A Sustainable Multi-Criteria Optimization Approach for the Energy Retrofit of Collective Housing in Algeria Using the ELECTRE III Tool

Abstract

This study proposes a sustainable multi-criteria optimization framework for the energy retrofit of collective residential buildings in Algeria, particularly those constructed between the 1970s and 1980s. Through on-site surveys, energy consumption analysis, and seasonal temperature measurements, the high energy demand of these buildings was confirmed. Using EnergyPlus simulations based on Meteoblue weather data, 16 retrofit strategies were assessed—incorporating various insulating materials applied internally or externally (via rendering or cladding). The ELECTRE III decision-making tool was employed, supported by the Simos Revised Framework (SRF) for weighting environmental, economic, and social criteria. Results demonstrate that all strategies significantly reduce energy demand—by up to 72.5%, with reductions reaching 94.4% in winter and 43.5% in summer, depending on insulation type and placement. Improvements in indoor thermal comfort were also observed, with exterior insulation beneath cladding offering the best performance during winter, while exterior rendering also proved effective in the summer. The ELECTRE III analysis identified rock wool and polyurethane with fiber cement cladding as optimal insulation solutions. The proposed approach supports national energy policies and aligns with the Sustainable Development Goals (SDGs), offering a replicable model for large-scale building retrofits in similar climatic and architectural contexts.

1. Introduction

Buildings represent a major sector in global energy consumption, accounting for 30% to 50% of total energy demand worldwide. This demand continues to rise, particularly in developing economies, where the annual growth rate is estimated at 3.2%, compared to 1.1% in developed nations [1,2]. In Algeria, the residential and tertiary sectors together consume 47% of the country’s total energy and contribute 21% of greenhouse gas emissions [3]. Forecasts suggest that energy demand in Algeria’s housing sector will escalate from 117.4 TWh/year in 2008 to 413.4 TWh/year by 2050 [4]. In response to this growing challenge, the Algerian government launched the National Energy Efficiency Program (NEEP), which aims to retrofit 100,000 homes annually by 2030. The program focuses primarily on enhancing building envelopes through the insulation of walls, roofs, and windows, with 80% of costs subsidized by the National Fund for Energy Efficiency (NFEE) [5]. However, the program lacks specific guidance on intervention methods and the optimal selection of insulation materials.

Energy retrofitting is widely recognized as a cost-effective strategy for reducing both energy consumption and CO₂ emissions [6]. Improvements in insulation and airtightness are particularly significant contributors to these reductions [7]. In the Algerian context, research has largely focused on the role of the building envelope in improving energy efficiency [8]. For instance, Bentoumi et al. [9] demonstrated that applying insulation to roofs and floors can reduce heating energy consumption by 55% and air-conditioning demand by 18%. Similarly, Ahn et al. [10] showed that modifying the U-value of windows in poorly insulated buildings can lead to reductions in energy demand ranging from 7.9% to 16.7%. Despite these contributions, further investigation is still needed, particularly concerning the positioning of insulation and the comparative effectiveness of internal versus external retrofitting.

In recent years, the research focus has broadened to include more comprehensive retrofit strategies. Shu et al. [11], for example, explored large-scale retrofitting in smart and connected communities, identifying research opportunities in building design, mechanical systems, and human-centered approaches. Desvallées [12] highlighted the challenge of combining energy efficiency with social inclusion, particularly in southern Europe, where social housing providers tend to prioritize envelope retrofitting over renewable energy solutions—sometimes at the expense of addressing deeper issues of energy poverty. In Algeria, Djafri et al. [13] emphasized the urgency of improving housing quality, given the country’s ongoing housing shortage. Benmicia [14] also underlined the need for residential energy retrofits tailored to local thermal comfort needs. Elsewhere, Taylor et al. [15] analyzed the impact of retrofitting in Florida’s multifamily housing sector and reported substantial electricity savings, while Hens [16] demonstrated through long-term observation that improvements in insulation, airtightness, and heating systems often yield greater benefits than the installation of solar panels.

Further studies have underscored the pivotal role of insulation techniques in improving building energy performance. Zhang et al. [17,18] reported that external wall insulation can reduce heating loads by approximately 30%. Ozel [19] examined the influence of insulation placement, concluding that internal insulation results in the smallest phase shift, whereas external insulation yields the lowest decrement factor. Al-Sanea and Zedan [20] highlighted the substantial impact of insulation under transient thermal conditions. Nevertheless, despite their demonstrated benefits, natural insulation materials remain underutilized, primarily due to functional limitations and the limited availability of research on their real-world applications [21].

This study focuses on energy retrofitting through building envelope insulation, specifically investigating the impact of insulation positioning on energy consumption and evaluating a range of retrofit strategies. Although prior research has examined energy optimization based on cost and life-cycle performance, comparative assessments—particularly between rendering and cladding in external insulation applications—remain scarce. Bridging this gap is essential for refining retrofit practices and improving the effectiveness of insulation strategies. This study targets prefabricated houses built in Algeria during the 1970s and 1980s, a period when construction techniques resulted in buildings with high energy demand and limited thermal performance. These structures, concentrated in some of Algeria’s most energy-intensive regions, represent a strategic priority for intervention under the country’s national energy efficiency framework.

The selection of appropriate retrofit strategies is a complex decision-making problem shaped by the interplay of environmental, economic, and social considerations. In this context, Multiple Criteria Decision Analysis (MCDA) methods are widely used to assist decision makers in evaluating and comparing alternatives. Among these methods, partial aggregation techniques such as ELECTRE (Elimination and Choice Expressing Reality) and PROMETHEE II (Preference Ranking Organization METHod for Enrichment Evaluation) have proven to be particularly effective [22,23]. For example, PROMETHEE II has been successfully applied in Italy to assess both the economic and environmental performance of nearly zero-energy buildings (NZEBs) [24]. In Algeria, Seddiki et al. [5] applied the PROMETHEE GDSS framework to evaluate retrofitting strategies for heritage buildings, while Daniel et al. [25] employed ELECTRE TRI for categorizing residential retrofit solutions. Despite their usefulness, classification methods such as ELECTRE TRI can sometimes fall short in providing the precision needed for robust decision making in retrofit projects.

In this regard, ELECTRE III represents a more advanced ranking methodology, offering greater flexibility and precision in prioritizing retrofit alternatives [26]. Several authors, including Salminen et al. [27] and Kokaraki et al. [28], have recommended ELECTRE III over methods such as SMART and PROMETHEE, particularly for sustainability-focused assessments. Its ability to handle uncertainty and address the incomparability between alternatives makes ELECTRE III especially suited to the complex nature of energy retrofit decisions [29,30]. Notably, the method has already been applied in the context of office building rehabilitation. One study, supported by the Swiss Academy of Engineering Sciences (SATW), used ELECTRE III to rank façade intervention scenarios [31]. Similarly, the European Joule-Thermie Office project employed ELECTRE III for multi-criteria evaluations, incorporating criteria such as energy performance, environmental impact, indoor environmental quality, and cost [32].

Despite these promising examples, the use of ELECTRE III in energy retrofit studies remains limited. For instance, Catalina et al. [33] applied the method to compare renewable energy systems for individual buildings, and Almeida et al. [34] developed a five-criteria model for selecting facade retrofit solutions—although their analysis did not fully account for dynamic factors such as energy consumption, CO₂ emissions, or economic costs. Given the method’s comprehensive and structured evaluation capabilities, ELECTRE III is particularly well-suited for this research.

In contrast to previous studies, which often rely on static or partial evaluation criteria, this research combines dynamic energy simulations with the ELECTRE III method to compare a variety of retrofit scenarios. This study also integrates the Simos Revised Framework (SRF) to assign weights to criteria in a coherent and structured manner. A key strength of this work lies in its investigation of different insulation configurations, including both internal and external solutions. The selected evaluation criteria reflect the environmental, social, and economic priorities specific to the Algerian context, ultimately providing a decision-support tool tailored to local needs.

To address this research objective, the remainder of this paper is structured as follows:

• Section 2 presents the methodology, detailing both analytical and experimental components;
• Section 3 discusses the case study;
• Section 4 presents and discusses the results;
• Section 5 provides the conclusions and outlines future research directions.

2. Methodology and Tools

2.1. The Methodological Approach

The proposed approach addresses both quantitative and qualitative aspects related to building rehabilitation. As shown in the flowchart of Figure 1, the work is structured into three main sections with corresponding sub-steps. First, an analytical section is conducted in which the energy performance of buildings in their initial state is evaluated (Steps 1–4). This evaluation requires both a preliminary diagnosis and a comprehensive assessment to verify compliance with the Algerian Thermal Regulations (RETA code) [35], a national regulatory framework that establishes the minimum performance thresholds for residential energy efficiency. Introduced in 1999 and derived from Law No. 99-09, RETA is supported by technical documents that define seasonal requirements—DTR C3-2 for winter conditions [36] and DTR C3-4 for summer conditions [37]. These regulations directly influence the retrofit decision-making process by defining whether a proposed intervention meets the required thermal performance standards. Only retrofit strategies that achieve compliance with RETA and DTR benchmarks are considered viable under national policy and are eligible for financial support through the National Fund for Energy Efficiency (NFEE). Accordingly, the assessment phase included a detailed analysis of four years of gas and electricity billing records, supplemented by resident questionnaires. These provided insights into occupancy patterns, household appliance use, ventilation practices, perceived thermal comfort, and the number of occupants—factors essential for accurate simulation and strategy selection within the regulatory framework.

Next, a range of rehabilitation solutions is proposed to improve energy efficiency and reduce energy consumption and CO₂ emissions (step 5). These solutions are designed to enhance the building envelope, including insulation of walls, roofs, and windows, in accordance with RETA and DTR guidelines. The final section introduces a decision-support method, ELECTRE III, to rank the alternatives and provide recommendations (step 6).

Building design parameters, indoor conditions, and weather data were obtained from Meteoblue [38] and integrated into the EnergyPlus software 9.2 [39] to generate the simulation model. To validate the model, indoor air temperature readings were collected and compared with simulation predictions. For experimental measurements, wireless ambient temperature sensors (Figure 2) were employed to monitor indoor air temperature. These sensors (Arexx, Zwolle, The Netherlands) featured an integrated temperature probe and a high-frequency radio transmitter, which relayed data to the BS-500 recording system via radio frequency (RF). The sensors operated within a measurement range of −30 °C to 80 °C, with an effective transmission range of approximately 50 m (up to 100 m in open areas).

2.2. Decision-Support Method: ELECTRE III

ELECTRE III is a multi-criteria decision-making (MCDM) method designed for complex problems involving conflicting criteria, such as evaluating energy retrofit strategies for collective housing. It enables the comparative assessment of different alternatives using both qualitative and quantitative data. The method’s structured approach aids in identifying globally beneficial solutions, making it relevant across fields concerned with sustainability, public policy, and strategic urban planning.

The following section presents the conceptual framework and computational steps, emphasizing clarity in the role and purpose of each element of the methodology.

Conceptual Framework of the ELECTRE III Method

The ELECTRE III method was applied using the ULaval software 0.6.28 [40], enabling the comparison of retrofit strategies based on predefined criteria. These criteria cover aspects for three insulation configurations: interior insulation, exterior cladding, and exterior rendering. The selected criteria encompass environmental, economic, and social dimensions, as illustrated in Figure 2. Performance data were sourced from published comparisons [20,41,42,43,44] and various regulatory and technical documents [45,46,47].

The methodology, outlined in Figure 3, follows these steps:

(1) 

Performance Matrix Construction:

Following the approach outlined by Figueira et al. [48], the process begins by defining two finite and consistent sets: A and F. The set $A=\left\{a_{\mathsf{1}},a_{\mathsf{2}}\dots a_m\right\}$ represents the potential solutions to the problem, while $F=\left\{j=\mathsf{1}\dots n\right\}$ with $n\ge \mathsf{3}$, consists of the pseudo-criteria used to evaluate each alternative.

The next step involves constructing the performance matrix $g_j\left(a_i\right)$ where strategies (S) are organized in rows and criteria in columns. Each criterion is assigned a weight to reflect its relative importance, as determined by the decision maker.

(2) 

Weighting the Criteria:

To establish these weights, the Simos Revised Framework (SRF) method is applied (Figure 3). This approach requires the decision maker to rank a set of criteria cards from least to most important. Blank cards are placed between criteria cards to create gaps, which increase by one or more u units each time, thereby refining the ranking.

Each criterion must be assigned a numerical importance to reflect its influence in the decision-making process. These values begin as non-normalized weights, denoted k(r), which simply represent how the decision maker initially perceives the importance of each criterion based on their ranking. These values stem from an intuitive ranking process, where the decision maker prioritizes each criterion based on their subjective judgment. However, these raw values do not yet sum to 1 or 100, so they require normalization. Let $w_j$ represent the coefficient of relative importance for criterion $g_j$, ensuring that the sum of all coefficients satisfies ${\sum }_{j=\mathsf{1}}^n{w}_j=\mathsf{1}$. A detailed explanation of the SRF method is provided by Figueira and Roy [49].

$$z={\displaystyle \frac{({\sum }_{i=\mathsf{0}}^{(q-\mathsf{1})}\left(T-i\right))p}{({\sum }_{i=\mathsf{0}}^{(p-\mathsf{1})}\left(\mathsf{1}+i\right))q}}$$

(1)

where, z is the fraction between the sum of the weights (ranks) of the most important criteria rated q and those of the least important rated p with T total number of cards.

This coefficient (z) is used in the revised Simos’ procedure to recalculate the new numerical value of the unit u:

$$u={\displaystyle \frac{z-1}{e}}$$

(2)

$$e={\sum }_{r=\mathsf{1}}^{\overline{n}-\mathsf{1}}{e}_r \mathrm{and} e_r={e^{\prime }}_r+r$$

(3)

where $\overline{n}$: number of equivalence classes, ${e^{\prime }}_r$ is the number of blank cards between cards r and r + 1 (criterion cards).

From the non-normalized weights $k\left(r\right)$ we deduce the normalized weights:

$$k^{\prime }=k\left(r\right); K={\sum }_{i=\mathsf{1}}^n{k^{\prime }}_{i }$$

(4)

where ${k^{\prime }}_i$ is the non-normalized weight of criterion g_i of rank r:

$$k_i^{*}={\displaystyle \frac{\mathsf{100} \times {k^{\prime }}_i}{k^{\prime }}}$$

(5)

where,$k_i^{*}$ is non-standardized weight with decimals.

Normalized weights need to be rounded to whole numbers using numerical calculation techniques to approximate the decimal places to determine weights with whole numbers whose total is equal to 100.

To define the preference thresholds that determine how alternatives are judged against each other, ELECTRE III requires statistical insights into the performance data. Specifically, the method computes the arithmetic mean (μ) and standard deviation (σ) for each criterion. These statistical values help calibrate thresholds that distinguish between weak preferences, strict preferences, and vetoes. According to Roy and Bouyssou [50], the three comparison thresholds are added to the matrix; ($p_j{g}_j(a_i))$ is the strict preference threshold,$q_j(g_j\left(a_i\right))$ is the weak preference threshold, and $v_j(g_j(a_i))$ is the veto threshold for each of the actions $a_i$ varying from 1 to n. The performance distribution of ${ g }_j{(a}_i)$ actions has an arithmetic mean value of $\mu$ and a standard deviation value of:

$$\sigma =\sqrt[\mathsf{2}]{{\displaystyle \frac{\mathsf{1}}{n}}}{\sum }_{i=\mathsf{1}}^n({g_j{(a}_i)-\mu )}^{\mathsf{2}}$$

(6)

$$v_j=\gamma \times \sigma$$

(7)

$$q_j=\alpha \times \sigma$$

(8)

$$p_j=\beta \times \sigma$$

(9)

Equations (7)–(9) utilize predefined percentage values, where γ is initially set at 50%, α at 5%, and β at 10%. The performance objective can be either maximization or minimization.

Each comparison is the binary outranking relationship noted $S_j$ on $A\times A$ to construct a subset $R=\left[\left(a_{\mathsf{1}},a_{\mathsf{2}}\right);\left(a_{\mathsf{1}},a_{\mathsf{3}}\right);\dots ;(a_m,a_n)\right]$ of each pseudo-criterion according to the preference thresholds determined. The method uses the two thresholds noted $q_j(g_j\left(a_i\right)),p_j(g_j\left(a_i\right))$ to compare them to the value of the numerical difference between the two performances of two actions $a_{\mathsf{1}} \mathrm{and} a_{\mathsf{2}}$ as well as to all other pairs. Once thresholds are defined, the method assesses how much better or worse one alternative is compared to another. This is captured by outranking relationships using the thresholds. To illustrate the influence of thresholds on decision making, consider two retrofit strategies evaluated on the economic cost criterion. Suppose Strategy A costs 1000 DZD and Strategy B costs 1050 DZD. If the weak preference threshold (q) is 60 DZD and the strong preference threshold (p) is 100 DZD:

• If the cost difference is below q (e.g., 50 DZD), the two strategies are considered indifferent.
• If the cost difference falls between q and p (e.g., 70 DZD), a weak preference is expressed.
• If the difference exceeds p (e.g., 120 DZD), a strong preference is established.
• If the difference exceeds the veto threshold (e.g., 350 DZD), the alternative is considered unacceptable, and the outranking is blocked.

This framework enables the method to incorporate the decision maker’s tolerance for uncertainty or imprecision, reflecting more realistic decision behaviors.

Equations (10)–(13) describe these pairwise decision rules, guiding how to interpret the comparison between two actions under a given criterion. According to Figueira [48], preferences are defined as follows:

$$g_j\left(a_{\mathsf{1}}\right)- g_j\left(a_{\mathsf{2}}\right) >{ p_j(g}_j(a_{\mathsf{2}}))\iff a_{\mathsf{1}}{P}_j a_{\mathsf{2}}$$

(10)

$$q_j{(g}_j\left(a_{\mathsf{2}}\right)) <{ g}_j\left(a_{\mathsf{1}}\right)-g_{j }\left(a_{\mathsf{2}}\right) \le {{ p}_j(g}_j(a_{\mathsf{2}}))\iff a_{\mathsf{1}}{Q}_j{a}_{\mathsf{2} }\mathrm{hesitation} \mathrm{between} I_j \mathrm{and} P_j$$

(11)

$${-q}_j{(g}_j(a_{\mathsf{1}})) \le { g}_j\left(a_{\mathsf{1}}\right)-g_j\left(a_{\mathsf{2}}\right){\le q}_j(g_j\left(a_{\mathsf{2}}\right)\iff a_{\mathsf{1} }{I}_j{a}_{\mathsf{2}}$$

(12)

Equations (10)–(12) highlight that $a_{1 }$ is at least as good ${ a}_2$ for criterion j.

$$a_{\mathsf{1}}{ S}_j{a}_{\mathsf{2}} \mathrm{with} S_j={ P}_j\bigsqcup Q_j\bigsqcup I_j$$

(13)

(3) 

Concordance and Discordance Indices:

The method next evaluates how many criteria support the outranking assertion between two alternatives. This is called the concordance index.

According to Stephan [51] partial concordance is relative to each criterion j by comparing all pairs of actions in set A. It is defined for j by:

$${ c}_j(a_{\mathsf{1}},a_{\mathsf{2}})=\left\{\begin{array}{l}\mathsf{1},if g_j(a_{\mathsf{1}})+q_j\ge { g}_j(a_{\mathsf{2} })\\ \mathsf{0},if g_j(a_{\mathsf{1}})+p_{j }\le g_j(a_{\mathsf{2} })\\ otherwise,{\displaystyle \frac{{ g}_j\left(a_{\mathsf{1}}\right)+p_j-g_j\left(a_{\mathsf{2}}\right)}{p_j- q_j}}\end{array}\right.$$

(14)

The global concordance indices $C$($a_i$, ${ a}_j)$ on the m rows and m columns for any $(a_i,a_j)\in A\times A$, therefore allowing all comparisons of all pairs of actions. The next step in the method is to determine the global concordance indices between each of the action pairs evaluated by the set of all criteria and defined by Equation (15). $C^S(a_{\mathsf{1}},a_{\mathsf{2}})$= {j:$a_{\mathsf{1}}{S}_j{a}_{\mathsf{2}}$} forms the group of criteria favorable to the assertion $a_{1}S a_2$ and $C^Q(a_{\mathsf{1}},a_{\mathsf{2}})=\left\{j:a_{\mathsf{1}}{Q}_j{a}_{\mathsf{2}}\right\}$ is the group hesitating between indifference and opposition:

$$C(a_{\mathsf{1}},a_{\mathsf{2}})={\sum }_{j Є{ C}^S(a_{\mathsf{1}},a_{\mathsf{2}})}{W}_j+{\sum }_{j Є{ C}^Q(a_{\mathsf{1}},a_{\mathsf{2}})}{W}_j{\phi }_j$$

(15)

$${\phi }_j={\displaystyle \frac{g_j(a_{\mathsf{1}})-g_j(a_{\mathsf{2}})+p_j(g_j(a_{\mathsf{1}}))}{p_j(g_j(a_{\mathsf{1}})) -q_j(g_j(a_{\mathsf{1}}))}}$$

(16)

The veto threshold plays a crucial role in the discordance calculation. It represents a performance level so poor that, regardless of favorable outcomes in other criteria, the alternative is considered unacceptable. It acts as a hard constraint, effectively nullifying the outranking relation if violated. Discordance expresses opposition to the assertion $a_{\mathsf{1}}S a_{\mathsf{2}}$ with the veto threshold, which can at the same time be weakened to avoid the overly unfair exclusion of positive results acquired by ${ a}_{\mathsf{1}}$. The partial discordance index is expressed by Equation (17):

$$d_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)=\left\{\begin{array}{l}\mathsf{1},if{ g}_j\left(a_{\mathsf{2}}\right)>{ g}_j\left(a_{\mathsf{1}}\right)+v_j(g_j(a_{\mathsf{1}}))\\ \mathsf{0},if {g_j\left(a_{\mathsf{2}}\right) \le g}_j\left(a_{\mathsf{1}}\right)+p_j(g_j(a_{\mathsf{1}}))\\ otherwise,{\displaystyle \frac{g_j\left(a_{\mathsf{1}}\right)-g_j\left(a_{\mathsf{2}}\right)+p_j(g(a_{\mathsf{1}}))}{{p_j(g}_j(a_{\mathsf{1}}))-v_j(g_j(a_{\mathsf{1}}))}}\end{array}\right.$$

(17)

However, not all criteria may agree. Some may strongly oppose the outranking relation—especially when the performance difference violates the veto threshold. This opposition is captured by the discordance index, defined in Equation (17). A high discordance can cancel out the concordance and prevent outranking.

(4) 

Credibility Index and Final Ranking:

The result of the distillation procedure is typically a partial preorder: a ranking system where alternatives are compared in pairs, but not all pairs are strictly ranked. Some alternatives may be incomparable or deemed equivalent, reflecting indifference or hesitation. This partial ordering is more realistic for complex, multi-criteria problems than a rigid total order. For instance, a partial preorder in ELECTRE III means that Strategy A might be ranked higher than B, and B higher than C—but A and C may remain incomparable if evidence is inconclusive. This reflects real-world uncertainty.

For the credibility index, according to Stephan [51], each pair of ordered actions $\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)\in A\times A$ is evaluated by criteria $g_j\in F$ to judge the assertion $a_{\mathsf{1}}{S}_j{a}_{\mathsf{2}}$. It is characterized by a credibility index ${\sigma }_s\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)\in [\mathsf{0},\mathsf{1}]$:

$${ \sigma }_s\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)=C\left(a_{\mathsf{1}},a_{\mathsf{2}}\right){\prod }_{j=\mathsf{1}}^n{T}_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right), j Є D_c$$

(18)

With

$$D_c\left(a_{\mathsf{1}},a_{\mathsf{2} }\right)=\left\{j Є F: d_j(a_{\mathsf{1}},a_{\mathsf{2}}) > C\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)\right\}$$

(19)

And

$$T_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)={\displaystyle \frac{\mathsf{1}-d_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)}{\mathsf{1}-C\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)}}$$

(20)

If and only if

$$d_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right) > C\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)$$

(21)

And

$$T_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)=\mathsf{1} \mathrm{when}{ d}_j\left(a_{\mathsf{1}},a_{\mathsf{2}}\right) \le C\left(a_{\mathsf{1}},a_{\mathsf{2}}\right), \mathrm{So} {\sigma }_s\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)=C\left(a_{\mathsf{1}},a_{\mathsf{2}}\right)$$

(22)

According to Roy and Bouyssou [50], it is first necessary to construct the square matrix of credibility indices with values varying from [0, 1] using the above Equations (20)–(22). A credibility index discrimination threshold s(λ) with ${\lambda =\sigma }_s(a_{\mathsf{1}},a_{\mathsf{2}})$ is applied to the indices to determine a set of hierarchical equivalence classes D included in A. A top-down distillation results in a ranking from the best to the least good alternative in a complete preorder Z1, while a bottom-up distillation, following a similar iterative process but starting from the least good to the best, produces Z2, a complete preorder constructed by antagonistic action. A partial preorder Z, resulting from the intersection of Z1 and Z2, provides the final ranking. A partial pre-order Z resulting from the intersection of Z1 and Z2 gives the final ranking.

(5) 

Sensitivity Analysis:

In ELECTRE III, a monotonic function ensures evaluation consistency by maintaining a logical and predictable relationship between criterion performance and ranking. Specifically, an improvement in a criterion’s value—such as reduced CO₂ emissions or lower energy consumption—should result in a stable or improved ranking for the corresponding alternative. This prevents scenarios where a better-performing strategy is unjustifiably ranked lower than a weaker one. For example, if Strategy A is ranked above Strategy B and A subsequently improves its insulation performance, monotonicity guarantees that A will retain its position above B, unless B also improves.

In the context of sensitivity analysis, the monotonic function is used to regulate the discrimination threshold applied to the credibility index, ensuring that as the index increases, so does the level of preference. This mechanism allows ELECTRE III to maintain the relative coherence of rankings under changes to threshold parameters. The discrimination threshold is typically modeled using a linear monotonic function:

s(λ) = α + βλ

(23)

where the parameters are commonly set to α = 0.3 and β = −0.15. Adjusting these values allows exploration of how sensitive the ranking is to variations in credibility, further reinforcing the robustness and interpretability of the decision-making process.

3. Case Study

The case study is situated in the town of Tlemcen, within the municipality of Mansourah. This municipality falls under zone B according to the Algerian technical regulations [36,37], a region identified by Ouahab [52] as one of the most energy-intensive areas in the country. Tlemcen, located in northwestern Algeria at 34.56° latitude, 1.19° longitude, and an altitude of 830 m, experiences a Mediterranean climate with two distinct seasons (Figure 4). The cold winter, lasting from October to April, features significant diurnal temperature variations, with an average daily minimum of 3 °C and a humidity level of 74%. In contrast, the hot, dry summer lasts from June to September, with an average daily maximum temperature of 33 °C and a humidity level of 61%. Seasonal variations also influence wind patterns, with prevailing southwest winds in winter and cooler northwest winds in summer.

Between 1970 and 1985, Algeria extensively developed prefabricated housing, particularly in climate zones A and B, using various industrialized construction techniques. The buildings analyzed in this study were constructed using the tool formwork method, specifically the half-shell transverse tunnel technique, for the execution of transverse walls, floor slabs, and roof elements.

The case study focuses on Cité des Roses, a residential complex located west of Tlemcen. The complex comprises 20 identical buildings, each consisting of a ground floor and three upper stories, totaling 320 dwellings. Each floor contains four apartments accessed via a central stairwell. The buildings are elevated on a 1.50 m crawl space and were constructed without any thermal insulation—one of the defining characteristics of Algeria’s aging housing stock. Additionally, the buildings’ layout, with their parallel configuration and generous spacing, facilitates pronounced thermal interaction between indoor and outdoor environments (Figure 5 and Figure 6).

Cité des Roses exemplifies the broader thermal inefficiencies that typify prefabricated housing built in Algeria during the 1970s and 1980s. Its construction is marked by a lack of insulation, the use of single-glazed wooden windows, and high levels of air infiltration due to poor airtightness at panel joints. These deficiencies are particularly problematic in Tlemcen’s Mediterranean climate, which is characterized by significant seasonal thermal variation. Furthermore, the uniform architectural design, repetitive apartment layouts, and consistent construction materials across the site make this complex an ideal model for testing scalable and replicable retrofit solutions. These features justify the selection of Cité des Roses as a representative case for assessing energy retrofit strategies within the framework of Algeria’s national energy efficiency policy.

Table 1. Building’s materials.

Elements	Outside to Inside Layers	Composition	Thickness (m)	Thermal Conductivity λ (W·m−1·K−1)	$\mathbf{Density}\mathsf{\rho }$ (Kg/m3)	Specific Heat Capacity Cp (J·Kg−1·K−1)
North exterior wall (load-bearing)	1	Cement mortar	0.02	1.15	1800	1080
	2	Concrete	0.15	2.5	2500	1000
	3	Plaster	0.02	0.57	1300	1000
Exterior wall (East/West)	1	Cement mortar	0.02	1.15	1800	1080
	2	Hollow brick	0.1	0.48	900	936
	3	Air gap	0.05	0.025	1.23	1008
	4	Hollow brick	0.05	0.48	900	936
	5	Plaster	0.02	0.57	1300	1000
Interior wall (load-bearing)	1	Plaster	0.02	0.57	1300	1000
	2	Concrete	0.15	2.5	2500	1000
	3	Plaster	0.02	0.57	1300	1000
Interior wall	1	Cement mortar	0.02	1.15	1800	1080
	2	Hollow brick	0.10	0.48	900	936
	3	Cement mortar	0.02	1.15	1800	1080
Ground and upper floors	1	Concrete	0.10	2.5	2500	1000
	2	Concrete screed	0.05	1.15	1800	1080
	3	Tiles	0.03	2.1	2200	336
Roof	1	Water-tightness	0.02	0.04	670	200
	2	Concrete screed	0.07	1.15	1800	1080
	3	Concrete	0.1	2.5	2500	1000
	4	Cement mortar	0.02	1.15	1800	1080

presents the composition of building elements from the exterior to the interior. The structures feature load-bearing walls cast on-site using specialized formwork. Both the floors and roofs are constructed from reinforced concrete. The north and south exterior load-bearing walls are made of reinforced concrete, while the east and west walls consist of masonry with an air gap. The windows are single-glazed with wooden frames. Table 1 details the building envelope components, referenced according to technical documents [36,37,53].

3.1. Energy Balance

This study focused on a ground-floor, three-room apartment to assess its compliance with thermal regulations implemented through the RETA application [35], as described by Imessad et al. [54]. Winter heat loss was estimated at 380 W/°C, exceeding the reference value of 345 W/°C, indicating non-compliance with DTR C3-2 [36]. Additionally, the apartment does not meet the requirements of DTR C3-4 [37] due to excessive heat gain through both opaque and glazed walls, with the main issue stemming from opaque walls and floors. To analyze energy consumption, a survey was conducted among 80 ground-floor, three-room apartments (67.48 m² each), yielding responses from 66 units.

After calculating the average annual energy consumption for this type of apartment over four years, the results indicate a cumulative average gas and electricity consumption of 214.43 kWh/m² per year. The survey, based on responses from 66 apartments, provided insights into indoor thermal comfort (Figure 7). During summer, most residents reported discomfort, while in winter, opinions were nearly evenly split between those who found the apartment comfortable and those who experienced discomfort.

The analysis also reveals that occupants used heating from October to March and cooling from June to September.

Table 2. Equipment layout and power.

Spaces	Equipment	Design Level (W)	Lighting Level (W)
Living room	Television	140	40
	Iron	925
	Vacuum cleaner	720
	Laptop	60
Bedrooms	Hairdryer	450	30
	Laptops	60
Kitchen	Refrigerator	175	20
	Stove with oven	1500
	Robots	150
Bathroom	Washing machine	500	20

presents the most commonly used electrical equipment and lighting sources, with specific characteristics referenced from the literature [55]. These parameters were incorporated into EnergyPlus 9.2 for simulation. The apartment was assumed to be occupied by a family of four, with occupancy patterns and appliance usage derived from the survey responses.

3.2. Validation of the Simulation Model

On-site measurements were conducted in the target apartment, a ground-floor, three-room unit. Measuring devices were installed in the parents’ bedroom (Figure 6a), which faces southwest and connects to the exterior through two walls of different compositions. Residents identified this room as the least comfortable. Heating and air conditioning were excluded from the measurements. The indoor air temperature sensor was positioned at the center of the room at a height of 0.80 m. To compare recorded indoor temperatures with simulated values, a Meteoblue weather data file was integrated for the measurement period.

Figure 8 illustrates the outdoor temperature variation on 13 January 2018, a winter day characterized by an exponential rise in temperatures. The lowest temperature, 4.44 °C, was recorded at 1 a.m., while the maximum of 13.40 °C occurred at 4 p.m. Indoor temperatures, both measured and simulated, reached their lowest point of approximately 12 °C at 1 a.m. As outdoor temperatures increased, indoor temperatures followed a similar trend, peaking at 5 p.m. with a one-hour time lag before declining in the evening. The measured and simulated temperatures exhibited a comparable pattern, with the simulated values slightly lower at the start of the day. However, calculations indicate a low relative mean deviation over 24 h.

Figure 9 presents the outdoor temperature variation on 23 July 2019. The minimum temperature of 23.68 °C was recorded at 6 a.m., rising to a peak of 32.08 °C around 3 p.m. before decreasing in the evening. The simulation and measurement temperature curves followed a similar trend, with indoor temperatures reaching their peak around 6 p.m., showing a three-hour delay compared to outdoor conditions. Although the recorded experimental temperatures were slightly lower than the simulated values, the average relative deviation remained within an acceptable range.

Table 3. Relative deviations between measurements and simulation.

Hours	Day of 13 January			Day of 23 July
	Measures (°C)	Simulation (°C)	Relative Deviation	Measures (°C)	Simulation (°C)	Relative Deviation
1	11.92	11.83	0.007	26.99	27.38	0.014
2	11.99	11.87	0.009	26.92	26.62	0.011
3	12.17	11.66	0.041	26.80	26.26	0.020
4	12.11	11.44	0.054	26.74	25.96	0.028
5	12.05	11.25	0.065	26.61	25.79	0.030
6	11.99	11.10	0.073	26.49	25.62	0.032
7	11.92	10.98	0.078	26.61	27.55	0.035
8	11.99	11.00	0.081	26.49	27.90	0.053
9	12.17	10.89	0.104	26.96	28.17	0.044
10	12.36	11.17	0.096	27.15	28.49	0.049
11	13.01	11.68	0.101	27.99	28.90	0.032
12	13.86	12.35	0.108	28.35	29.47	0.039
13	14.42	13.26	0.080	28.75	30.07	0.045
14	14.61	14.26	0.023	29.45	30.68	0.041
15	14.55	15.10	0.038	29.67	31.26	0.053
16	14.67	15.80	0.077	29.53	31.77	0.075
17	14.99	16.08	0.075	29.82	32.17	0.078
18	14.74	15.97	0.083	29.99	32.32	0.077
19	14.55	15.64	0.075	29.99	32.21	0.074
20	14.74	15.40	0.045	29.56	31.78	0.075
21	14.74	15.25	0.035	29.20	31.36	0.073
22	14.61	15.41	0.054	28.97	29.42	0.015
23	14.49	14.80	0.021	28.35	28.83	0.016
24	14.42	14.42	0.000	28.25	27.83	0.014
1	14.36	14.16	0.013	28.15	27.33	0.028

presents the relative deviation calculations, with an average deviation of 5% on 13 January 2018, and 4% on 23 July 2019. In engineering applications, deviations below 10% are considered acceptable. Such discrepancies likely result from internal disturbances and the limitations of measuring equipment. Consequently, the simulation model can be considered validated.

Prefabricated buildings are known for their rapid construction; however, they often suffer from poor airtightness due to inadequate panel connections and material degradation [56,57]. Additionally, poorly fitted windows and doors contribute to high infiltration rates in these structures, as noted by Halik et al. [58].

Figure 10 illustrates the impact of different air infiltration rates per hour on energy consumption, as determined through simulation. Under uncontrolled air renewal conditions (V = 2), the top-floor dwelling exhibits the highest energy demand, estimated at 178 kWh/m² per year. For a ground-floor dwelling, the estimated annual energy consumption is 162.89 kWh/m², with 115.51 kWh/m² allocated to heating and 47.38 kWh/m² to cooling. When lighting, electrical appliances, and gas equipment consumption are included, the total energy demand reaches 212.48 kWh/m² per year. This value closely aligns with the previously calculated average consumption based on utility bills, which was approximately 214.43 kWh/m² per year.

It should be noted that in the winter, high levels of air infiltration significantly increase consumption. The primary energy consumption for this type of dwelling is estimated at 324.2 kWh_pe/(m²·year) for the ground floor and 372.93 kWh_pe/(m²·year) for the top floor. These buildings are classified as F under the European Energy Label and G under the Climate Label [59].

4. Results and Discussion

4.1. Energy Consumption After Retrofit

Retrofit strategies can be implemented through both interior and exterior interventions. The selection and placement of insulation are determined by the decision maker, considering the building’s architectural, economic, and climatic contexts. Exterior retrofitting offers various installation and finishing options, allowing flexibility in the facade’s appearance. Since the studied buildings are not classified as protected heritage, this study explores two exterior insulation options—cladding and rendering—alongside interior insulation (Figure 11).

Various insulation materials were selected for the proposed retrofit strategies (

Table 4. Retrofit strategies for internal insulation.

Type of Insulation	Strategy	Composition	Thickness (m)	Thermal Conductivity λ (W·m−1·K−1)	Density $\mathsf{\rho }$ (Kg/m3)	Specific Heat Capacity Cp (J·Kg−1·K−1)
Internal insulation	S1	Rock wool	0.2	0.041	26	612
	S2	Cork panels	0.2	0.040	120	1670
	S3	Expanded polystyrene (EPS)	0.15	0.038	30	1404
	S4	Polyurethane (PU)	0.15	0.029	25	1300
	S5	Cellular glass	0.23	0.045	120	1100
	S1, S2, S3, S4, S5	Plasterboard	0.013	0.35	900	1460

,

Table 5. Retrofit strategies for external wall insulation with render.

Type of Insulation	Strategy	Composition	Thickness (m)	Thermal Conductivity λ (W·m−1·K−1)	Density $\mathsf{\rho }$ (Kg/m3)	Specific Heat Capacity Cp (J·Kg−1·K−1)
External wall insulation with render	S6	Rock wool	0.2	0.041	26	612
	S7	Cork panels	0.2	0.040	120	1670
	S8	Expanded polystyrene (EPS)	0.15	0.038	30	1404
	S9	Polyurethane (PU)	0.15	0.029	25	1300
	S10	Phenolic foam	0.11	0.022	30	1300
Render	S7	Organic base coat	0.007	0.87	1800	1080
		Organic finishing render	0.006	0.87	1800	1080
	S6, S8, S9, S10	Mineral base coat	0.007	0.57	1400	1080
		Mineral finishing render	0.006	0.76	1700	1080

and

Table 6. Retrofit strategies for external wall insulation with cladding.

Type of Insulation	Strategy	Composition	Thickness (m)	Thermal Conductivity λ (W·m−1·K−1)	Density $\mathsf{\rho }$ (Kg/m3)	Specific Heat Capacity Cp (J·Kg−1·K−1)
External wall insulation with cladding	S11	Rock wool	0.2	0.041	26	612
	S12	Cork panels	0.2	0.040	120	1670
	S13	Expanded polystyrene (EPS)	0.15	0.038	30	1404
	S14	Polyurethane (PU)	0.15	0.029	25	1300
	S15	Glass wool	0.15	0.04	40	800
	S16	Cellular glass	0.23	0.045	120	1100
Cladding	S11, S12	Scots pine wood	0.022	0.15	450	2160
	S13, S15	Polyvinyl chloride	0.015	0.17	1380	1046
	S14, S16	Fiber cement	0.012	0.58	1800	1500

) to facilitate a comparative analysis. The chosen solutions include both durable and less environmentally friendly materials, all of which effectively reduce energy consumption and CO₂ emissions. Common intervention strategies include roof insulation, low floor insulation, and window replacement to assess the impact of insulation placement, whether interior or exterior. The proposed window replacement involves PVC (polyvinyl chloride) frames with 4 mm double glazing and a 6 mm air gap. Additionally, both types of exterior facade insulation require the restoration of the original facade.

In addition to the specific retrofit configurations applied to internal and external walls, several construction layers are common across all the proposed strategies. These include standardized treatments for the ground and upper floors as well as for the roof components.

Table 7. Materials used across all retrofit strategies.

Type of Insulation	Strategy	Composition	Thickness (m)	Thermal Conductivity λ (W·m−1·K−1)	Density $\mathsf{\rho }$ (Kg/m3)	Specific Heat Capacity Cp (J·Kg−1·K−1)
Ground floor and upper floor		Polystyrene (EPS)	0.15	0.038	30	1404
	For all	Concrete	0.10	2.5	2500	1000
	strategies	Concrete screed	0.05	1.15	1800	1080
		Tiles	0.03	2.1	2200	336
Roof		Water-tightness	0.02	0.04	670	200
		Airium®	0.1	0.05	180	1001
	For all	Concrete	0.1	2.5	2500	1000
	strategies	Rock wool	0.2	0.041	26	612
		Plasterboard	0.013	0.35	900	1460

presents the thermal and physical properties of these shared materials, ensuring consistency in the comparative analysis of the retrofit scenarios.

The simulation of various retrofit strategies demonstrated a significant reduction in initial energy consumption. Figure 12 and Figure 13 illustrate the improvements for the top-floor apartment, which initially consumed 178 kWh/(m²·year), including 106.26 kWh/(m²·year) for heating and 71.74 kWh/(m²·year) for cooling. Figure 12 presents three proposed strategies that achieve a total energy consumption reduction of 70.3% to 72.5%.

The heating demand saw the most significant reduction, ranging from 88.9% to 94.4%, while air-conditioning consumption decreased by 39.2% from 42.7%. After retrofitting, the first-floor apartment’s energy consumption is estimated at 200.77 kWhpe/(m²·year), placing it in class D on the energy label. Among the retrofit strategies, cladding insulation proved to be the most effective in reducing heating demand, whereas rendered external insulation was the best for lowering air-conditioning consumption, second only to internal insulation.

Figure 13 illustrates that combining heating and cooling savings can result in a reduction of up to 129 kWh/(m²·year), with the most notable impact observed in heating requirements. The total energy consumption across different strategies shows no significant variations, with the largest difference estimated at 4.74 kWh/(m²·year). Heating demand varies slightly between the strategies, with a maximum difference of 6.4 kWh/(m²·year), while cooling differences remain minor at 3.27 kWh/(m²·year). These small variations indicate that optimal insulation (achieving a 70% to 72.5% energy reduction) effectively regulates energy gains and losses, ultimately limiting the differences between strategies.

The thermal properties of the materials remained similar, and the simulation parameters were kept constant. Among the three insulation methods, exterior insulation strategies proved to be the most effective. In winter, cladding strategies perform well by limiting thermal bridges, utilizing air space as a buffer between the interior and exterior, and preserving the thermal inertia of the walls. However, as shown by the histogram, their performance declines in summer. The exposure of the air space to solar gain, along with the materials used for cladding, can reduce overall efficiency.

Rendered exterior insulation strategies offer a more balanced performance, as they minimize thermal bridges through insulation continuity and homogeneity while maintaining the walls’ thermal inertia. In contrast, interior insulation strategies are generally less effective, particularly in winter, due to the presence of thermal bridges and limited thermal inertia, making them more susceptible to climatic fluctuations.

4.2. Variation in Indoor Temperature After Retrofit

To identify additional differences between strategies, the thermal behavior of the building envelope in relation to indoor temperatures was analyzed. A comparison of indoor temperature variations over time before and after the energy retrofit was conducted for two extreme seasons (21 January and 6 August). The simulation results illustrate temperature fluctuations in the southwest-facing parents’ bedroom on the top floor.

The simulated strategies provide insight into how insulation positioning influences interior temperatures. Polyurethane insulation can be applied internally (S₄), externally under plaster (S₉), or externally under fiber cement cladding (S₁₄). This comparison is based on identical insulation technical characteristics, including thickness, thermal conductivity, and specific heat while maintaining internal heat gains and excluding heating.

On the winter day shown in Figure 14, the highest and most comfortable indoor temperature, ranging from 19 °C to 20 °C, was achieved with exterior insulation under cladding (S₁₄). A maximum temperature difference of approximately 9 °C was observed between the pre-retrofit state and insulation under cladding (S₁₄), while the difference between insulation under cladding (S₁₄) and interior insulation (S₄) was nearly 3 °C. The temperature variation between insulation from the inside (S₄) and exterior insulation under plaster (S₉) reached 1.21 °C.

Additionally, in all three insulated scenarios, interior temperatures remained stable due to the reduction in both external and internal disturbances. As illustrated in Figure 14, a sharp indoor temperature peak of 2.87 °C occurred around 7–8 a.m. in the initial state, triggered by internal heat gain (such as the use of a hairdryer), leading to a sudden rise in room temperature.

This disturbance persisted for some time before stabilizing around 9 a.m. In insulated cases, peak temperatures were reduced as heat gradually dissipated, with less heat lost through the envelope due to the wall’s thermal inertia. Rehman [60] confirmed the impact of insulation on interior temperature fluctuations caused by both climatic conditions and internal heat gains. In uninsulated buildings, temperature disturbances resulting from envelope heat loss and internal gains contribute to occupant discomfort and increase energy demand, as heating and air-conditioning systems operate at full capacity to maintain comfort.

Figure 15 illustrates the differences between outdoor and indoor temperatures on August 6th, a day characterized by high temperatures reaching a maximum of 34.30 °C before decreasing in the evening. The simulation conditions included night ventilation without air conditioning. Indoor temperatures followed the same pattern as outdoor temperatures, with higher values in the pre-retrofit state, highlighting sensitivity to external climatic variations.

Indoors, the highest temperature occurred around 6 pm, with a two-hour lag compared to the outdoor peak. After retrofitting, all insulation strategies effectively reduced indoor temperatures, though differences were minor compared to the winter scenario. The S₉ and S₁₄ insulation strategies, when superposed, yielded identical results and proved the most effective, with a maximum difference of 3.61 °C at 8 h from the pre-retrofit state. The S₄ strategy showed similar performance, with a maximum temperature difference of nearly 1 °C at 18 h. Due to controlled ventilation, post-retrofit temperatures remained consistent in the morning and evening across all three strategies.

The difference between strategies was less significant in the summer, although all solutions effectively limited solar gain. In contrast, the effectiveness of insulation and the variation in indoor temperatures were more pronounced during the winter. According to Bendouma [61], the air gap in under-slab insulation acts as a barrier that reduces heat loss in winter while facilitating the evacuation of accumulated heat from the cladding in summer. However, in high-temperature climates, this air gap may also introduce warm air, reducing its overall effectiveness. The presented results highlight the relevance of using a selection aid method to further analyze other comparative parameters.

4.3. Applying the ELECTRE III Method

As outlined in the Section 2, the potential actions defined by Figueira et al. [48] as A = {a₁, a₂, …, aₘ} are referred to as strategies in our case and denoted as S = {S₁, S₂, …, Sₘ}. The selection of criteria is tailored to align with the decision maker’s needs, which, in this study, is assumed to be the state. Accordingly, the priorities (criteria) have been determined. For interior and exterior insulation strategies (S₁ to S₁₀), the same selection criteria apply, whereas for exterior insulation under cladding (S₁₀ to S₁₆), different criteria are introduced due to the distinct analytical requirements of this study. The SRF method is employed to compute normalized weights for z = 6.5 and z = 8.67. The normalized weights are illustrated in the appendix

Table A1. Determination of normalized criteria weights with z = 6.5 and T = 13.

Position	Criteria	Non-Normalized Weights	Normalized Weights
1	CO2	1	4.82
1	Sustainability	1	4.82
1	Health hazard	1	4.82
(2) *	/	/	/
3	Acoustic comfort	2.10	10.12
(4), (4)	/	/	/
5	Fire resistance	3.75	18.07
(6), (6)	/	/	/
7	Economic cost	5.40	26.02
(8)	/	/	/
9	Energy consumption	6.50	31.33

* Positions in brackets () indicate blank cards. Criteria are ranked from least to most important.

and

Table A2. Determination of normalized criteria weights with z = 8.67 and T = 13.

Position	Criteria	Non-Normalized Weights	Normalized Weights
1	CO2	1	3
1	Installation	1	3
(2) *	/	/	/
3	Acoustic comfort	2.53	7.59
(4)	/	/	/
5	Maintenance	4.07	12.21
5	Service life	4.07	12.21
6	Fire resistance	4.84	14.53
(7)	(7)	/	/
(8)	(8)	/	/
9	Economic cost	7.14	21.43
(10)	(10)	/	/
11	Energy consumption	8.67	26.03

* Positions in brackets () indicate blank cards. Criteria are ranked from least to most important.

.

Table 8. Performances of the strategies and thresholds for internal insulation.

Strategies	Criteria
	C1	C2	C3	C4	C5	C6	C7
Rock wool (S1)	43	3	2,526,154.00	617,134.00	7	8	6
Cork panels (S2)	−27	8	2,512,601.00	883,748.00	4	7	8
Expanded polystyrene (EPS) (S3)	10	2	2,548,504.00	638,794.00	4	3	2
Polyurethane (PU) (S4)	16	3	2,519,706.00	703,781.00	3	5	2
Cellular glass (S5)	25	6	2,511,489.00	812,089.00	8	5	5
Normalized weight z = 6.5	4.82	4.82	31.33	26.020	18.07	10.12	4.82
Indifference threshold	6.92	0.67	4046.12	30,628.10	0.58	0.52	0.7
Preference threshold	18.45	1.79	10,789.67	81,674.94	1.55	1.39	1.87
Veto threshold	34.6	3.36	20,230.64	153,140.53	2.9	2.62	3.5
Objective	MIN	MAX	MIN	MIN	MAX	MAX	MAX

,

Table 9. Performances of the strategies and thresholds for insulation with render.

Strategies	Criteria
	C1	C2	C3	C4	C5	C6	C7
Rock wool (S6)	43	3	2,397,499.00	717,736.00	7	8	6
Cork panels (S7)	−27	8	2,323,415.00	934,377.00	4	7	8
Expanded polystyrene (EPS) (S8)	10	2	2,412,908.00	739,423.00	4	3	2
Polyurethane (PU) (S9)	16	3	2,395,679.00	804,410.00	3	5	2
Phenolic foam (S10)	85	1	2,397,955.00	804,277.00	6	3	6
Normalized weight z = 6.5	4.82	4.82	31.33	26.02	18.07	10.12	4.82
Indifference threshold	3.72	0.24	3164.95	7553.40	0.14	0.20	0.24
Preference threshold	11.17	0.72	9494.85	22,660.22	0.44	0.61	0.72
Veto threshold	33. 51	2.17	28,484.56	67,980.66	1.32	1.83	2.16
Objective	MIN	MAX	MIN	MIN	MAX	MAX	MAX

and

Table 10. Performances of the strategies and thresholds for insulation with cladding.

Strategies			Criteria
	C1	C2	C3	C3′	C4	C5	C6	C8
Rock wool + wood (S11)	63	30	2,364,784.00	3	1,452,781.00	6	8	6
Cork panels + wood (S12)	−7	30	2,429,512.00	4	1,698,986.00	3	6	6
Expanded polystyrene (EPS) + PVC (S13)	35	40	2,365,168.00	5	1,184,716.00	2	4	8
Polyurethane (PU) + fiber cement (S14)	36	50	2,361,545.00	7	1,356,139.00	5	6	4
Glass wool + PVC (S15)	68	40	2,360,687.00	4	1,139,540.00	7	6	6
Cellular glass + fiber cement (S16)	45	50	2,361,207.00	8	1,464,424.00	8	6	2
Normalized weight z = 8.67	3	12.21	26.03	12.21	21.43	14.53	7.59	3
Indifference threshold	3.25	2.64	9173.75	0.65	68,846.06	0.78	0.42	0.69
Preference threshold	10.85	8.80	30,579.17	2.16	229,486.88	2.59	1.41	2.30
Veto threshold	27.71	17.61	61,158.35	4.33	458,973.75	5.18	2.83	4.62
Objective	MIN	MAX	MIN	MAX	MIN	MAX	MAX	MAX

present the performance evaluation of different insulation strategies based on a set of eight criteria, labeled from C1 to C8 for clarity and consistency. These criteria include:

• C1—CO₂ emissions (Kg CO₂/m²);
• C2—Sustainability and recycling potential;
• C3—Energy consumption (Wh/year);
• C3′—Maintenance;
• C4—Economic cost (DZD);
• C5—Fire resistance scoring;
• C6—Acoustic comfort scoring;
• C7—Health hazard scoring;
• C8—Installation convenience scoring.

The table also outlines the normalized weights, indifference, preference, and veto thresholds for each criterion, which are essential parameters for the multi-criteria decision-making process applied in this study.

Sustainability and recycling, fire resistance scoring, acoustic comfort scoring, and health hazard scoring are evaluated on a scale from 1 to 8, where 1 represents the lowest rating (poor) and 8 signifies the highest rating (excellent).

4.3.1. Interior Insulation

The most important criteria are considered to be energy consumption and economic cost, followed by fire resistance in third place. Acoustic comfort ranks next, while health hazard, durability, recycling, and CO₂ emissions are regarded as equally significant.

To clarify how the ELECTRE III thresholds influence the outranking decisions, a specific comparison based on the results in Table 8 is presented. Strategy S₁ (rock wool) and Strategy S₃ (expanded polystyrene) exhibit respective energy consumptions of 2,526,154.00 Wh/year and 2,548,504.00 Wh/year. The absolute difference (22,350 Wh/year) exceeds both the preference threshold (10,789.67 Wh) and the veto threshold (20,230.64 Wh). In this case, energy consumption is a criterion to be minimized. Thus, Strategy S₁, which consumes less energy, is not only preferred over S₃, but this preference is considered strong, as the difference exceeds the veto threshold. Consequently, S₃ is disqualified in comparison to S₁, as its performance is deemed unacceptable beyond the rejection threshold.

The concept of partial preorders is also evident in the case of Strategy S₂ (cork panels) versus Strategy S₅ (cellular glass). While S₂ performs better in environmental terms (C1 = −27 kg CO₂/m²; C2 = 8), S₅ offers advantages in energy consumption (C3 = 2,511,489.00 Wh/year) and fire resistance (C5 = 8). Due to these trade-offs and performance differences that may fall within threshold margins, the ELECTRE III method may classify these strategies as incomparable. This reflects real-world decision-making complexity, where no single alternative dominates across all criteria.

The radar diagram (Figure 16) illustrates the performance of various strategies across different criteria. The results indicate minimal differences in energy consumption, highlighting the complexity of the decision-making process. Among the strategies, S₅, which utilizes cellular glass insulation, has the lowest energy consumption. S₁, incorporating rock wool insulation, is the most effective in terms of acoustic comfort and economic cost but has a negative carbon footprint during production. Compared to S₁, S₂ (cork insulation) is the most environmentally friendly, excelling in CO₂ emissions, durability, and recycling. Regarding the risk of inhaling toxic gases during a fire, S₂ offers the best performance. Strategies S₃ and S₄ produce lower emissions than those using cellular glass (S₅) and rock wool (S₁). In terms of fire resistance, S₅ ranks the highest.

4.3.2. Exterior Insulation with Rendering

According to Figure 17, S₁₀, which includes resolving foam, is highly polluting but performs well in recycling and sound insulation. S₇ is the least energy-intensive, with a positive environmental impact, but it has the highest economic cost when compared to the others. S₆ (rock wool) provides the best acoustic comfort and fire resistance. S₈ and S₉ remain more balanced than S₁₀ in terms of environmental criteria (CO₂ emissions and recycling).

4.3.3. Exterior Insulation with Cladding

Insulation strategies with cladding require the consideration of more subjective criteria, such as the exterior cladding’s resistance to ultraviolet rays, weathering, and mold. Cleaning time, treatment with special products, and reinforcement of the cladding depend on the materials used in its construction. The ease of installation of both insulation and cladding is also taken into account. To ensure a fair comparison, various insulating materials were combined with different claddings of natural, organic, or synthetic origin. As a result, the strategies offer a diverse range of sustainable options. The weights of the criteria are ranked by importance using the revised Simos method (z = 8.67).

Figure 18 shows that the most polluting strategies are S₁₁ and S₁₅, followed by S₁₆. S₁₃ is the most user-friendly installation strategy, while S₁₆ and S₁₅ offer the best fire resistance. Economically, S₁₅ is the least expensive, whereas S₁₂ is the costliest and requires the most maintenance due to its wood cladding, though it is also the most durable. The energy performance of the strategies is comparable, but S₁₅ is the most cost-effective. Strategies S₁₄ and S₁₆, featuring fiber cement cladding, have the longest service lives and do not require routine maintenance. The ranking results are detailed in the following subsection.

To ensure consistency in evaluating the criteria, the direct mode was chosen for the thresholds. A dynamic adaptation allows for a strict analysis based on tolerance that increases with the criterion’s value. Thresholds p, q, and v vary depending on performance or relative gaps between strategies. The discrimination index threshold function s(λ) is used for the sensitivity analysis, as outlined in the Section 2 (Equation (23)).

4.4. Results and Sensitivity Study of the ELECTRE III Method

Figure 19a shows that for interior retrofit strategies with α = 0.3, S₁ is the optimal solution, followed by S₅ in second place. In third place, the decision maker can choose between S₂ and S₄, as their performances are similar. The upward and downward distillation graphs (Figure 19b) reveal a conflict between S₂ and S₄, with no clear dominance between them. In the upward distillation, S₂ ranks first while S₄ is third, whereas in the downward distillation, S₄ takes third place and S₂ falls to fourth.

Several variation scenarios were tested, including reducing indifference thresholds from 30% to 10% of the standard deviation, increasing the preference threshold to 85% with the veto, and adjusting the weights of the criteria while maintaining their relative importance. Despite these modifications, the ranking remains unchanged. Additionally, increasing α from 0.3 to 0.8 does not alter the ranking, confirming the stability and robustness of the results.

Figure 20 illustrates the ranking variations when α = 0.9. Rock wool (S₁) outperforms the selected criteria, eliminating incomparability. In the second and third positions, the strategies are nearly indistinguishable. The ranking becomes less clear due to the high values assigned to the discrimination threshold of the credibility index.

Figure 21a presents the ranking of exterior insulation strategies applied under plaster, with rock wool (S₆) emerging as the dominant option. Its performance reflects a balance across multiple criteria, making it a competitive choice. As shown in the distillation graph (Figure 21b), S₇ ranks second. Despite its high cost, cork insulation (S₇) may be a preferable option for the decision-maker due to its superior environmental and energy performance compared to other strategies. S₈ takes third place, outperforming S₉ and S₁₀, whose rankings remain unchanged. This is primarily because the two most critical criteria—energy efficiency and economic cost—exhibit minimal differences between them.

Figure 21b indicates that rock wool insulation (S₆) remains the dominant strategy in this group. As α increases, the ranking remains stable. When α reaches higher values (α ≥ 0.75), outranking becomes more restricted, causing some strategies to be considered indifferent. This effect is evident in Figure 22 with α = 0.9, where strategies with strong credibility, such as S₆, maintain their ranking. However, as the ranking criteria become more stringent, S₇ and S₈ are now classified as indifferent.

As with internal insulation, changing the threshold parameters q from 10% to 30% and p from 30% to 50% yields the same results. The rankings remain stable, with rock wool continuing to dominate.

Figure 23 and Figure 24 show different rankings for exterior insulation strategies under cladding. The variation in the parameter α affects the final ranking. Setting α = 0.3 reduces tolerance for performance differences between strategies. The model is overly sensitive and takes into account only minor differences. Figure 23a shows that the two best-performing strategies, S₁₄ and S₁₆, are indifferent. This is due to their similar, and sometimes identical, performance characteristics, such as cladding service life and annual energy consumption.

S₁₂ and S₁₅ are incomparable, as shown in Figure 23b, with S₁₂ ranking first and S₁₅ second in the downward breakdown. S₁₃ is ranked third, and S₁₁ is ranked last, dominated by the other strategies, particularly in the maintenance criterion because rock wool combined with wood cladding is more prone to moisture and settlement problems and requires more frequent maintenance.

Raising the threshold to α = 0.6 results in a clearer and more hierarchical ranking, effectively grouping strategies with similar performance, as shown in Figure 24a. S₁₄ remains the top-ranked solution, outperforming S₁₆ in second place, as confirmed by the top-down distillation in Figure 24. This ranking also reinforces S₁₁’s position in last place across both distillations.

In contrast, intermediate strategies shift positions under this less strict threshold. S₁₂ and S₁₃ are now considered indifferent and outperform S₁₅. Further increasing the α parameter to 0.8, as observed in other interior and undercoated scenarios, leads to more clustering of strategies and increased indifference. The variation in α facilitated a sensitivity analysis of the models. However, the literature [50] recommends setting α at 0.3 and β at −0.15.

4.5. Broader Implications for Retrofit Decision Making and Sustainability

The results of this study highlight the complexity inherent in selecting retrofit strategies, particularly in contexts where energy savings, material sustainability, and social factors intersect. The adoption of ELECTRE III as a decision-support tool demonstrates its strength in navigating these conflicting priorities, offering a structured way to handle both technical performance and qualitative aspects such as health, comfort, and ease of installation. This addresses a gap often observed in energy retrofit research, where decisions are typically driven by cost or energy performance alone, overlooking the social and environmental dimensions essential to sustainable development.

These findings resonate with the work of Wu et al. [62], who emphasized the importance of integrating human-centered design, energy optimization, and interdisciplinary approaches in indoor environment strategies. Although their study focused on educational buildings, the methodological parallels are clear: both studies advocate for moving beyond purely energy-focused evaluations to embrace holistic, user-informed frameworks that account for comfort, adaptability, and broader sustainability goals. The convergence of these viewpoints reinforces the growing consensus that future retrofit frameworks must incorporate both objective performance and subjective user experience to be truly effective.

In practice, the identification of optimal strategies—such as rock wool or polyurethane with fiber cement—underscores the need for retrofit guidelines in Algeria to evolve beyond prescriptive technical specifications. Incorporating multi-criteria decision making into policy design could ensure that future retrofitting projects not only meet energy efficiency goals but also contribute to occupant well-being and long-term material sustainability. This aligns with the broader reflections given by Wu et al. [62], which advocate for more adaptable, dynamic, and human-aware building evaluation systems that can respond effectively to diverse climatic and operational conditions.

On a broader scale, this study supports global energy transition priorities by demonstrating that deep energy retrofits can substantially reduce carbon emissions while improving indoor environmental quality. The flexible, criteria-driven methodology proposed here is well-suited for replication in regions with similar architectural and climatic profiles, including much of the Mediterranean and North African context. By combining quantitative simulations, stakeholder-centered evaluation, and regulatory compliance, the approach contributes to Algeria’s sustainability ambitions while offering valuable insights into the future of building retrofits as envisioned by international frameworks such as the UN Sustainable Development Goals (SDGs).

5. Conclusions and Perspectives

This study proposed and validated a sustainable multi-criteria optimization framework for the energy retrofit of collective housing buildings constructed in Algeria between the 1970s and 1980s. Through a combination of on-site surveys, dynamic energy simulations using EnergyPlus, and multi-criteria decision making with the ELECTRE III method, 16 retrofit strategies were evaluated across environmental, economic, and social criteria.

The initial assessment confirmed the poor thermal performance of the studied buildings, with top-floor apartments consuming an average of 178 kWh/(m²·year)—classifying them in energy label class G. After applying the proposed retrofit strategies, simulations demonstrated that total energy consumption could be reduced by up to 72.5%, with heating demand reduced by 94.4% and cooling demand by 43.5%, depending on the choice of insulation material and its placement.

This study compared three types of insulation configurations—internal insulation, external insulation with rendering, and external insulation with cladding. The results show that exterior insulation under cladding (particularly polyurethane combined with fiber cement) offers the highest winter energy savings and the most stable indoor temperatures. For summer cooling demand, rendered exterior insulation proved slightly more efficient.

The multi-criteria analysis identified rock wool as the optimal solution for both internal and rendered exterior insulation, while polyurethane with fiber cement ranked highest among cladding-based strategies, offering a balanced compromise between thermal performance, cost, fire safety, health impact, and sustainability.

Beyond technical outcomes, this study emphasizes the potential for informed, criteria-based retrofit decisions to contribute to Algeria’s national energy transition goals and its commitments under the Sustainable Development Goals (SDG 7 and SDG 11). The framework is designed to be adaptable to other regions and building types, providing a valuable tool for decision makers seeking to enhance the energy efficiency, sustainability, and resilience of existing housing stock.

Future work will explore the impact of hygrothermal conditions on insulation performance and expand the evaluation to include heating system upgrades, renewable energy integration, and solar protection measures, to develop even more comprehensive retrofit strategies.