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Article

Materials and Technology Selection for Construction Projects Supported with the Use of Artificial Intelligence

Civil Engineering Faculty, Warsaw University of Technology, Armii Ludowej 16, 00-637 Warszawa, Poland
Materials 2022, 15(4), 1282; https://doi.org/10.3390/ma15041282
Submission received: 8 December 2021 / Revised: 3 February 2022 / Accepted: 6 February 2022 / Published: 9 February 2022
(This article belongs to the Special Issue Advanced Construction Materials and Processes in Poland)

Abstract

:
The choice of material solutions and the appropriate technology for the execution of works have a significant impact on the success of construction projects. The earlier in the investment cycle of a project, the greater the possibility of improving the project’s success indicators. The currently used planning methods assume late integration of schedules with material and technological solutions. This limits the possibility of optimizing construction projects. The author proposed a new approach. The new method is based on the value engineering principles. The article presents a computational model supported by a case study—construction of an office building. Thanks to the use of artificial intelligence and metaheuristic algorithms, the economic results of construction projects have improved. This new method can help construction managers select materials and technologies in a way that will improve project parameters.

1. Introduction

The construction projects are characterized by a high level of complexity, a long investment life cycle, and high costs. It results in the necessity to implement special diligence and analysis during their planning [1,2,3,4,5,6]. Choosing both the right material solutions and the appropriate technology for the execution of works has a significant impact on the success of construction projects [7,8,9,10]. According to market research, material costs correspond to most of the construction costs [11,12,13]. What’s more, the selection of appropriate materials translates into many other parameters that are crucial for the projects, including structural safety, fire safety, safety of usage, acoustical comfort, visual comfort, hygrothermal comfort, serviceability, durability, sustainability, and energy conservation [14,15].
However, the choice of materials cannot be made excluding aspects related to specificity of market conditions and the construction industry (including billing systems or contract terms). Restrictions, such as construction duration (deadlines), technological and organizational dependencies, and resources should also be considered while planning construction projects [16].
When building decision-making models, one should also properly select parameters that measure the potential success of projects. According to practitioners and theorists, the success of projects is based on aspects related to cost, time, and quality (meeting the requirements) [17,18,19]. From the contractors’ point of view, the high level of customer satisfaction has a positive effect on winning new contracts, and significantly reduces the probability of being involved in harmful disputes and court hearings and incurring additional costs. If the investor decides to implement the project on their own, it is in their own interest to meet the requirements [20,21,22].
Current value management practices are carried out in the conceptual phase and in the planning phase of project implementation. Meanwhile, the optimization of schedules and related indicators is carried out much later. This oversight causes potential losses in the process of maximizing the value of construction projects in reference to its key economic parameters (net present value, cash flow [14,16,18]), existing conditions, and technological and organizational limitations.
Some of the problems related to the design of the construction process and the choice of materials are attempted to be solved by introducing data-based technologies that work with AI, i.e., novel BIM-based technologies and methodologies working with AI-based systems [1,23,24,25,26,27]. Modern solutions are proposed based on Digital Twins, Extended Reality (XR), Virtual Reality (AR), Augmented Reality, Mixed Reality (MR), Laser Scanners, Drones, etc. Such a comprehensive approach to the topic of construction planning and management results in the creation of complex project models. Despite great advances in IT, the practical construction problems are NP-hard (non-deterministic polynomial time hard) [14,18]. Currently, it is indicated that metaheuristic algorithms are the best way to deal with such problems. However, even they are not guaranteed to find the best solutions [22,28,29]. Therefore, there is a need for ways to support them.
This article presents a concept of solving the above problems. Section 2 describes the value engineering methodology, which is one of the foundations of the new approach. Then, an innovative proprietary optimization model for construction projects was presented. It also describes an innovative way to optimize construction schedules using artificial intelligence.
Section 3 provides a thorough case study showing the benefits of the new method. The example is based on the construction of a modern office building. It deals with the selection of the right materials and the technology of building the facility. This section also summarizes the results of additional studies.
The article ends with a discussion and conclusions. The conclusions drawn from the research were described and further directions of research were indicated.

2. Materials and Methods

2.1. Value Engineering

Value Engineering (VE) is a methodology or set of principles for defining, maximizing, and achieving the best value of goods, services, or products [14]. The VE term is often used as a synonym of Value Management (VM) [30,31]. VE ensures that the good meets the investor’s needs, especially in terms of materials, costs, and quality. Numerous sources [14,15] underline that the benefits of using VM are especially important during the initial stages of projects. VE/VM is described in detail in many publications [14,15,30,31,32,33].
To use VE, it is important to properly quantify and measure values (functions). The most common practice is to analyze each function/object/element and determine its actual cost of implementation (including principles of sustainable development). Usually, the experts (performing VE) distinguish basic and additional functions influencing the value of an investigated object. They need to analyze all the functions of the element to assess its actual value. For example, when considering material solutions, the primary function of a granite floor is that of a pedestrian walkway. The same role can be played by concrete slabs, the cost of which is lower. However, a granite floor also performs other, additional functions, among which aesthetics (a subjectively measurable function) may play an important role. Granite is also more durable than its concrete counterpart due to its greater abrasion resistance (objectively measurable function) [15].
The author already presented a proprietary approach to the VE in which value (V) was defined as a weighted sum of assessments of the fulfillment of individual functions and aspects related to sustainable development [14]. The approach is based on the value profile tables that use the value creation factors proposed by renowned organizations, such as The International Council for Building (CIB—Conseil International du Bâtiment), the International Organization for Standardization (ISO), the United Nations (UN), and the European Economic Community (EEC).
In the aforementioned approach, individual criteria/factors of creating value get assigned weights, depending on the preferences of a decisionmaker. The results are normalized so that the sum of the weights is equal to 1. As a result, a vector Q of weights of individual factors for creating the value is created (Equation (1)) [14]:
Q = q j j = 1 n q j = 1   .
Then, individual variants are being assessed in terms of all included criteria (only the ones with scores higher than 0). As a result, the evaluation matrix P is created. In the next step, variant assessments under individual criteria are being standardized. The elements of the normalized matrix P ¯ are calculated according to the Equation (2) [14]:
p ¯ i j = p i j   i = 1 m p i j 2 i = 1 , m ¯   ,   j = 1 , n ¯   ,
where n is the number of value creation factors (criteria), and m is the number of assessed variants.
In the next step of the procedure, a normalized V rating matrix is calculated considering the importance of individual criteria. The elements of the normalized matrix V are calculated as follows [14]:
V i j = p ¯ i j · q j i = 1 , m ¯   ,   j = 1 , n ¯   .
The sum of the matrix components in the rows corresponding to the variants is the result of V i , which is the score of the individual variants in terms of value creation factors:
V i = j = 1 n V i j i = 1 , m ¯   ,   j = 1 , n ¯   .
The results are subject to linear-maximum standardization; thus, we obtain the V values for all variants of all activities in the schedule. The procedure is presented in detail in [14] and the case study—Section 3 of this paper.

2.2. Optimization Model

As already mentioned in the introduction, for the project to be successful, an appropriate analysis must be performed. The author believes that many factors contributing to the success of the project should be analyzed simultaneously, including the specificity of the market and the construction industry, the way of settling works, potential contract conditions, contract terms, technological and organizational dependencies, the life cycle of the facility, the materials used, etc. The author has already presented the appropriate model in the previous work [14]. In this article, the model has been further developed to meet the needs of construction companies. The model uses tested and recommended methods of assessing construction projects: Net Present Value (NPV) minimizing monthly cash flows (CF) [4,16,18].
Let R ρ and R ν be sets r ρ and r ν , respectively, of renewable and non-renewable resource types. Their availability: a k ρ , k R ρ and a l ν , l R ν . Each activity j consumes r j k t ρ renewable resources and r j l t ν non-renewable resources during day t.
M j   different modes (variants, for example, use of alternative materials or technology) are introduced in which the activity j, m M j = 1 , , M j can be performed. The duration of action j performed in the m j mode is equal to d j m . Each of the m variants requires r j m k ρ renewable and r j m l ν non-renewable resources. Such notation is characteristic for the MRCPS (Multi-Mode Resource—Constrained Project Scheduling Problem) problems [34,35,36]. It also includes binary variable x j m t , taking the value 1, if the activity j performed in the mode m M j = 1 , , M j   is finished at the end of the period of time t. Otherwise x j m t = 0 . E F j and L F j   are respectively the earliest (early) and late dates for completing the activity j.
The new, improved objective function (OF) aims to maximize parameters such as Net Present Value (NPV) and usage/functional value (V) while minimizing monthly cash flows (CF).
max O F : O F = h = 1 H + Δ P h I C h 1 + α h   T I h = 1 H m = 1 | M j | j = 1 n q = max t , E F j min t + d j m 1 , L F j C F j m d j m   1 + α t   x j m q   w 1 + m = 1 | M j | j = 1 n t = E F j L F j f j m   x j m t J     w 2 max t m = 1 | M j | j = 1 n q = max t , E F j min t + d j m 1 , L F j C F j m d j m   1 + α t   x j m q   w 3 , H = L F j T I , t = 1 ,   ,   H  
m = 1 | M j | t = E F j L F j x j m t = 1 ,   j = 0 ,   , n + 1
m = 1 | M j | t = E F i L F i t   x i m t m = 1 | M j | t = E F j L F j x j m t   t d j m ,   i , j P
j = 1 n m = 1 | M j | q = max t , E F j min t + d j m 1 , L F j r j m k ρ   x j m q a k ρ ,   k = 1 , ,   r ρ   ,   t = 1 ,   ,   H
j = 1 n m = 1 | M j | t = E F j L F j r j m l ν   x j m t a l ν ,   l = 1 , ,   r ν
t = E F j L F n + 1 t   x n + 1 , m , t D   ,   j = 0 ,   , n + 1
x j m t 0 , 1 ,   j = 0 , ,   n + 1 ,   m M j ,   t = E F j , ,   L F j
where:
  • P h are profits for the period ending on h, h = 1, 2, …, H;
  • I C h are indirect costs for the period ending on h, h = 1, 2, …, H;
  • TI is a known time interval, and in the analyzed model it corresponds to one working month and is expressed in days;
  • Δ is a variable for modelling payment delays, where payment delay is ε [working days], Δ = ε / T I ;
  • C F j m   is cash flow of activity j performed in mode m ;
  • α is an interest rate;
  • f j m   is the assessment of the VM functions of activity j performed in mode m ;
  • w i is a weight of individual parts of the optimization objective function subject to equation 1 n w i = 1 ;
  • D is a deadline for completion of construction.
Equation (6) ensures that each activity is performed only once and in only one of the possible modes. (7) models the relations between tasks. The constraints for renewable (8) and non-renewable (9) resources can also be used to model doubly constrained resources. Equation (10) models a deadline for construction completion while constraint (11) is responsible for modeling binary decision variables.
The conceptual notation of the objective function used for computer modeling is similar to the one presented in [14], however, improvements were made to involve the importance of the CF parameter:
O F = w 1 · N P V r + w 2 · V r w 3 · C F r o 1 · R o 2 · d u r
where:
  • ( w 1 · N P V r + w 2 · V r ) is an objective part of the function,
  • ( w 3 · C F r o 1 · R o 2 · d u r ) are restrictions (penalties), w i are the weights of individual parts of the objective function subject to optimization,
  • o i are the weights of individual parts of the objective function responsible for constraints (penalties).
The sum of w i is equal to 1, while o i values are significantly greater than those of the first part of the objective function (goal), so that failure to meet any of the constraints results in the disqualification of a given solution.
NPVr is the objective function component responsible for the optimization of the relative NPV value [14]:
N P V r = N P V N P V m i n N P V m a x N P V m i n   ,
where:
  • N P V   is the NPV value for the currently examined case,
  • N P V m a x   is the maximum NPV value found for the unconstrained version of the project,
  • N P V m i n   is the minimal NPV value found for the unconstrained version of the project.
Vr is a component of the objective function that corresponds with the score obtained by a given solution in terms of VM principles [14]:
V r = V V m i n V m a x V m i n   ,
where:
  • V   is the value rating for the currently studied case,
  • V m a x   is the maximum value rating found for the unconstrained version of the tested example,
  • V m i n   is the minimum value grade found for the unconstrained version of the tested example.
CFr is the objective function component responsible for the optimization of the relative CF value:
C F r = C F C F m i n C F m a x C F m i n   ,
where:
  • C F   is the CF value for the currently examined case,
  • C F m a x   is the maximum CF value found for the unconstrained version of the project,
  • C F m i n   is the minimal CF value found for the unconstrained version of the project.
R is a binary variable responsible for meeting the condition of not exceeding the maximum availability of resources (e.g., workers, machinery, materials) [14].
R = 1   i f   c o n d i t i o n   8   o r   9   i s   n o t   m e t 0   i n   o t h e r   c a s e s
dur is a binary variable responsible for meeting the condition of not exceeding the contractual construction date [14].
d u r =   1   i f   c o n d i t i o n   10   i s   n o t   m e t   0   i n   o t h e r   c a s e s
Other aspects and elements of the model presented in [14] remain unchanged.

2.3. Optimization Procedure Supported by AI

The procedure described in detail in [14] was modified by introducing artificial intelligence (AI). AMTANN (Approach for MRCPSP Transformation with the use of Artificial Neural Networks) procedure [29] was modified and implemented to improve obtained results. The modified procedure is presented in Figure 1. The AMTANN procedure is presented separately in Figure 2 while AMTANN principles are described in the author’s previous paper [29].
The procedure begins with the preparation of the original (initial) version of the project schedule. This version is based on the functional and operational plan of the project. Then alternative versions of the project are created. The possible use of different materials, the use of different technologies, etc., are distinguished. The value of individual variants is assessed. As a result, the schedule is updated with additional modes (multi-mode version).
In the next step, metaheuristic algorithms are used to search for maximum and minimum values of optimized parameters. The constraints are not considered at this stage (UPS—Unconstrained Project Scheduling). The solutions found help to build a mathematical model and carry out the AMTANN analysis (Figure 2).
Finally, the results are assessed. If several acceptable solutions are obtained for different w i weight configurations, one of them should be selected. First of all, it should be checked whether some solutions are dominated by others. Only Pareto optimal solutions are eligible for the final selection. The final decision may be made by the decisionmaker arbitrarily or on the basis of one of the multi-criteria decision support methods, e.g., the AHP, TOPSIS, or ELECTRE method [37,38,39].
It may also happen that, despite finding acceptable schedules, the decisionmaker will not decide to implement the project, considering the obtained results to be insufficient. In this case, the presented approach can help to avoid losses of the enterprise related to the implementation of an inappropriate project.
The detailed procedure is presented on the real-life example in Section 3.

3. Results

3.1. Case Study

3.1.1. Basic Information

The subject of the case study is a public utility building with two underground and seven above-ground stories, located at Domaniewska street in Warsaw, Poland. The object is described in detail in [40]. It is an office building (with commercial premises) about 30 m high. The analyzed building consists of two independent parts separated by a fire wall, and their only connection is in the underground garages. The basic parameters of the planned facility are presented in Table 1.
In this case, the analysis covered the construction of the building in three different material variants. With the use of different materials, it was necessary to use a specific technology. The selection of materials also influenced the duration and cost of the project. The three original timetables for each option are as follows:
  • variant 1 (V1)—reinforced concrete structure made of steel and concrete materials on the construction site (Figure 3),
  • variant 2 (V2)—main structural elements in the prefabricated elements technology (Figure 4),
  • variant 3 (V3)—mixed technology with the ceiling which consists of beams with a spatial truss and blocks made of light aggregate concrete (after laying the beams and blocks, the ceiling is flooded with concrete) (Figure 5).

3.1.2. Value Analysis

Based on the original schedules and descriptions of individual variants, including materials [40], a table of variants was prepared with a short description of the assessed methods (Table 2). The duration of individual activities and the relationship between tasks were introduced on the basis of a previously prepared study [40]. In this example, the project manager considers the constraints of renewable resources (Z1: workers, Z2: concrete pumps, and Z3: cranes) and non-renewable resources (costs related to the implementation of individual activities, including material costs, which were calculated in the study [40]). The values of Vi were determined on the basis of the value profile table (the evaluation of the values is presented below, using the example of the item “partition walls”). Table 3 shows the assessment of the various variants.
In the given example, some of the works at the beginning of construction are the same for all variants; their value has been assessed as equivalent and amounts to 1.0. Three material/technological variants described above were considered, while it was assumed that for economic and organizational reasons, the concept of the entire facility should be consistent, therefore for most works: level -1 (excluding the entry ramp) to level 6 (with a flat roof) a common/total value analysis was done. Each of the activities, depending on the selected design variant, received the same value within the corresponding variant. A separate analysis was performed only for three variants of the partition walls because this activity does not depend on the construction variant. The table of the value profile along with the significance of individual criteria assessment is presented below on the example of the partition wall (Table 4).
Based on the opinion of the expert team, after normalization, a vector of weights was obtained for the individual factors of creating the value-Q (Table 5).
After normalization, a normalized evaluation matrix with scores is obtained, as presented in Table 6.
A normalized V rating matrix is calculated, considering the importance of individual value-creating factors (Table 7).
The final scores for the individual variants (material solutions) are obtained by way of summation and standardization, and are presented in Table 8.

3.1.3. Project Update

After the analysis, the calculated V values were entered into the schedules, and the relationships between tasks were updated, at the same time introducing the possibility of delaying activities, allowing for optimization of project parameters, and considering resource constraints and material solutions. The schedule also includes data on the contractual period, 130 weeks, and the deadline, 150 weeks. Indirect costs are also included.

3.1.4. UPS Optimization

In the next step, a metaheuristic algorithm was used (the case study was calculated using OptQuest® Engine, OptTek Systems, Inc.’s) to calculate maximum and minimum values of NPV, CF, and V: NPVmax, NPVmin, CFmax, CFmin, Vmax, and Vmin. The cash flow calculated in this example considered only the flows starting from the 10th month of construction because the work carried out in the first 9 months of the construction period was the same for all variants. It was assumed that the decisionmaker wants to optimize the cash flow during the construction of the above-ground part of the facility. The results are presented in Table 9. The analyzed variables were variants of materials used/works execution (three possible options for the structure and three for partition walls) and activity delays (zero to eight weeks depending on the activity). Such delays can help spread the cash flow caused by material orders or employee payments over time.

3.1.5. MRCPS Optimization and Materials/Technology Selection

Penalties for exceeding the directive deadline (EUR 50 000 for a week of delay) were introduced into the computer model. Additionally, resource limitations were introduced: construction workers (64 workers), concrete pumps (5 pumps), cranes (2 cranes). The introduced limitations made the original three variants of the schedule unacceptable (they did not meet the imposed resource availability constraints). MRCPS optimization was performed for the ten sets of weights shown in Table 10.
The best results for each set of weights were recorded for later comparison with the results obtained by the AMTANN procedure. These results, along with random suboptimal solutions, were used as a sample for learning, validating, and testing the artificial neural network (2000 records in total). In the described case AMTANN was used to reduce the range of the variables.
The method of selecting the reduced variables is presented in the example of activity 13—non-reduced variable (Level 0: Walls 2) and the construction variant—reduced variable (variable 1). After processing the neural network and establishing weights for each variable, solution profiles were examined to establish relationships between predictors (variables) and outcomes (output) and interactions between the predictors. For the constant (minimum, intermediate, and maximum) values of the predictors, the behavior of each of the variables in relation to the predicted result was checked. The profile of the analyzed variable, and possible delay of activity no. 13 in three variants is shown in Figure 6, Figure 7 and Figure 8.
Due to the lack of consistency of the profiles, it was decided not to reduce the value range of the variable corresponding to activity no. 13.
A similar analysis was performed on variable 1, corresponding to the selection of the construction variant of the object. As can be seen in Figure 9, Figure 10 and Figure 11, this variable has the same impact on the expected result, regardless of the value of the other variables, which qualifies it to reduce its range. As a result, it was decided to exclude variant 3 from further calculations.
As a result of the procedure, the range of 13–35 variables was reduced. This procedure reduced the solution space significantly (by about 2∙1024 possible variants). The results before and after the application of AMTANN are presented below in Table 11 and Figure 12 (additional views are available in the Appendix A: Figure A1, Figure A2 and Figure A3).
In the individual columns of Table 11, the corresponding results (the same weights of the objective function) achieved better values after using the AMTANN procedure. As shown in Figure 12 and Appendix A, the results after using artificial neural networks showed less randomness and were generally better (greater average distance from the origin of the coordinate system and greater values of the objective function within the same sets of weights). Importantly, AMTANN assumes the preservation of the original results to confront them with the final results at the later stage, thanks to which some solutions belonging to the Pareto front are not lost.

3.1.6. Variant Selection

Solutions belonging to the Pareto set (not dominated by any others) are presented in Figure 13 (in Appendix B, projections of points on the NPV, CF plane have been added to improve the legibility of the drawings—Figure A4, Figure A5 and Figure A6). Only these solutions were considered when selecting the variant of the final project. An alternative decision could have been to reject the project entirely. One of the multi-criteria decision-making methods (some presented here [41]) can be used in the final selection.
In the analyzed case, the decisionmaker decided to choose the NPV variant: 0.7; CF: 0.15; and V: 0.15 from the AMTANN procedure; it has the highest possible V value and the highest NPV value among the options considered. An illustrative schedule of the selected variant is presented in Figure 14. Selected materials’ variants and delays’ values (final variable values) are presented in Table 12.

4. Discussion

The example presented above shows the effectiveness of the use of metaheuristic algorithms when selecting materials and technologies for a construction project. Moreover, according to the data in Table 11, these results can be further improved using artificial intelligence tools. Importantly, the presented methodology does not impose the only correct solution. Instead, it gives managers the option to choose from among the many advantageous solutions that make up the Pareto front (Figure 13). The summary of results for the final selection of weights is presented in Table 13.
Thanks to the use of metaheuristic optimization, a significant improvement in the results were achieved. Objective function value improved by 51.01% (in case of variant 2)–499.61% (variant 3). Moreover, thanks to the use of AMTANN, a further improvement of 12.43% was achieved (a total improvement over the initial options: 69.79–574.16%). Not only was there a significant improvement in the NPV parameter, which was dominant in this case. The parameter V, which is crucial from the point of view of durability and serviceability of the object, was also improved.
To confirm the effectiveness of AMTANN, additional tests (calculations) were carried out for the example studied in this article. The mean results are shown in Figure 15 and in Appendix C (Figure A7, Figure A8 and Figure A9). Mean results after the application of ANN are characterized by higher values of OF and parameters NPV, V, and CF.
The presented method is so flexible that it can be used for projects of various sizes. So far, the author has studied single-family house-sized cases as well as multi-unit housing estates and commercial buildings. However, the method requires careful model building, which means that an experienced manager must be employed. However, this is now the standard for major projects.
Based on the conducted research and analyses, the following conclusions can be drawn:
  • It is possible to improve the functionality/usability of the facility by using appropriate materials and technological solutions.
  • It is possible to obtain a reliable assessment result and to select the variant of the undertaking most adequate to the formulated expectations of the decisionmaker.
  • It is possible to optimize the construction schedule by considering the economic and utility value of a construction project with the use of artificial intelligence tools.
  • Artificial neural networks can be effectively used to support the metaheuristic algorithm to improve project outcomes.
Moreover, the approach proposed by the author is structured in such a way that it can use various tools. In the future, the author plans to test and compare various artificial intelligence tools and optimization algorithms.

5. Conclusions

The proposed procedure allowed for the selection of the best available material/technological solution from the point of view of the decisionmaker. The use of AMTANN made it possible to find potential solutions better than those obtained using only the metaheuristic algorithm.
In the tests so far, improvement has been achieved in the majority of cases. Importantly, AMTANN retains the results from the original optimization, so even if the original results are not improved, the user retains the best results obtained during initial metaheuristic optimization. The proposed approach comprehensively reflects the complexity of construction processes. At the same time, it allows users to be flexible and adjust the tested parameters to their own needs. Thanks to the appropriate selection of material and technological solutions, the analyzed projects can achieve better economic results.
In the future, further development of the method is planned, including the use of other artificial intelligence tools.

Funding

The APC was funded by Warsaw University of Technology.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Conflicts of Interest

The author declares no conflict of interest.

Appendix A

Projections for Figure 12.
Figure A1. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and CF.
Figure A1. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and CF.
Materials 15 01282 g0a1
Figure A2. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and V.
Figure A2. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and V.
Materials 15 01282 g0a2
Figure A3. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF, and V)—2D view: CF and V.
Figure A3. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF, and V)—2D view: CF and V.
Materials 15 01282 g0a3

Appendix B

Projections for Figure 13.
Figure A4. Solutions belonging to the Pareto front—2D view: NPV and CF.
Figure A4. Solutions belonging to the Pareto front—2D view: NPV and CF.
Materials 15 01282 g0a4
Figure A5. Solutions belonging to the Pareto front—2D view: NPV and V.
Figure A5. Solutions belonging to the Pareto front—2D view: NPV and V.
Materials 15 01282 g0a5
Figure A6. Solutions belonging to the Pareto front—2D view: V and CF.
Figure A6. Solutions belonging to the Pareto front—2D view: V and CF.
Materials 15 01282 g0a6

Appendix C

Projections for Figure 15.
Figure A7. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and CF.
Figure A7. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and CF.
Materials 15 01282 g0a7
Figure A8. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and V.
Figure A8. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF, and V)—2D view: NPV and V.
Materials 15 01282 g0a8
Figure A9. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF, and V)—2D view: V and CF.
Figure A9. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF, and V)—2D view: V and CF.
Materials 15 01282 g0a9

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Figure 1. Block diagram of the proposed algorithm—modified on a base of [14].
Figure 1. Block diagram of the proposed algorithm—modified on a base of [14].
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Figure 2. Block diagram of the AMTANN procedure.
Figure 2. Block diagram of the AMTANN procedure.
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Figure 3. Case study—Variant 1 schedule—a pictorial screenshot.
Figure 3. Case study—Variant 1 schedule—a pictorial screenshot.
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Figure 4. Case study—Variant 2 schedule—a pictorial screenshot.
Figure 4. Case study—Variant 2 schedule—a pictorial screenshot.
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Figure 5. Case study—Variant 3 schedule—a pictorial screenshot.
Figure 5. Case study—Variant 3 schedule—a pictorial screenshot.
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Figure 6. The expected value of OF depending on the value of the analyzed decision variable (activity 13)—maximum values of other variables.
Figure 6. The expected value of OF depending on the value of the analyzed decision variable (activity 13)—maximum values of other variables.
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Figure 7. The expected value of OF depending on the value of the analyzed decision variable (activity 13)—minimum values of other variables.
Figure 7. The expected value of OF depending on the value of the analyzed decision variable (activity 13)—minimum values of other variables.
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Figure 8. The expected value of OF depending on the value of the analyzed decision variable (activity 13)—intermediate values of other variables.
Figure 8. The expected value of OF depending on the value of the analyzed decision variable (activity 13)—intermediate values of other variables.
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Figure 9. The expected value of OF depending on the value of the analyzed decision variable (variable 1)—maximum values of other variables.
Figure 9. The expected value of OF depending on the value of the analyzed decision variable (variable 1)—maximum values of other variables.
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Figure 10. The expected value of OF depending on the value of the analyzed decision variable (variable 1)—minimum values of other variables.
Figure 10. The expected value of OF depending on the value of the analyzed decision variable (variable 1)—minimum values of other variables.
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Figure 11. The expected value of OF depending on the value of the analyzed decision variable (variable 1)—intermediate values of other variables.
Figure 11. The expected value of OF depending on the value of the analyzed decision variable (variable 1)—intermediate values of other variables.
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Figure 12. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF and V)—3D view.
Figure 12. Results before and after the application of AMTANN for various configurations of weights of the objective function (NPV, CF and V)—3D view.
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Figure 13. Solutions belonging to the Pareto front—3D view.
Figure 13. Solutions belonging to the Pareto front—3D view.
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Figure 14. Case study—final schedule—illustrative screenshot.
Figure 14. Case study—final schedule—illustrative screenshot.
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Figure 15. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF and V)—3D view.
Figure 15. Average results before and after the application of AMTANN for different configurations of weights of the objective function (NPV, CF and V)—3D view.
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Table 1. Basic parameters of the office building.
Table 1. Basic parameters of the office building.
IDDataUnitsValue
1Number of underground stories-2
2Number of above-ground stories-7
3Ground floor levelm above water level24.5
4Total aream244,875.67
4.aUnderground aream214,426.03
4.bAbove-ground aream230,449.64
5Usable aream236,784.17
5.aOffice aream222,445.40
5.bService premises area (ground floor)m21,042.59
5.cAuxiliary aream21,483.98
5.dGarage aream212,051.53
6Traffic aream22454.82
7Cubaturem3169,124.90
7.aUnderground volumem355,251.68
7.bAbove-ground volumem3113,873.30
8Approximate number of employees-2556
9Parking spacesunit431
9.aIn the garageunit394
9.bOutside of the buildingunit41
9.cNumber of parking spaces per 1000 m2 of service area-25
9.dNumber of parking spaces per 1000 m2 of office area-18
Table 2. Description of materials’ variants—case study.
Table 2. Description of materials’ variants—case study.
TaskVariant 1Variant 2Variant 3
IDNameDescriptionDescriptionDescription
--Monolithic constructionPrefabricated technologyMixed technology with the use of light aggregate concrete blocks
1Start---
2Preparatory worksSite fencing, tree clearing, temporary road laying, container assembly (the same for all variants)
3Earth worksRemoval of plant soil, diaphragm walls, excavations, ceiling trim of level -2, temporary columns, excavation of level -2 (the same for all variants)
4Level -2Lean concrete under the bottom slab, bottom slab, reinforced concrete columns, reinforced concrete walls, entry ramp, reinforced concrete stairs (the same for all variants)
5Level -1: ColumnsReinforced concrete columns formed in the system formwork.Prefabricated columnsPrefabricated columns
6Level -1: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
7Level -1: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
8Level -1: Access rampReinforced concrete ramp 25 cm thick (the same for all variants)
9Level -1: Stairs, beams, joistsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm; reinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3Prefabricated stairs and beamsPrefabricated stairs and beams
10Level -1: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick, with a degree of reinforcement of 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
11Level 0: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
12Level 0: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
13Level 0: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
14Level 0: StairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
15Level 0: Beams, joistsReinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
16Level 0: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick, with a degree of reinforcement of 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
17Level 1: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
18Level 1: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
19Level 1: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
20Level 1: StairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
21Level 1: Beams, joistsReinforced concrete beams 50 cm × 30 cm. Reinforcement degree: 110 kg/m3Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
22Level 1: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick, with a degree of reinforcement of 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
23Level 2: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
24Level 2: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
25Level 2: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
26Level 2: StairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
27Level 2: Beams, joistsReinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
28Level 2: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick, with a degree of reinforcement of 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
29Level 3: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
30Level 3: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
31Level 3: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
32Level 3: StairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
33Level 3: Beams, joistsReinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
34Level 3: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick, with a degree of reinforcement of 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
35Level 4: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
36Level 4: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
37Level 4: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
38Level 4: StairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
39Level 4: Beams, joistsReinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
40Level 4: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick, with a degree of reinforcement of 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
41Level 5: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
42Level 5: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
43Level 5: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
44Level 5: StairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
45Level 5: Beams, joistsReinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3.Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
46Level 5: CeilingsMonolithic reinforced concrete ceilings, 28 cm thick; reinforcement degree: 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
47Level 6: ColumnsReinforced concrete columns formed in the system formworkPrefabricated columnsPrefabricated columns
48Level 6: Walls 1Reinforced concrete walls 25 cm thick (the same for all variants)
49Level 6: Walls 2Reinforced concrete walls 20 cm thick (the same for all variants)
50Level 6: Stairs Reinforced concrete landings and flights of staircases with a slab thickness of 15 cmPrefabricated stairsReinforced concrete landings and flights of staircases with a slab thickness of 15 cm
51Level 6: Beams, joistsReinforced concrete beams 50 cm × 30 cm; reinforcement degree: 110 kg/m3Prefabricated beams 600 cm × 30 cm × 30 cmPrefabricated beams 600 cm × 30 cm × 30 cm
52Partition wallsNIDA plasterboardsSILKA sand-lime blocksYTONG cellular concrete
53RoofReinforced concrete roof, 28 cm thick; reinforcement degree: 95 kg/m3Ceilings made of prefabricated hollow-core slabsThick-ribbed ceiling
54Finish---
Table 3. Assessment of variants materials/technology—case study.
Table 3. Assessment of variants materials/technology—case study.
Variant 1Variant 2Variant 3
IDCost
[1000 EUR]
Duration
[Weeks]
Value VZ1Z2Z3Cost
[1000 EUR]
Duration
[Weeks]
Value VZ1Z2Z3Cost
[1000 EUR]
Duration
[Weeks]
Value VZ1Z2Z3
10.001.000000.001.000000.001.00000
2203.511.001001203.511.001001203.511.001001
36714.0231.0024006714.0231.0024006714.0231.002400
45875.0161.0028205875.0161.0028205875.0161.002820
5245.731.002220285.510.871201285.510.851201
665.331.00282065.330.87282065.330.852820
7303.341.002820303.340.872820303.340.852820
885.011.00161085.011.00161085.011.001610
916.411.001210172.910.872402178.130.851210
102068.371.004020902.620.8712021238.040.852000
11215.331.001610357.320.87801357.320.85801
12192.731.003220192.730.873220192.730.853220
1316.311.00322016.310.87322016.310.853220
1416.311.008200 *00.8700016.310.85810
1530.021.00710218.810.87801196.210.85701
16920.221.004020480.310.871202659.020.852000
17180.921.001610299.110.871201299.310.851201
18140.431.003220140.430.873220140.430.853220
1917.211.00322017.210.87322017.210.853220
2016.311.0016200 *00.8700016.310.85810
2116.921.00810218.810.87801196.210.85701
221109.631.004020573.810.871202787.420.852000
23199.831.001610339.810.871201340.110.851201
24144.031.003220144.030.873220144.030.853220
2517.211.00322017.210.87322017.210.853220
2616.341.0016200 *00.8700016.310.85810
2716.931.00810218.810.87801196.210.85701
281108.631.004020572.810.871202786.320.852000
29199.831.001610339.810.871201340.110.851201
30144.031.003220144.030.873220144.030.853220
3117.211.00322017.210.87322017.210.853220
3216.341.0016200 *00.8700016.310.85810
3316.931.00810218.810.87801196.210.85701
341104.831.004020572.810.871202786.320.852000
35199.831.001610339.810.871201340.110.851201
36144.031.003220144.030.873220144.030.853220
3717.211.00322017.210.87322017.210.853220
3816.341.0016200 *00.8700016.310.85810
3916.931.00810218.810.87801196.210.85701
401104.831.004020572.810.871202786.320.852000
41199.831.001610339.810.871201340.110.851201
42144.031.003220144.030.873220144.030.853220
4317.211.00322017.210.87322017.210.853220
4416.341.0016200 *00.8700016.310.85810
4516.931.00810218.810.87801196.210.85701
461104.831.004020572.810.871202786.320.852000
47200.131.001610339.810.871201340.110.851201
48144.831.003220144.830.873220144.830.853220
4917.311.00322017.310.87322017.310.853220
5016.341.0016200 *00.8700016.310.85810
5165.431.00810218.810.87800196.210.85701
52890.450.623200495.851.003200416.940.993200
531349.151.003220716.530.873220930.240.853220
540.001.000000.001.000000.001.00000
* In variant 2, the stairs are made together with beams and joists as part of the activities: Beams, joists.
Table 4. Value profile table (evaluation matrix P)—case study—partition walls.
Table 4. Value profile table (evaluation matrix P)—case study—partition walls.
Criteria ScoreV1V2V3
1 Safety1.1 Structural safety0---
1.2 Fire safety10155
1.3 Usage safety0---
2 Comfort2.1 Acoustic comfort6542
2.2 Visual comfort (lighting)0---
2.3 Hygrothermal comfort2244
2.4 Serviceability2534
3 Health3.1 Air quality0---
3.2 Water supply and other utilities0---
3.3 Waste disposal0---
4 Durability4.1 Durability10245
5 Sustainable development5.1 Energy saving0---
5.2 Greenhouse gas emissions0---
5.3 Economics (running costs)10355
5.4 Dismantling and utilization2543
Table 5. Illustrative representation of the vector of weights for individual value-creating factors—Q.
Table 5. Illustrative representation of the vector of weights for individual value-creating factors—Q.
CriterionWeight
1.1 Structural safety0
1.2 Fire safety0.238095
1.3 Usage safety0
2.1 Acoustic comfort0.142857
2.2 Visual comfort (lighting)0
2.3 Hygrothermal comfort0.047619
2.4 Serviceability0.047619
3.1 Air quality0
3.2 Water supply and other utilities0
3.3 Waste disposal0
4.1 Durability0.238095
5.1 Energy saving0
5.2 Greenhouse gas emissions0
5.3 Economics (running costs)0.238095
5.4 Dismantling and utilization0.047619
Table 6. Normalized evaluation matrix P ¯ .
Table 6. Normalized evaluation matrix P ¯ .
1.11.21.32.12.22.32.43.13.23.34.15.15.25.35.4
V10.5770.1400.5770.7450.5770.3330.7070.5770.5770.5770.2980.5770.5770.3910.707
V20.5770.7010.5770.5960.5770.6670.4240.5770.5770.5770.5960.5770.5770.6510.566
V30.5770.7010.5770.2980.5770.6670.5660.5770.5770.5770.7450.5770.5770.6510.424
Table 7. Assessment matrix V.
Table 7. Assessment matrix V.
1.11.21.32.12.22.32.43.13.23.34.15.15.25.35.4
V101.40004.47200.6671.4140002.981003.9061.414
V207.00103.57801.3330.8490005.963006.5091.131
V307.00101.78901.3331.1310007.454006.5090.849
Table 8. Assessment of material variants for activity 52 of the schedule.
Table 8. Assessment of material variants for activity 52 of the schedule.
VariantScore V
V1-NIDA0.617
V2-SILKA1.000
V3-YTONG0.989
Table 9. Calculated extreme values of NPV, CF, and V (UPS optimization).
Table 9. Calculated extreme values of NPV, CF, and V (UPS optimization).
IndicatorValue
N P V m a x 1,705,955 EUR
N P V m i n 130,827 EUR
C F m a x 1,961,197 EUR
C F m i n 0 EUR
V m a x 1.000
V m i n 0.853
Table 10. Configurations of objective function’s weights—a case study.
Table 10. Configurations of objective function’s weights—a case study.
w 1 (NPV)0.3(3)0.70.150.150.60.60.20.10.20.1
w 2 (CF)0.3(3)0.150.70.150.20.10.60.60.10.2
w 3 (V)0.3(3)0.150.150.70.10.20.10.20.60.6
Table 11. Results for various weight configurations before and after use of AMTANN.
Table 11. Results for various weight configurations before and after use of AMTANN.
w 1 (NPV)0.330.70.150.150.60.60.20.10.20.1
w 2 ( V)0.330.150.150.70.10.20.10.20.60.6
w 3 ( CF)0.330.150.70.150.20.10.60.60.10.2
After use of AMTANN
NPVr0.987020.987700.840190.949220.986040.987210.872490.850770.948990.94912
Vr1.000001.000000.178321.000001.000001.000000.179770.178321.000001.00000
CFr0.336290.352320.070450.347950.336290.352320.067730.006280.327800.33629
OF0.5496930.7885420.1034650.7901890.6243690.7570910.1518360.1169730.7570180.627654
Duration [d]128128100132128128112104132132
NPV [EUR]1,685,5071,686,5801,454,2341,625,9651,683,9721,685,8011,505,1111,470,8911,625,6031,625,812
V110.8795771110.8797880.87957711
CF [EUR] 659,527 690,964138,159682,408659,527690,964132,83512,318642,875659,527
Before use of AMTANN
NPVr0.947360.863670.859670.948190.948540.949590.918560.873900.863450.86316
Vr1.000001.000000.178321.000001.000001.000000.050260.179771.000001.00000
CFr0.356840.354860.131820.353910.342030.336290.152050.065620.343490.34349
OF0.5296440.701340.0634220.7891420.6007170.7361260.0975090.0839710.7383410.617618
Duration [d]132136108132132132112112136136
NPV [EUR]1,623,0421,491,2171,484,9221,624,3461,624,8971,626,5561,577,6721,507,3311,490,8731,490,416
V110.8795771110.8608080.87978811
CF [EUR]699,835695,946258,534694,083670,794659,527298,192128,695673,655673,655
Table 12. Results for various weight configurations before and after use of AMTANN.
Table 12. Results for various weight configurations before and after use of AMTANN.
Variable No.Variable NameSelected Variant
Variables concerning materials and technological variants (execution modes)
1Construction material variant1
2Partition walls variant2
Delay variables (values in weeks)
35. Level -1: Columns3
46. Level -1: Walls 10
57. Level -1: Walls 20
68. Level -1: Access ramp2
711. Level 0: Columns2
812. Level 0: Walls 10
913. Level 0: Walls 20
1014. Level 0: Stairs0
1117. Level 1: Columns0
1218. Level 1: Walls 10
1319. Level 1: Walls 23
1420. Level 1: Stairs0
1523. Level 2: Columns0
1624. Level 2: Walls 10
1725. Level 2: Walls 23
1826. Level 2: Stairs0
1929. Level 3: Columns2
2030. Level 3: Walls 13
2131. Level 3: Walls 22
2232. Level 3: Stairs0
2335. Level 4: Columns3
2436. Level 4: Walls 12
2537. Level 4: Walls 22
2638. Level 4: Stairs0
2741. Level 5: Columns3
2842. Level 5: Walls 13
2943. Level 5: Walls 22
3046. Level 5: Stairs0
3147. Level 6: Columns2
3247. Level 6: Walls 10
3349. Level 6: Walls 21
3451. Level 6: Beams, joists (in variant 2, together with the stairs)0
3552. Partition walls0
Table 13. The summary of results for the final selection of weights.
Table 13. The summary of results for the final selection of weights.
Metaheuristic Optimization ResultsInitial Solutions
After AMTANNBefore AMTANNVariant 1Variant 2Variant 3
OF0.7890.7010.3860.4640.117
NPV [EUR]1,686,5801,491,217759,3241,210,342488,605
V1.0001.0000.9930.8800.861
CF [EUR]690,964695,946468,775552,907645,295
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Rosłon, J. Materials and Technology Selection for Construction Projects Supported with the Use of Artificial Intelligence. Materials 2022, 15, 1282. https://doi.org/10.3390/ma15041282

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Rosłon J. Materials and Technology Selection for Construction Projects Supported with the Use of Artificial Intelligence. Materials. 2022; 15(4):1282. https://doi.org/10.3390/ma15041282

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Rosłon, Jerzy. 2022. "Materials and Technology Selection for Construction Projects Supported with the Use of Artificial Intelligence" Materials 15, no. 4: 1282. https://doi.org/10.3390/ma15041282

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