves the way for studying sustainability strategies by offering the ability to simultaneously analyze the mechanisms specific to each strategy and their impact on the optimality of the solutions they produce. In this regard, the developed framework stands out through several key features: it provides independence from design platforms, which are often costly and technically complex, and integrates functional requirements and regulatory constraints as optimization levers for space planning. It also enables the direct use of regulatory databases and comprehensive, approved calculation procedures while offering the flexibility to incorporate various evaluation criteria. Moreover, its adaptability ensures effective application regardless of geographic context or local specifics. Finally, its holistic approach promotes informed, global, and generic decision-making from the earliest design phases.

Four future development directions for the proposed approach are envisioned. The first aims to expand the number of sustainability criteria analyzed simultaneously. The second focuses on optimizing the macroprocesses it comprises, with particular attention to automatic space planning and multi-objective decision-making. The third focuses on integrating the approach into a collaborative environment, particularly through direct connectivity with BIM. Finally, the fourth direction aims at the generalization of the approach, both in international contexts and the infrastructure sector.

## CRediT authorship contribution statement

**Catherine Bouillon:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. **Benjamin Cohen Boulakia:** Writing – review & editing, Validation, Software, Project administration, Methodology, Formal analysis. **Karim Beddiar:** Writing – review & editing, Validation, Project administration, Funding acquisition. **Yves Jaboin:** Writing – original draft, Validation, Supervision, Software, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Fabrice Duval:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Funding acquisition.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

We gratefully acknowledge the support of the ANRT (Association Nationale de la Recherche et de la Technologie) and the Essor Group, whose contributions were invaluable to the success of our research.

## Data availability

The data that has been used is confidential.
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