An Adaptive Selection of Urban Construction Projects: A Multi-Stage Model with Iterative Supercriterion Reduction

Abstract

A high level of urbanization, the growing role of cities, and the increasing urban population have led to a rise in the relevance of the problem of selecting investment projects in urban construction. Along with the usual factors considered in such a selection, regional peculiarities of conducting economic activity in the field of urban construction are gaining particular importance. The necessity of taking them into account requires an improvement in decision-making methods. This study develops a multi-stage adaptive method for multi-criteria project selection in urban construction. The method integrates regulatory requirements, the customer’s vision, and retrospective data on previously implemented projects in the region. It comprises the following sequential stages: the elimination of projects that do not meet the requirements; the construction of integral criteria (weighting functions) using logarithmic transformation; and an iterative reduction in the set of criteria. An experimental verification of the developed method demonstrated its application and revealed its potential for practical use. The proposed method can be effectively employed in urban planning systems and the smart management of urban spaces.

1. Introduction

Relentless urbanization, the growing role of cities, and the increasing urban population have become pressure factors on urban infrastructure, land management, and construction systems [1,2]. Sustainable development, the resilience of urban infrastructure, and the financial and psychological security of the population directly depend on the effectiveness of management decisions made in the field of urban construction [3].

Among the processes of urban construction management, the project selection process plays a significant role. The decisions made during this process directly affect the likelihood of delays and suspended or unfinished construction projects, which in turn influence the social, esthetic, and even environmental condition of cities [4]. Unfinished objects may potentially pose a danger to the population; moreover, they lead to the degradation of urban areas and the loss of funds by the population or investors.

In decision-making regarding project selection, the restrictions derived from regulatory documents and conclusions based on the analysis of the founding and financial documents of potential developers are usually taken into account [5]. In addition, the selection process is directly influenced by the results of surveys conducted among competent experts, the opinion of the project customer, and the decisions of the relevant commission [6]. When analyzing construction applications, a key factor is the correctness of the application formulation and the feasibility of achieving the expected indicators [7,8].

However, an important factor that influences the successful implementation of a construction project is the geographical, social, and economic characteristics of the project implementation region. Potentially, the success of the project depends on the availability of labor, the economic condition of the region, the mental characteristics of the developers, the presence of frequent force majeure circumstances, etc. [9]. And although it may be expected that these factors are reflected in expert conclusions and the opinion of the decision-maker, it is important to develop less subjective tools to take these factors into account.

The main aim of this study is to promote innovations and the development of decision-making technologies in the field of urban construction. This research proposes a new methodology for an adaptive multi-criteria selection of investment projects in urban construction. The approach makes it possible to take into account the requirements derived from regulatory and legal acts and those provided by construction customers, as well as regional and national specificities of construction project implementation. The method consists of several sequential stages: the formulation and classification of criteria, a compliance check with constraints, the construction of supercriteria (integral criteria that aggregate assessments from multiple sources) based on weighting functions (including logarithmic ones), an iterative reduction in the set of criteria, and the elimination of ineffective alternatives. This sequence ensures flexibility in decision-making even under conditions of uncertainty or limited data.

The main contribution of this paper can be summarized as follows:

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A multi-stage decision-making method for selecting urban construction projects has been proposed. It allows for the integration of regulatory, customer-oriented, and retrospective criteria. This ensures the possibility of considering not only regulatory and subjective requirements but also regional peculiarities of a project implementation of this type.

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A logarithmic model for identifying weighting functions has been developed, enabling the numerical expression of the impact of criterion values on the project success factor. This approach allows for the straightforward derivation of quantitative characteristics based on small data samples.

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An iterative approach to reducing the number of criteria in the task of multi-criteria optimization for construction project selection has been proposed. A reduction in criteria enables a semi-automated process of finding an alternative that best satisfies the two constructed supercriteria.

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An experimental verification of the developed method has been conducted for the task of selecting investment projects in construction in the western region of Ukraine.

The practical value of the obtained results lies in the fact that the developed method can become an effective decision-making tool in the field of urban construction. The method is universal, easy to apply, and does not require large amounts of input data. In addition, the proposed method can be integrated into smart city strategies, decision support systems in public investment policy, and infrastructure planning at the local and regional levels.

The structure of the paper is as follows. The second section analyzes current scientific sources devoted to decision-making in urban construction and related fields. The third section provides an analysis of the problem, a verbal–mathematical formulation of the task, and a detailed description of the developed method. The fourth section is devoted to the experimental verification of the proposed method. A discussion and conclusions are presented in the final section of the paper.

2. Literature Review

A selection of construction projects is traditionally carried out considering criteria of various nature, which may include the financial capacity of the investor, compliance with technical requirements, the experience of the contractor, and socio-economic benefits. Different countries apply various approaches to project ranking, ranging from expert assessments and analytical methods to multi-criteria decision-making (MCDM) models. In this context, the task of selecting construction projects can be reduced to a problem of multi-criteria selection. Several well-known methods exist to solve problems of this class.

In study [10], the authors focus on examining the use of various powerful MCDM methods for sustainable development. They compare AHP, FAHP, TOPSIS, ELECTRE, and VIKOR and highlight the strengths and weaknesses of each approach. As a result, it is shown that although each of these methods has advantages, there is no single approach that simultaneously accounts for subjective assessments and qualitative data, analyzes the closeness to the ideal solution, and handles conflicting criteria.

Study [11] demonstrates the advantages of using the Analytic Network Process (ANP) method to prioritize projects in the field of population studies. It is shown that this approach provides the decision-maker with a specific mathematical tool for decision support. However, this method is sensitive to small changes in subjective assessments and loses effectiveness when dealing with a large number of criteria or alternatives.

In article [12], the authors analyze the decision-making process regarding tenders in the construction sector. The study shows the effectiveness of considering the relative importance of criteria in the decision-making process.

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is demonstrated in works [13,14] as part of analytical multi-criteria decision-making for environmental and civil construction tasks. The core idea of this method is that the desired alternative is the one closest to the positive ideal solution and farthest from the negative ideal solution. TOPSIS involves ranking alternatives through the normalization and weighting of performance indicators, calculating the Euclidean distances to the ideal and negative-ideal solutions based on criteria of maximum and minimum effectiveness, and finally, deriving a relative closeness coefficient for each model. The drawbacks of the method include its dependence on normalization and the selection of weighting coefficients, which may be subjective [15].

The problem of selection based on Complex Proportional Assessment (COPRAS) and the evaluation of mixed data (EVAMIX) is addressed in study [16]. The authors demonstrate the need for a simple and systematized mathematical approach to guide the decision-maker in making an appropriate choice.

Despite the aforementioned strengths and proven effectiveness of these methods, all of them are highly subjective in nature, and the outcomes of their application depend on the characteristics of the experts and the decision-maker, as demonstrated in study [17]. To reduce such subjectivity, researchers often use modifications of classical methods based on fuzzy set theory [18]. For instance, study [19] presents an integrated fuzzy multi-criteria group decision-making approach for selecting research and development projects under incomplete information. The authors proved the effectiveness of the method compared to others. A specific feature of the proposed method is the use of the fuzzy integral method for ranking alternatives. This approach eliminates the requirement for the mutual independence of criteria and makes the method more versatile in application.

A fuzzy method for planning and selecting tenders for the design of public office buildings is presented in study [20]. To determine the weights of the criteria, the authors applied the fuzzy analytic hierarchy process (FAHP). However, despite the use of linguistic variables and other fuzzy analysis tools, these methods primarily rely on subjective data. They are based on expert opinions and may involve high computational complexity.

Although fuzzy methods help objectify subjectivity and are more flexible compared to classical approaches, they still significantly depend on expert conclusions. To reduce the influence of these factors, there is growing interest in hybrid and data-driven models in the scientific literature. Such models allow for the analysis of both subjective assessments obtained from experts or decision-makers and conclusions derived from retrospective data analysis. For example, study [21] is devoted to predicting the potential occurrence of specific properties in projects using the k-nearest neighbors algorithm and artificial neural networks. The authors developed a model for forecasting the cost of a construction project and time overruns during its implementation. The estimates obtained through this model can potentially be used in project selection processes. However, it is worth noting that a feature of neural network methods is the requirement for sufficiently large sets of retrospective data [22,23].

Bayesian classification methods allow for effective work with smaller data volumes and serve as the basis for developing efficient decision-making algorithms [24,25]. In study [26], the authors applied a Bayesian classifier to predict cost overruns in construction project implementation. The study demonstrated that the developed tool established direct correlations among all risks and identified the most critical risks based on the number of correlations between them. Additionally, study [24] showed how the Bayesian sequential analysis method enables effective decision-making based on relatively small datasets.

Support Vector Machine (SVM) is also an effective tool for classification and regression in decision-making tasks. For instance, study [27] proposed an SVM model based on Epsilon-SVR RBF kernel functions to solve the problem of predicting the cost of building construction projects. The obtained results were sufficiently accurate. However, it is well known that this model has high computational complexity when dealing with large datasets, and its application requires a high level of expertise from the analyst due to the model’s sensitivity to the choice of kernel function and the tuning of other parameters.

Another group of methods used in construction decision-making includes Case-Based Reasoning (CBR), which applies analogies from past cases to make decisions. These methods allow for the use of knowledge from previous projects in a simple and intuitive format. In study [28], the authors provided a review and justification of the CBR approach. Despite its interdisciplinary advantage, the authors highlighted some drawbacks, such as the method providing only approximate answers and its limited applicability in unsupervised learning scenarios. Nevertheless, CBR holds promise in the development of decision support systems with explainable CBR and deep CBR models.

Study [29] proposed a case-based reasoning model for leveraging past experience and knowledge to address scheduling delays in prefabricated construction projects. The research showed that such models can be an effective decision support tool during project evaluation stages, provided there are similar historical cases available—this being a significant limitation.

Thus, a certain methodological gap exists among decision-making methods for construction project selection. The analyzed methods demonstrate high effectiveness under various conditions, but they are often either overly dependent on expert assessments, require large datasets, or fail to consider the structure of criteria originating from different sources. This issue is especially relevant in the context of rapid urbanization, where the effectiveness of decision-making directly affects the resilience of urban infrastructure, the financial and psychological security of the population, and other vital indicators.

This study presents a new approach to organizing the decision-making process for selecting construction projects. This approach combines the structuring of the criteria space according to the source of origin, a multi-stage iterative decision adaptation process based on retrospective analysis results, and adaptive multi-criteria optimization.

3. Materials and Methods

3.1. Problem Analysis and Verbal–Mathematical Problem Formulation

Modern scientific research in the field of urban studies indicates that by 2050, approximately 6 billion people will live in cities [30]. Despite the fact that many developed countries are gradually entering the post-urbanization stage, developing countries are experiencing rapid growth in the role of cities and urbanization [31]. This continuous increase in the role of cities in the development and functioning of society creates the need to develop modern tools, relevant to current challenges, for strengthening the resilience of urban infrastructure [32].

The expansion and enlargement of cities place a significant burden on the construction sector [33]. According to the Global Construction Market Report published by The Business Research Company in January 2025, the size of the global construction market is projected to grow from USD 16,152.39 billion in 2024 to USD 17,045.95 billion in 2025 and reach USD 21,260.28 billion by 2029 [34]. The construction of new facilities is closely linked to ensuring urban resilience, particularly in the context of developing residential, transport, utility, and energy infrastructure. However, as modern sources indicate, a large portion of construction projects fail. According to estimates by McKinsey, the Construction Industry Institute (CII), and other industry analysts, approximately 30% of all projects fail. Projects are considered to have failed if their completion exceeds the planned cost and duration by 20%. Similar studies show that the failure rate among large/megaprojects is significantly higher—around 80% of large/megaprojects do not meet their planned objectives [35]. In some cases, construction projects are completed late and over budget [36].

The main causes of construction project failures include the following [37,38,39]:

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Financial risks (inflation and poor budget planning);

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Technical challenges (insufficient preparation and planning errors);

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Delays due to bureaucracy (regulatory barriers and document approval);

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The impact of macroeconomic and political factors (crises, pandemics, and instability), etc.

Given these factors and the relatively high rate of failed projects in urban construction, the project selection process deserves special attention. An analysis of decision-making processes related to the selection of construction projects has shown that the task of project selection can be reduced to a multi-criteria decision-making problem [40]. Typically, construction projects are evaluated based on a set of values according to a defined system of criteria and indicators. Moreover, such a system of criteria is shaped by various decision-making entities: regulators and construction customers [41,42]. Criteria provided by regulators may include regulatory requirements and standards arising from current legislative norms and environmental, and urban planning constraints. As a rule, these criteria are strict and mandatory to comply with. In turn, construction customers (a municipality, institution, or entrepreneur) may introduce more flexible criteria, including financial, technical, or other aspects.

However, the criteria of both groups reflect only the necessary conditions for successful project implementation. Even when all the requirements set by regulators and construction customers are met, a large portion of projects still turn out to be unsuccessful. This is due to unforeseen difficulties faced by investors. One of the reasons for this situation is that the success factor of a construction project also directly depends on the regional characteristics of economic activity, socio-economic conditions of the region, the availability of a sufficient labor force, etc. [43]. To identify such criteria and the degree of their influence, it is proposed to take into account retrospective data on construction projects implemented in previous periods in the respective region and under similar conditions. The use of retrospective data makes it possible to identify patterns of success and failure in past projects under similar conditions, allowing for the adaptive adjustment of criterion weights to improve forecasting accuracy.

In this study, the task of selecting an investment project in urban construction is considered. Let us construct its verbal–mathematical formulation in the following form:

Let $N$ be the number of projects available for selection;

$P=\{P_1,P_2,\dots ,P_N\}$ is the set of projects, each of which is evaluated according to the criteria sets $K=\{K_1,K_2,\dots ,K_M\}$, where $M$ is the number of criteria, $K_j$ is the set of possible values of the criterion under number $j$, $j=\overline{1,M}$, and $X_i=(x_{i1},x_{i2},\dots ,x_{iM})$ are vectors whose components are the values of criteria in the corresponding projects; that is, $x_{ij}$ is the value of criterion $K_j$ for project $P_i$.

It is necessary to develop rule $\Omega$, which implements Mapping (1):

$$〈P,K〉\stackrel{\Omega }{\to }{P}^{\ast },$$

(1)

where $P^{\ast }$ is the most effective project in a certain sense.

In this formulation, the task can be referred to the multi-criteria decision-making problem. By the effectiveness of the project, we will understand its compliance with the constraints imposed on projects of this type and its advantage in certain characteristics over other projects.

An important stage in this case is the formation of the set of criteria $K$. The system of criteria is shown in Figure 1:

As seen in Figure 1, the system of criteria may have a complex structure; that is, sets of criteria obtained from different sources may intersect. For example, constraints from the construction customer on the value of a certain indicator may be stricter than those imposed by the regulators.

• Let us introduce the notation. $J^{norm}$—the set of indices of criteria provided by the regulators;
• $J^{cust}$—indices of criteria provided by customers;
• $J^{retro}$—indices of criteria obtained based on retrospective data analysis.

The following condition must be satisfied, $J^{norm}\cup J^{cust}\cup J^{retro}=\{1,2,\dots ,M\}$, and the sets themselves may intersect.

Next, we will consider the proposed algorithm of the method for selecting investment projects in construction to solve the multi-criteria selection task developed within the framework of this study.

3.2. Method for Selecting Investment Projects in Urban Construction

Within the framework of this study, a multi-stage adaptive decision-making method for the selection of investment projects in urban construction was developed. The construction of the model is based on a number of assumptions that define the boundary conditions for its application and determine the limits of result interpretation. In particular, the following is considered:

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The hypothesis of project independence, according to which all considered projects (alternatives) are independent of each other;

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The hypothesis of the relative stability of project implementation conditions, according to which regulatory, economic, and political conditions are assumed to be conditionally unchanged during the period covered by the model;

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The hypothesis of data reliability: all data are assumed to be accurate and representative.

It should be noted that minor violations of these assumptions do not have a critical impact on the stability of the results. However, when forming the training sample, it is advisable to consider the conditions under which the projects were implemented. These conditions should be as similar as possible to the forecasted conditions for the implementation of the selected project.

According to the developed method, the process of selecting investment projects in urban construction is divided into several stages as follows:

Stage 0. Analysis of retrospective data. This stage is not a direct part of the project selection method and is preparatory. However, the effectiveness of the entire method depends on its quality. At this stage, based on the analysis of the experience of implementing similar projects in the given area, numerical indicators of the degree of influence of criteria on project success are determined. These indicators will be used in the subsequent stages of the method:

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The determination of criterion weights reflecting their importance in the selection process;

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The formation of super-criteria that aggregate criteria of different types;

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The construction of a multi-criteria model for evaluating alternatives.

Stage 1. Elimination of unpromising options. This stage involves analyzing the elements of the project set $P$ for compliance with the requirements set by regulators and customers. Those elements of set $P$ that do not meet at least one of the requirements are excluded from consideration as unpromising.

Stage 2. Project evaluation using a multi-criteria model. At this stage, a supercriterion is constructed for each category of criteria, and the multi-criteria selection problem is solved. If, at this stage, it is possible to select a project that maximizes all supercriteria, the selection process ends; otherwise, the process proceeds to the next stage.

Stage 3. Adaptive optimization with gradual reduction in supercriteria. At this stage, criteria are gradually excluded from the supercriteria, taking into account their degrees of influence on the resulting evaluation. The process continues until an acceptable project is found or the permissible limits of criteria reduction are exhausted.

Figure 2 shows the block diagram of the sequence of stages in the method implementation.

Next, the implementation approaches for each of the mentioned stages are presented.

3.2.1. Logarithmic Model for Identifying Weighting Functions

To identify weighting functions for criteria from the set $K$ with indices from set $J^{retro}$, we form a sample consisting of three types of projects:

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The first type includes projects that were successfully completed;

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The second type includes projects that were completed but during their implementation faced difficulties that led to a deterioration of the expected result;

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To the third group, we assign projects that, for certain reasons, were not completed.

Let us introduce the following notation:

$n_1, n_2, n_3$—the respective number of projects of the first, second, and third types;

$V_1,V_2,\dots ,V_{n_1}$—vectors with criterion values for projects of the first type;

$V_{n_1+1},V_{n_1+2},\dots ,V_{n_1+n_2}$—vectors with criterion values for projects of the second type;

$V_{n_1+n_2+1},V_{n_1+n_2+2},\dots ,V_{n_1+n_2+n_3}$—vectors with criterion values for projects of the third type;

$V_l=(v_{l{j}_1},v_{l{j}_2},\dots ,v_{l{j}_{\left|J^{retro}\right|}})$, $l=\overline{1,n_1+n_2+n_3}$, $\{j_1,j_2,\dots ,j_{\left|J^{retro}\right|}\}=J^{retro}$, $v_{lj}\in K_j$.

We introduce into consideration the function, a set of weighting functions $\{f_j(x)\}$, such that they satisfy (2):

$$f_j(x):K_j\to R, j\in J^{retro}.$$

(2)

The weighting functions will reflect the strength of the relationship between the criterion value x and the probability of a successful project implementation. The weighting function for each criterion j is constructed according to the following logarithmic dependency:

$$f_j(x)=\lg \left({\displaystyle \frac{count(V_l:l=\overline{1,n_1} and v_{lj}\equiv x)+\alpha \cdot count(V_l:l=\overline{n_1+1,n_2} and v_{lj}\equiv x)+\epsilon }{count(V_l:l=\overline{n_1+n_2+1,n_1+n_2+n_3} and v_{lj}\equiv x)+(1-\alpha )\cdot count(V_l:l=\overline{n_1+1,n_2} and v_{lj}\equiv x)+\epsilon }}\right)$$

(3)

where $\alpha \in [0;1]$ and $\epsilon >0$—model parameters.

As we can see, using model (3), for each value of each criterion, based on retrospective data, it is possible to calculate the value of the corresponding weighting function. By their nature, these functions for each criterion value represent the ratio between successful and unsuccessful projects. That is, they make it possible to formalize such relationships.

The use of a logarithmic model is justified by the following features and advantages:

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The logarithmic function allows us to interpret the ratio between types of projects in negative, zero, or positive values: when the number of successful and unsuccessful projects is equal, the weight equals zero; if there are more successful ones, the weight is positive, and vice versa. This enables the use of weighting function values in score-based models.

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The logarithmic function smooths out sharp fluctuations in small samples, making it resistant to local peaks and instability—unlike linear or power functions.

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This form reflects an approach close to log-odds, which is widely used in probabilistic analysis and logistic regression [44,45], making it both familiar and validated.

In this form, functions of type (3) can be regarded as weighting functions, and their values can be interpreted as the degree of quality of a certain criterion value for a successful project implementation. Thus, in this study, the logarithmic function is not used for classification but for an automatic generation of a weight estimate for each criterion value, allowing the subjective assessment to be replaced with empirically grounded evaluation.

Model (3) introduces two additional parameters that allow us to adapt the model to the context as follows:

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Parameter $\alpha$ indicates to what extent projects of the second group (those that encountered certain problems during implementation) can be considered successful. If $\alpha =0$, they are considered unsuccessful and formally assigned to the third group; if $\alpha =1$, they are considered successful and assigned to the first group. In all other cases, for $\alpha \in (0;1)$, they are partially assigned to the first and third groups in proportions $\alpha :\left(1-\alpha \right)$. This allows us to tune the model to the specifics of the risk acceptance policy.

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Parameter $\epsilon$ > 0 in model (3) prevents instability in calculations. Its use guarantees that neither the numerator nor the denominator of the fraction equals zero, and the argument of the logarithmic function stays within permissible bounds. The closer this parameter is to zero, the less it affects the values of the weighting functions.

Further in the following sections, the sensitivity of the model to changes in the values of these parameters will be analyzed.

It is worth noting that the general form of the functions (3) is formalized. The equality $v_{lj}\equiv x$, depending on the nature of the values of the given criterion, may mean exact matching or belonging to the same category, numerical interval, range, or set of values. Thus, in this context, $v_{lj}$ and $x$ are equivalent in a certain sense.

After identifying the weighting functions (3), the next stage is the implementation of the first stage of project selection, for which the following procedure of sequential analysis of alternatives is proposed.

3.2.2. Procedure for Sequential Analysis of Alternatives for Elimination of Unpromising Projects

At the first stage of selection, it is necessary to check whether the projects from the set $P$ comply with the constraints established by the regulators and the customer. The elimination of projects that do not meet the established requirements allows us to reduce the initial set of projects and simplify the selection procedure itself.

To implement the elimination procedure, it is necessary to formalize the requirements and constraints imposed on projects. Let us denote the sets of admissible values of the corresponding criteria by $D_1^{norm}, D_2^{norm}, \dots , D_{\left|J^{norm}\right|}^{norm}$ and $D_1^{cust}, D_2^{cust}, \dots , D_{\left|J^{cust}\right|}^{cust}$, which represent the respective requirements and constraints.

It is worth noting that there may be cases where the same criteria belong to both categories. For such criteria, we check the condition of non-contradiction (4):

$$if j\in J^{norm} and j\in J^{cust} then D_j^{norm}\cap D_j^{cust}\ne \varnothing .$$

(4)

If condition (4) is not met for at least one criterion, this means that the requirements and constraints set by the customer contradict the normative ones. In this case, the selection problem has no solution, and the customer should reconsider their requirements for the projects.

To perform the elimination, we apply the methodology of the sequential analysis of alternatives, which we present in the form of (5)–(6):

$$\forall i=\overline{1,N}: if \exists j\in J^{norm}: x_{ij}\notin D_j^{norm} then P:=P\backslash \left\{P_i\right\}, N:=N-1,$$

(5)

$$\forall i=\overline{1,N}: if \exists j\in J^{cust}: x_{ij}\notin D_j^{cust} then P:=P\backslash \left\{P_i\right\}, N:=N-1.$$

(6)

If, as a result of one of the iterations of procedures (5)–(6), set $P$ becomes empty, then we conclude that none of the initially declared projects complies with the established requirements. At the same time, if some projects were eliminated during the execution of procedure (6), it is possible for the customer to revise the requirements that were imposed on the projects in order to expand the set of admissible criterion values. After such a revision, the initial project set $P$ should be re-subjected to the elimination procedure.

If the elimination occurred solely based on procedure (5), then the project selection task is completed, and it is impossible to make a decision on the selection of a specific project.

After executing procedures (5)–(6), only those projects that meet the specified requirements remain in set $P$. Then, according to the developed method, we proceed to the next stage of selection.

3.2.3. Model of Multi-Criteria Selection Based on Supercriteria

The implementation of the project selection procedure from the set $P$ involves searching for such project $P^{\ast }$, which is, in a certain sense, the best among the available projects. According to the developed model, the best project is the one that is the best from the point of view of the customer’s requirements and the characteristics most similar to the characteristics of projects $V_1,V_2,\dots ,V_{n_1}$, that is, those projects that were successfully implemented in previous periods of time.

To formalize the selection process, we construct two supercriteria:

$F^{cust}(x_1,x_2,\dots ,x_m)$—supercriterion for the criteria set by the customer;

$F^{retro}(x_1,x_2,\dots ,x_m)$—supercriterion for the criteria obtained from retrospective data.

Let us construct $F^{retro}(x_1,x_2,\dots ,x_m)$ in the form of (7):

$$F^{retro}(x_1,x_2,\dots ,x_m)={\displaystyle \sum _{j\in J^{retro}}{f}_j(x_j)}.$$

(7)

Considering the method of identification of weighting functions $f_j(x)$, the supercriterion (7) equals the sum of weights for the respective criterion values of the considered project.

To identify $F^{cust}(x_1,x_2,\dots ,x_m)$ we introduce a system of functions $g_j(x)$ and $j\in J^{cust}$, which will reflect the weights of the criterion values obtained from the customer. In the general case, the identification of these functions must be performed by the customer based on their vision of the desired characteristics. We assume that the more desirable a value is, the higher the weight the customer will assign to it. Under such conditions, the supercriterion $F^{cust}(x_1,x_2,\dots ,x_m)$ is constructed in the form of (8):

$$F^{cust}(x_1,x_2,\dots ,x_m)={\displaystyle \sum _{j\in J^{cust}}{g}_j(x_j)}.$$

(8)

Next, to find the optimal project $P^{\ast }$, we solve the bicriteria selection problem in the form of (9):

$$\left\{\begin{array}{l}{F}^{cust}(X)\to \max ,\\ F^{retro}(X)\to \max ,\\ X\in \{X_1,X_2,\dots ,X_N\}.\end{array}\right..$$

(9)

When solving problem (9), the following cases are possible:

Case 1—problem (9) has one solution; that is, the following holds:

$$\exists !i^{\ast }\in \{1,2,\dots ,N\}: X_{i^{\ast }}=\arg \underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{cust}(X)\right\} and X_{i^{\ast }}=\arg \underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{retro}(X)\right\}$$

(10)

In this case, the optimal project for selection is $P_{i^{\ast }}$.

Case 2—problem (9) has several solutions; that is, the following holds:

$$\left|\left(A\mathrm{rg}\underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{cust}(X)\right\} \right)\cap \left(A\mathrm{rg}\underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{retro}(X)\right\}\right) \right|>1.$$

(11)

In this case, we form the set

$P^{opt}=\left(A\mathrm{rg}\underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{cust}(X)\right\} \right)\cap \left(A\mathrm{rg}\underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{retro}(X)\right\}\right)$, which contains equally valuable projects from the perspective of the criteria (7)–(8). The further selection of a project from set $P^{opt}$ can be based either on the decision of the decision-maker or on the refinement of weighting functions and construction of new supercriteria.

Case 3—problem (9) has no solutions, i.e., $\left(A\mathrm{rg}\underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{cust}(X)\right\} \right)\cap \left(A\mathrm{rg}\underset{X\in \{X_1,X_2,\dots ,X_N\}}{\max }\left\{F^{retro}(X)\right\}\right) =\varnothing$. This means that set P $P$ contains no project for which the values of the criteria simultaneously maximize both supercriteria. Therefore, in such a system of criteria, it is impossible to determine the best project. To make a decision in such a case, one can apply different strategies—from forming a new set of criteria to generating a new set of projects. Within this study, we propose using the following method: iterative reduction in supercriteria via internal optimization.

3.2.4. Method of Iterative Reduction in Supercriteria via Internal Optimization

The main idea of this method lies in the step-by-step elimination of those criteria within the supercriteria that have the lowest degree of importance. At each iteration, the criterion with the minimal weight is excluded from the supercriterion, and a new optimization condition is applied. This process is iterative and continues until a project satisfying the updated conditions is found or until all possibilities are exhausted.

Let us denote the set of indices of criteria for which adjustments (relaxations) are allowed as $J^{soft}$, with the initial state being $J^{soft}=\varnothing$.

Let us describe a single iteration of the method:

Step 1. We identify the criteria that can be relaxed in the current iteration. The indices of the criteria are determined according to rule (12):

$$\begin{array}{c}{j_1}^{\ast }\in Arg\underset{j\in J^{cust}}{\min }\left(\underset{i=\overline{1,N}}{\max } g_j(x_{ij})-\underset{i=\overline{1,N}}{\min } g_j(x_{ij})\right),\\ {j_2}^{\ast }\in Arg\underset{j\in J^{retro}}{\min }\left(\underset{i=\overline{1,N}}{\max } f_j(x_{ij})-\underset{i=\overline{1,N}}{\min } f_j(x_{ij})\right)\end{array}$$

(12)

Rule (12) is based on the assumption that the criteria whose weighting function values for projects in the given sample fall within the smallest numerical interval (i.e., are the closest to each other in value) have the least influence on the differentiation of projects according to the corresponding supercriteria. In other words, such a criterion makes the least significant contribution to the ranking of alternatives, since the values of its weighting function differ the least across all considered projects. Therefore, its step-by-step elimination is justified and allows for a reduction in the dimensionality of the problem.

Step 2. For the indices ${j_1}^{\ast }, {j_2}^{\ast }$, we apply the transformation shown in (13):

$$J^{soft}:=J^{soft}\cup \left\{{j_1}^{\ast }\right\}, J^{cust}:=J^{cust}\backslash \left\{{j_1}^{\ast }\right\}, J^{retro}:=J^{retro}\backslash \left\{{j_2}^{\ast }\right\}.$$

(13)

Step 3. If $J^{cust}\ne \varnothing$ and $J^{retro}\ne \varnothing$, we construct a bicriteria selection problem in the form of (14):

$$\left\{\begin{array}{l}{F}^{cust}(X_i)={\displaystyle \sum _{j\in J^{cust}}{g}_j(x_{ij})}\to \max ,\\ F^{retro}(X_i)={\displaystyle \sum _{j\in J^{retro}}{f}_j(x_{ij})}\to \max ,\\ g_j(x_{ij})\ge {\delta }^j, j\in J^{soft},\\ X_i\in \{X_1,X_2,\dots ,X_N\},\end{array}\right.$$

(14)

where ${\delta }^j$—the minimum allowable value of the criterion $K_j$ set by the customer.

In the case where $J^{cust}=\varnothing$ or $J^{retro}=\varnothing$, we solve the corresponding single-criterion decision-making problem (15) or (16), find the optimal project $P^{\ast }$ and complete the execution of the method as follows:

$$\left\{\begin{array}{l}{F}^{retro}(X_i)={\displaystyle \sum _{j\in J^{retro}}{f}_j(x_{ij})}\to \max ,\\ g_j(x_{ij})\ge {\delta }^j, j\in J^{soft},\\ X_i\in \{X_1,X_2,\dots ,X_N\},\end{array}\right.$$

(15)

$$\left\{\begin{array}{l}{F}^{cust}(X_i)={\displaystyle \sum _{j\in J^{cust}}{g}_j(x_{ij})}\to \max ,\\ g_j(x_{ij})\ge {\delta }^j, j\in J^{soft},\\ X_i\in \{X_1,X_2,\dots ,X_N\}.\end{array}\right.$$

(16)

Step 4. We analyze problem (14) similarly to problem (9) and make a decision regarding the termination of the method if a solution is found or proceed to the next iteration.

As a result of applying the described method, a decision may be made regarding the selection of the optimal project based on compromise optimization in an iteratively reduced set of criteria, which ensures flexible decision-making even under conditions of conflict between objective functions.

4. Results

4.1. Collection of Data

The rapid growth of the role of cities in human activity and the increasing urban population lead to a rise in the number of investment projects in urban construction. The success of a project depends both on its characteristics and on the characteristics of its executors, as well as on the specific features of the territory where the project is being implemented. A formal approach to the project selection process and the failure to consider all these factors may lead to the emergence of incomplete or unsuccessful projects, which negatively affects urban infrastructure and the economic security of the population.

The developed method for selecting investment projects in urban construction was verified in the western region of Ukraine. The problem under consideration is the selection of an urban construction project commissioned by a local self-government authority for the implementation of housing programs, which is defined as follows:

The local self-government authority plans to implement a municipal housing program for socially vulnerable categories of the population (young specialists, large families, and veterans). For this purpose, an open competition of investment projects was announced among developers who were ready to construct housing with partial funding from the city budget.

At the first stage, a set of criteria that may influence the project selection process was formed. The criteria and their characteristics are presented in

Table 1. Criteria system for project selection.

Number	Criterion Name	Criterion Type	Value Range	Comment
1	Urban Planning Compliance	Normative	Yes/No	Compliance with city master plan (mandatory)
2	Land Tenure Status	Normative, Retrospective	Owned/Leased/Not Available	Impact on timing and stability
3	Building Code (DBN) Compliance	Normative	Yes/No	Technical compliance check
4	Energy Efficiency Class	Normative, Customer	Class A/B/C/D	Regulated and of interest to customer
5	Price per m2	Customer, Retrospective	<USD 600/USD 600–800/>USD 800	Sale or construction price
6	Construction Duration	Customer, Retrospective	<12/12–24/>24 months	Project implementation timeline
7	Experience in Social Housing	Customer, Retrospective	Yes/Partial/No	Relevance of experience to customer
8	Share of Failed Projects	Retrospective	0%/1–25%/>25%	Risk indicator
9	Completion Rate of Previous Projects	Retrospective	<50%/50–80%/>80%	Ratio of completed to total projects
10	Use of Local Contractors	Customer	Yes/No	Support for local economy
11	Availability of Urban Infrastructure	Normative	Yes/No	Access to networks and transport
12	Number of Completed Projects	Retrospective	0/1–5/>5	Access to networks and transport
13	Ownership of Construction Equipment	Customer	Low/Medium/High	Level of contractor’s independence
14	Public Benefit Index	Customer	Low/Medium/High	Social significance of project
15	Environmental Zone Restrictions	Normative	Yes/No	Construction restrictions on site

.

Constraints and weight coefficients for certain criteria are provided in

Table A1. Constraints on regulatory criteria.

Number	Criterion Name	Value Range	Regulatory Constraint
1	Urban Planning Compliance	Yes/No	Must fully comply with urban zoning and general plan
2	Land Tenure Status	Owned/Leased/Not Available	Land must be legally owned or leased for project use
3	Building Code (DBN) Compliance	Yes/No	Project design must meet DBN construction code requirements
4	Energy Efficiency Class	Class A/B/C/D	Energy efficiency class must not be lower than Class C
11	Availability of Urban Infrastructure	Yes/No	Must be within reach of existing city infrastructure (utilities, roads)
15	Environmental Zone Restrictions	Yes/No	Construction not allowed if territory falls under environmental restriction

and

Table A2. Description of criteria provided by customer.

Number	Criterion Name	Value Range	Weight Coefficients
4	Energy Efficiency Class	Class A/B/C/D	{‘Class A’: 1.0, ‘Class B’: 0.7, ‘Class C’: 0.4, ‘Class D’: 0.1}
5	Price per m2	<USD 600/USD 600–800/>USD 800	{‘<USD 600’: 1.0, ‘USD 600–800’: 0.6, ‘>USD 800’: 0.2}
6	Construction Duration	<12/12–24/>24 months	{‘<12’: 1.0, ‘12–24’: 0.6, ‘>24 months’: 0.2}
7	Experience in Social Housing	Yes/Partial/No	{‘Yes’: 1.0, ‘Partial’: 0.5, ‘No’: 0.1}
10	Use of Local Contractors	Yes/No	{‘Yes’: 1.0, ‘No’: 0.0}
13	Ownership of Construction Equipment	Low/Medium/High	{‘High’: 1.0, ‘Medium’: 0.5, ‘Low’: 0.2}
14	Public Benefit Index	Low/Medium/High	{‘High’: 1.0, ‘Medium’: 0.6, ‘Low’: 0.2}

.

As can be seen from Table A2, the customer did not define specific constraints but only provided weight coefficients for certain criteria.

Next, a sample of retrospective data on projects implemented in the given area under similar conditions was formed. At the initial stage of this process, projects with missing or analytically unsuitable indicator values were filtered out. All criterion values were normalized according to the scales defined in Table 1. The classification of projects into three groups (successful, partially successful, and unsuccessful) was carried out based on an analysis of actual outcomes (implementation timeframes, budget compliance, and achievement of target indicators), as well as the assessment of their impact on the social and economic situation in the region.

The sample included 60 projects. The sample was divided into two parts—a training sample (40 projects) and a test sample (20 projects). In each sample, according to the methodology, the projects were of three types. In particular, the training sample included the following projects: those that were successfully completed ($n_1=21$); those that were completed, but whose implementation was accompanied by complications that led to a deterioration in the expected result ($n_2=7$); and those that, for certain reasons, were not completed ($n_3=12$). The size of the test sample by groups was $n_1=10$, $n_2=2$, $n_3=8$.

4.2. The Results of Applying the Developed Method

At the first stage, according to the developed method, an analysis of data from the training sample was carried out. For this analysis, the previously developed logarithmic model (3) with the following parameters was applied: $\alpha =0.2$, $\epsilon =0.01$. The data from the training sample and the results of the calculation of weight function values are provided in

Table 2. The results of calculating the values of weight functions for retrospective criteria.

Criterion	Criterion Value	Successful	Conditionally Successful	Unsuccessful	$\mathit{f}$(x)
Land Tenure Status	Owned	15	1	2	0.733423
	Leased	4	5	8	−0.37971
	Not Available	2	1	2	−0.10431
Price per m2	<USD 600	2	4	7	−0.56032
	USD 600–800	14	3	3	0.431453
	>USD 800	5	0	2	0.396642
Construction Duration	<12	4	3	10	−0.43007
	12–24	7	4	1	0.268369
	>24 Months	10	0	1	0.996113
Experience in Social Housing	Yes	14	2	1	0.742023
	Partial	5	2	6	−0.14819
	No	2	3	5	−0.45318
Share of Failed Projects	0%	7	1	2	0.409229
	1–25%	13	6	7	0.080344
	>25%	1	0	3	−0.47425
Completion Rate of Previous Projects	<50%	3	3	7	−0.41608
	50–80%	3	1	4	−0.17564
	>80%	15	3	1	0.660649
Number of Completed Projects	0	2	1	2	−0.10431
	1–5	11	4	7	0.063224
	>5	8	2	3	0.261095

.

As shown in Table 2, each criterion value was assigned a corresponding weighting function value calculated according to (3).

At the next stage, the sequential variant analysis procedure was applied to the projects of the control sample. As a result of this procedure, one conditionally successful project and four unsuccessful projects were filtered out. The results are presented in

Table A3. Control sample after filtering procedure.

Number	Price per m2	Construction Duration	Experience in Social Housing	Share of Failed Projects	Completion Rate of Previous Projects	Number of Completed Projects	Group	Use of Local Contractors	Ownership of Construction Equipment	Public Benefit Index
1	>800	>24 months	Yes	0%	50–80%	0	Successful	No	Low	Medium
2	USD 600–800	>24 months	Yes	>25%	>80%	1–5	Successful	Yes	Medium	High
3	USD 600–800	12–24	Yes	0%	50–80%	1–5	Successful	Yes	Medium	Medium
4	USD 600–800	12–24	Yes	1–25%	50–80%	1–5	Successful	No	Medium	Medium
5	<600	>24 months	Yes	0%	>80%	>5	Successful	No	Medium	High
6	USD 600–800	<12	Yes	0%	50–80%	1–5	Successful	No	Medium	High
7	>800	12–24	Yes	0%	>80%	1–5	Successful	Yes	Medium	Medium
8	>800	>24 months	No	1–25%	>80%	>5	Successful	Yes	Low	Low
9	USD 600–800	<12	Yes	0%	50–80%	>5	Successful	No	Low	Medium
10	USD 600–800	>24 months	Yes	1–25%	<50%	>5	Successful	Yes	High	Medium
11	USD 600–800	<12	Partial	1–25%	>80%	>5	Partially Successful	Yes	Medium	High
16	USD 600–800	>24 months	Yes	0%	50–80%	1–5	Unsuccessful	Yes	High	Medium
18	>800	>24 months	Yes	0%	50–80%	1–5	Unsuccessful	No	Medium	Medium
19	>800	<12	Yes	0%	5–80%	1–5	Unsuccessful	Yes	Medium	Low
20	>800	12–24	Yes	1–25%	>80%	>5	Unsuccessful	Yes	Medium	Medium

.

For the 15 projects that remained, supercriteria were constructed. The values of the supercriteria for the projects from Table A3 are shown in Figure 3 and Figure 4. Here, the horizontal axis represents the numbers of the projects remaining under consideration, and the vertical axis shows the values of the corresponding supercriterion. Additionally, to improve visual analysis, successful projects are highlighted in green, conditionally successful in orange, and unsuccessful in red.

As we can see from Figure 3 and Figure 4, problem (9) has no solution: $F^{retro}$ reaches its maximum for project number 5, while $F^{cust}$ for 12.

Next, according to the method, we select criteria for filtering. Among the normative criteria, the criterion “Number of Completed Projects” is selected; among the customer criteria, the “Energy Efficiency Class” criterion is excluded. Additionally, a restriction “Number of Completed Projects > 0” was introduced.

The results of constructing supercriteria are shown in Figure 5 and Figure 6.

As we can see, as a result of the introduction of constraints, the number of projects remaining under consideration decreased, and an unsuccessful project was excluded.

Similarly, two more iterations were carried out, after which only the first group of projects remained under consideration, among which the projects numbered 1 and 5 maximized the retrospective supercriterion.

4.3. A Sensitivity Analysis of the Logarithmic Model

To evaluate the impact of changes in the values of parameters α and ε on the weighting functions of type (3), a sensitivity analysis was carried out. This analysis made it possible to illustrate how changes in each parameter affect the values of the weighting function f(x).

For the calculations, the following values for the number of projects in the groups were fixed: $n_1=10$, $n_2=5$, $n_3=8$.

The first series of calculations was performed to analyze the impact of changes in parameter α with ε = 0.01

It is worth recalling that parameter α indicates the extent to which partially successful projects can be assigned to the group of successful projects. The results of the calculations are shown in Figure 7.

The calculation results demonstrate a monotonic increase in the values of the weighting function f(x) as parameter α increases. This is consistent with the logic of the proposed model: the higher the value of parameter α, the greater the number of successful projects and the smaller the number of unsuccessful ones. Consequently, the weight of the given criterion value increases.

In the second series of calculations, the value of parameter α was fixed at 0.5, while the value of parameter ε varied from 0.01 to 0.99. The results of the calculations are presented in Figure 8.

As shown in Figure 8, with an increase in ε, the absolute value of the weighting function decreases. However, this decrease is relatively insignificant and amounts to 8% when ε = 0.99 compared to ε = 0.01.

Additionally, the values of function f(x) were compared for ε = 0.01 (f(x) = 0.07565) and ε = 0 (f(x) = 0.07572). Thus, it can be concluded that the introduction of the stabilization parameter ε in this case resulted in a change in the value of the weighting function by less than 0.1%, which can be considered an acceptable compromise between computational accuracy and stability.

5. Discussion

5.1. Interpretation of Results

The experimental part of the study demonstrated how the developed method for selecting construction projects can be applied, using the example of selecting investment projects in urban construction in the western region of Ukraine. To verify the obtained results, a dataset of retrospective data on projects previously implemented in the same area under similar conditions was compiled. The projects were divided into three different groups: those successfully completed, those completed with complications during implementation, and those that, for certain reasons, could not be successfully completed. This dataset was divided into a training set (40 projects) and a control set (20 projects). A case was modeled involving the decision-making process for selecting one project from the control sample.

According to the developed methodology, a set of criteria was formed and divided into three subsets—criteria defined by regulators, criteria provided by the project client, and retrospective criteria (Table 1). It was also considered that these subsets may overlap. For the first type of criteria, constraints that projects must meet were defined (Table A1). For the second type, the constraints and the weighting function were provided by the project client (Table A2).

To identify the weight functions of the third type of criteria, the logarithmic model (3) developed in this study was applied. The data for the training dataset and the values of the weight functions are provided in Table 2. As shown in this table, the weight function takes a positive value if the criterion value predominantly appears in successful projects and a negative value in the opposite cases. If the criterion value, according to the model, does not influence project success, the weight function is close to zero (e.g., the criterion Number of Completed Projects, variant “1–5”).

Within the control sample, a baseline validation procedure of the method was implemented. After applying the elimination of projects according to the constraints provided by the regulators, 15 projects remained in the control sample (Table A2). Among the five eliminated projects, one was partially successful and four were unsuccessful. For the elements of the control sample, a multi-criteria selection model of type (9) was constructed. The results of calculating the values of the supercriteria for the control sample elements are presented in Figure 3 and Figure 4.

As can be seen from these figures, the criterion constructed on the basis of retrospective data attained higher values for projects of the first group (the maximum value was reached for project number 5), while the criterion formed based on the customer’s perspective allowed potentially unsuccessful projects to obtain higher values than successful ones (the maximum value was reached for project number 16). This indicates that if the decision had been made solely on the basis of regulatory constraints and the customer’s vision, the selection of an unsuccessful project would have been likely.

Next, in accordance with the developed method, the procedure of excluding criteria from the supercriterion and forming new supercriteria was demonstrated. The criteria were excluded automatically based on Rule (12), which enables identifying the criterion that has the least impact on the corresponding supercriterion. As a result of the implemented procedure, only potentially successful projects remained under consideration. Of course, the procedure can be continued until a unique solution to the multi-criteria selection problem is found; however, even at the stage when only potentially successful projects remain, it can already be concluded that the developed model enhances the substantiation of decision-making processes regarding the selection of investment projects in construction and reduces the risk of selecting inefficient alternatives.

The conducted sensitivity analysis confirmed that the logarithmic model is adaptive to parameter changes and allows for the flexible generation of weighting estimates depending on the customer’s strategic vision (via parameter α) or the quality of statistical data (via parameter ε). This combination of stability and flexibility is a key advantage of the proposed approach.

5.2. Comparison with Classical Multi-Criteria Decision-Making Methods

In contrast to classical multi-criteria selection methods such as AHP, TOPSIS, or VIKOR [10,14,15], the method developed in this study demonstrates lower dependence on expert evaluations and is less influenced by subjective judgments. The method is based on a retrospective analysis of data on the success of previously implemented projects, which allows us to take into account not only regulatory and subjective constraints but also the specific features of construction project implementation in a given area.

Moreover, unlike many multi-criteria models, it implements a procedure for eliminating unpromising projects and adaptively reducing criteria that have less influence on the objective functions under specific conditions. This approach is similar to the concepts of sequential concessions or the compromise selection method [46,47], but it is combined with data from past projects, forming a unique two-level decision-making procedure.

Thus, the developed method is not an alternative to classical MCDM approaches but rather an adaptive and complementary form, especially under conditions of insufficient expert information or the high variability of regional factors.

A comparison of the key characteristics of classical MCDM methods (AHP, TOPSIS, VIKOR) with the proposed approach is presented in

Table 3. Comparison of the proposed approach with classical MCDM methods.

Criterion	AHP/TOPSIS/VIKOR	The Proposed Method
Type of Data	Subjective expert assessments	Retrospective empirical data
Dependence on Experts	High	Minimal
Possibility to Consider Regional Specificity	Limited	Direct integration through historical data
Weight Coefficient Formation	Method of pairwise comparisons/heuristics	Automatic, logarithmic function based on frequency
Adaptive Criterion Reduction	Absent	Via iterative procedure
Alternative Ranking	Yes	After repeated execution of the procedure

.

The table demonstrates significant differences in data sources, approaches to weight formation, and the ability to adaptively reduce the set of criteria.

5.3. The Key Properties and Application Potential of the Method

The developed method is characterized by a number of key properties that determine its flexibility, scalability, and practical applicability in various urban planning contexts.

The method is adaptive and allows an adjustment to the specifics of input data (the set of projects submitted for the selection process), regional implementation conditions reflected in retrospective data, and the preferences and vision of the construction customer. Although the experimental verification of the developed method was carried out using the case of project selection in Western Ukraine, the structure and logic of the proposed methodology are universal. The method is independent of geographic location or construction type. Its effectiveness depends on the availability of a training sample that includes projects implemented in past periods under conditions as close as possible to the forecasted conditions for the selected project, as well as the customer’s awareness of the specifics of implementing such projects.

Moreover, the relevance of the method is confirmed in light of current research in the field of urban investment management. In particular, recent studies show that the introduction of high-speed railways contributes to the reduction of carbon emissions through the stimulation of environmental investments [48] and that digital financial infrastructure and ESG strategies of companies are increasingly being integrated into the evaluation procedures of urban projects [49]. All this highlights the relevance and necessity of developing methods that integrate the ability to simultaneously and effectively consider economic, environmental, financial, and social aspects in a unified model.

It is also worth noting that, although the method does not directly provide a ranking of projects, such ranking can be implemented by consecutively applying the method. After selecting the first (most effective) project, it can be excluded from the set of alternatives, and the evaluation procedure can be repeated on the updated sample to select the next one. This approach makes it possible to generate a ranked list of alternatives based on the same logic without the need to modify the core mechanism of the method.

The implementation of the developed method in the practice of decision-making in urban construction does not require significant resource expenditures. To apply the approach, construction customers must ensure the following conditions are met:

-

The availability of retrospective data on previously implemented projects in the corresponding area;

-

Regulatory constraints that projects must comply with;

-

Constraints provided by the customer;

-

A tool for performing calculations.

It should be emphasized that the method does not require specialized software or high computational resources.

6. Conclusions

This study is devoted to the development of an adaptive method for multi-criteria project selection in urban construction. A preliminary analysis of the problem and the scientific literature revealed a certain methodological gap among existing decision-making methods for selecting construction projects. As demonstrated in the paper, the developed method allows for the consideration of both regulatory and customer requirements, as well as the specific features of conducting business in the field of urban construction within a given territory. The method is multi-stage and is reduced to solving a multi-criteria selection problem using the developed method of an iterative reduction in supercriteria with internal optimization.

The developed method integrates regulatory, customer-oriented, and retrospective criteria, which allows for the consideration of not only regulatory requirements and customer expectations but also the specific features of project implementation in the given region. Its main advantage lies in the use of data on previously implemented projects, which ensures the substantiation of the selection process and adaptation to the specifics of the local environment.

The logarithmic model developed in this study enables the identification of weighting functions for criteria that potentially influence the success of construction project implementation. The application of this model allows for reducing subjectivity and quantitatively assessing regional specificities in urban construction. The sensitivity analysis of parameters α and ε demonstrated the stable behavior of the logarithmic model, confirming its reliability across various practical scenarios.

The developed procedure of iterative criterion reduction enables the step-by-step solving of the multi-criteria selection problem through the gradual elimination of less significant parameters. This approach facilitates decision-making in tasks involving a large number of criteria.

The numerical experiment conducted on a retrospective sample of projects implemented in past periods under similar conditions, with division into training and control subsets, demonstrated the ability of the proposed method to reliably eliminate unsuccessful projects and focus the selection process exclusively on potentially effective alternative solutions. This confirms the practical applicability of the developed approach as a decision-making model suitable for use in real-world conditions.

The developed method has a number of limitations, including the following:

-

The necessity of having retrospective data. In the absence of such data, the method is reduced to a single-criterion selection problem and may be less reliable.

-

The method does not provide project ranking, as it is designed to select one of the potentially effective projects.

-

When using continuous criteria, it is necessary to divide them into intervals.

In further research, it would be advisable to consider the following:

-

The modification of the method for analyzing projects that are already in the implementation phase;

-

The integration of the model with artificial intelligence technologies (in particular, machine learning) for automatic parameter tuning and adaptation to new data;

-

The enhancement of the logarithmic model to account for weighting functions in the context of continuous data without discretization.