75504 Magazine of Civil Engineering Magazine of Civil Engineering 2712-8172 10 10.34910/MCE.141.10 Adaptive cost-constrained optimization of concrete mixtures using machine learning-guided genetic algorithms Adaptive cost-constrained optimization of concrete mixtures using machine learning-guided genetic algorithms 0000-0002-0644-2657 Beigi Mohsen mohsenbeigi59@gmail.com Islamic Azad University 13 02 2026 19 1 141 14110 14110

This study presents an adaptive framework for optimizing high-performance concrete mixtures by integrating machine learning with a genetic algorithm under cost constraints. An experimental dataset was used to train an XGBoost model, which accurately predicts 28-day compressive strength. The trained machine learning model was embedded as the objective function within the genetic algorithm to maximize compressive strength while incorporating cost limitations defined by user-provided unit prices and budget. Unlike most previous studies that treat cost and strength as two separate objectives in multi-objective formulations, this work introduces cost as a constraint and strength as the sole optimization objective, thereby simplifying the decision-making process. To bridge the gap between theory and practice, an Android application was developed. The application enables users to input real-time material prices and budget limits, which are transmitted to a server hosting the machine learning model and genetic algorithm. The server computes optimized mix proportions and returns both the predicted compressive strength and the optimal design to the user interface. The proposed adaptive optimization framework was shown to effectively adjust to market price fluctuations and varying budget scenarios, providing a practical and flexible solution for real-world applications. Furthermore, the single-objective formulation ensures a unique optimal solution, avoiding the complexity of selecting among multiple Pareto-optimal alternatives.

 concrete mix optimization machine learning genetic algorithm compressive strength prediction cost constraint android application

1.Introduction

Concrete is one of the most widely used construction materials due to its versatility, durability, and cost-effectiveness. It is a composite material composed primarily of cement, aggregates, water, and chemical admixtures. Cement acts as the binding agent, holding the mixture together, while aggregates contribute to bulk and significantly influence the mechanical and durability properties of both fresh and hardened concrete. Water facilitates the hydration of cement and affects the porosity, strength, and durability of the hardened material. Chemical admixtures are employed to regulate physical properties and improve workability and performance [1, 2].

The 28-day compressive strength of concrete is a critical performance indicator in both research and practice. It is affected by multiple factors including mix proportions, water-to-cement ratio, curing conditions, and the properties of individual components. Accurate prediction of this property is essential for ensuring safety, performance, and compliance with standards [3, 4].

Cost is another significant factor in concrete production. Raw material expenses, such as cement, aggregates, and admixtures, can constitute more than half of the total production cost. Rising material prices, particularly for cement, can substantially impact project budgets. Optimizing concrete mixtures with supplementary materials like fly ash or slag can reduce costs while maintaining or enhancing performance [5, 6].

However, compressive strength and production cost are generally conflicting objectives, since an increase in strength is often associated with higher costs, and vice versa. In many studies, this trade-off has been addressed through multi-objective optimization approaches, where compressive strength and cost are treated as two separate objectives to be optimized simultaneously 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[7–17].

Predicting concrete compressive strength is a complex task due to nonlinear relationships between input variables, such as mix proportions and curing conditions, and output variables. Traditional empirical models often fall short in capturing these interactions. Machine learning techniques, such as extreme gradient boosting and artificial neural networks, have demonstrated high accuracy in estimating compressive strength, effectively managing complex datasets and improving prediction reliability [18, 19].

Integrating genetic algorithms with machine learning models has proven highly effective for optimizing concrete mix designs to achieve maximum compressive strength under specified constraints. Genetic algorithm explores vast solution spaces and identifies optimal solutions by mimicking natural selection. When combined with machine learning models predicting compressive strength, genetic algorithms can fine-tune mix proportions for enhanced performance. Studies have demonstrated that integrating machine learning estimators with genetic algorithms enables optimization of concrete mixtures, balancing strength, cost, and durability under quality constraints [20, 21].

In this study, an experimental dataset was employed to develop a machine learning model for predicting the 28-day compressive strength of concrete. The trained model was subsequently coupled with a genetic algorithm to optimize concrete mixture proportions subject to both technical and economic constraints. In contrast to previous studies, construction cost is not formulated as a secondary optimization objective; instead, it is explicitly imposed as a constraint. This formulation allows market price fluctuations to be flexibly incorporated into the optimization framework. By enabling users to specify material unit prices and a maximum allowable budget, the proposed approach ensures that compressive strength is maximized while strictly satisfying the prescribed cost limitation.

The novelty of this work lies in two main aspects. First, the optimization problem is formulated as a single-objective genetic algorithm, where the objective function is the compressive strength predicted by the machine learning model, while cost and proportional limitations are treated as constraints. This design offers a more flexible and practical framework compared to traditional multi-objective approaches. Second, to facilitate real-world application, an Android application was developed that allows users to input unit prices and budget information. These inputs are transmitted to a server hosting the machine learning model and genetic algorithm, which computes the optimal mixture proportions and returns the results to the application (Fig. 1). This user-oriented design makes the framework not only technically innovative but also highly accessible for practical decision-making in concrete mix design.

Figure 1. Schematic representation of the developed framework.

2.Materials and Methods

2.1.Problem Formulation

The present study addresses the optimization of high-performance concrete mixture proportions using a single-objective genetic algorithm. The objective function (cost function) is to maximize the 28-day compressive strength predicted by a trained machine learning model:

                                               (1)

where  represents the output of the machine learning model and the input variables  (all in kg/m3) the concrete constituents as defined in Table 1.

Table 1. Concrete components, specific gravities, and constraint ratios.

Component

Symbol

Specific Gravity (kg/m³)

Min Ratio

Max Ratio

Notes / Constraint Type

Cement

X1

3.15

—

—

Part of binder

Slag

X2

2.80

0

0.61

Slag-to-binder ratio

Fly Ash

X3

2.50

0

0.61

Fly Ash-to-binder ratio

Water

X4

1.00

0.23

0.90

Water-to-binder ratio

Superplasticizer

X5

1.35

0

0.13

SP-to-cement ratio

Coarse Aggregate

X6

2.50

1.18

5.62

Coarse-to-binder ratio

Fine Aggregate

X7

2.65

0.35

0.54

Fine-to-total aggregate ratio

The genetic algorithm aims to determine the optimal mixture proportions under a set of general, proportional, and cost constraints.

2.1.1. Volume constraint

The total volume of the concrete mixture must equal 1 m3, enforced using the specific gravities  of each component:

                                                                    (2)

This ensures that the genetic algorithm-generated mixture corresponds to a physically feasible 1 m3 concrete volume.

2.1.2. Ratio constraints

To maintain logical and practical mixture proportions, the ratio constraints listed in Table 1 are imposed [16].

2.1.3. Cost constraint

A user-defined budget constraint is introduced as an innovative aspect of this study. The user specifies the unit price  (per kg) for each material and the maximum allowable budget  is ensures that the optimized mixture maximizes compressive strength without exceeding the user’s budget.

2.2.Implementation

2.2.1. Framework description

As illustrated in Fig. 2, the proposed framework operates as follows. The user, through an Android application, inputs the unit prices of the concrete constituents (cement, slag, fly ash, water, superplasticizer, coarse aggregate, and fine aggregate) along with the maximum allowable budget. This information is transmitted to a web server via an API. On the server, a machine learning model – trained on an experimental dataset – is hosted to predict the 28-day compressive strength of concrete for given inputs  through  Simultaneously, a genetic algorithm is implemented on the server, where the output of the machine learning model serves as the fitness function to be maximized. The genetic algorithm searches for optimal mixture proportions while satisfying the volume constraint, ratio constraints (e.g., water-to-binder ratio, slag-to-binder ratio, fly ash-to-binder ratio, coarse-to-total aggregate ratio, fine-to-binder ratio, and superplasticizer-to-cement ratio), and the budget.

Finally, the genetic algorithm computes the optimal values of  that maximize the predicted compressive strength while ensuring that all constraints are satisfied. The optimized mix proportions are then returned to the Android application, enabling the user to conveniently view and utilize the results without requiring advanced knowledge of optimization methods.

Figure 2. Framework of the proposed methodology.

2.2.2. Modeling

In this study, a dataset of 425 samples of high-performance concrete was employed for developing the machine learning model. The input features consisted of seven variables – cement, slag, fly ash, water, superplasticizer, coarse aggregate, and fine aggregate – while the output variable was the 28-day compressive strength. The experimental data were originally obtained from the program reported by Yeh [22], in which ASTM Type I Portland cement was used. Aggregate properties were described qualitatively, indicating that the coarse aggregate consisted of crushed natural stone with a maximum size of 10 mm, whereas the fine aggregate was washed river sand with a fineness modulus of approximately 3 mm. This dataset provided sufficient diversity to capture the variability in mixture proportions and their influence on compressive strength.

To incorporate economic considerations, an additional column representing the cost of each mixture was computed using unit prices ($/kg) for all constituents: cement (0.11), slag (0.06), fly ash (0.055), water (0.000024), superplasticizer (2.94), coarse aggregate (0.01), and fine aggregate (0.006). Descriptive statistics for the dataset used in this study are presented in Table 2. The distributions of the input variables compressive strength and cost are shown in Fig. 3, illustrating the range and variability of the experimental data.

Table 2. Descriptive statistics for the concrete dataset.

mean

std

min

25 %

50 %

75 %

max

Cement

265.44

104.67

102.00

160.20

261.00

323.70

540.00

Slag

86.29

87.83

0.00

0.00

94.70

160.50

359.40

Fly Ash

62.80

66.23

0.00

0.00

60.00

120.00

200.10

Water

183.06

19.33

121.80

171.00

185.00

193.30

247.00

Superplasticizer

7.00

5.39

0.00

0.00

7.80

10.30

32.20

Coarse Aggregate

956.06

83.80

801.00

882.60

953.20

1013.20

1145.00

Fine Aggregate

764.38

73.12

594.00

712.00

769.30

811.50

992.60

Compressive Strength

36.75

14.71

8.54

26.23

33.76

44.39

81.75

Cost

72.55

19.05

34.93

59.24

72.07

83.67

166.86

Figure 3. Histograms of input and output variables used in the study.

The correlation map (Fig. 4) displays the pairwise Pearson correlation coefficients between the main concrete mix variables and cost. Strong positive correlations are observed between superplasticizer and cost, compressive strength and cement, and compressive strength and cost, indicating that higher amounts of superplasticizer and cement lead to increased compressive strength and higher overall cost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[23–26].

Figure 4. Correlation map of concrete mix variables and cost.

Three different machine learning models were considered: extreme gradient boosting [19], multilayer perceptron neural network [27], and random forest [28]. To ensure robust evaluation, a 10-fold cross-validation approach was employed during training. Model performance was compared using the mean squared error metric.

2.2.3. Optimization

Genetic algorithm is an evolutionary optimization technique inspired by the process of natural selection [29]. It operates by encoding potential solutions, known as chromosomes, and evolving them over successive generations to find the optimal solution. In the present study, each chromosome represents a possible concrete mixture, defined by the seven input variables  (cement, slag, fly ash, water, superplasticizer, coarse aggregate, and fine aggregate). The fitness of each chromosome is evaluated using the trained machine learning model, which predicts the 28-day compressive strength, while budget and proportional constraints are simultaneously enforced. As illustrated in Fig. 5, the genetic algorithm applies selection to retain high-performing chromosomes, crossover to recombine parent solutions, and mutation to introduce diversity and avoid premature convergence. Through iterative search of the solution space, the genetic algorithm gradually improves the population until the optimal mix proportions that maximize compressive strength without exceeding the budget are obtained.

Figure 5. Schematic representation of the genetic algorithm framework.

2.2.4. Implementation and deployment

After the machine learning model was trained and saved, it was deployed on the PythonAnywhere hosting platform. Along with the trained model, the genetic algorithm code was also implemented on the same host. To enable practical use, an Android application was developed using App Inventor, through which users could provide unit prices of concrete components and the maximum allowable budget. These inputs were transmitted via an API to the server. The Flask framework was employed to handle communication, ensuring efficient transfer of requests and responses between the application and the server. On the server side, the genetic algorithm utilized the user-provided information together with the trained machine learning model to compute the optimal mix proportions  The optimization process was carried out with the objective of maximizing compressive strength without exceeding the specified budget. Finally, the computed optimal proportions and the corresponding compressive strength were returned to the Android application through the API, enabling the user to conveniently access and interpret the results.

3.Results and Discussion

< >Modeling Results

Metrics and hyperparameters

Value

max_depth

4

n_estimators

500

Mean Squared Error

17.56

Root Mean Squared Error

4.19

Mean Absolute Error

2.82

R-squared

0.93

 

< >Genetic Algorithm

 

Figure 6. Pseudocode of the server-side implementation of the genetic algorithm integrated with the trained machine learning model and Flask framework.

< >Practical Implementation

 

Figure 7. Schematic representation of the developed framework integrating the Android application with the Flask-based server on PythonAnywhere.

In Fig. 8, the essential App Inventor blocks required for developing the Android application are illustrated. Two groups of blocks can be observed. The blocks on the left are responsible for sending the input information provided by the user – including the unit prices of concrete components and the maximum allowable budget – to the server. The blocks on the right handle the response received from the server, which contains the optimized mixture proportions of the seven components within the specified budget. Additionally, these blocks display the corresponding 28-day compressive strength predicted by the trained machine learning model for the optimized mixture design.

Figure 8. App Inventor blocks used in the Android application.

4.Conclusion

In this study, a machine learning-guided optimization framework was developed to design cost-effective and high-performance concrete mixtures. An XGBoost model was trained on an experimental dataset of 425 samples to accurately predict the 28-day compressive strength of concrete. The trained model was then integrated with a genetic algorithm to optimize mixture proportions under adaptive cost constraints, allowing flexible consideration of varying market conditions. Unlike conventional multi-objective approaches that simultaneously optimize strength and cost, this study formulated the problem as a single-objective optimization with compressive strength maximization, while cost was incorporated as a constraint. This approach enables practical adaptability while ensuring budget limits are not exceeded.

To bridge the gap between theory and practice, an Android application was developed using App Inventor. The application allows users to input unit prices of components and defines budget limits, which are then transmitted to a server hosting the machine learning model and genetic algorithm implemented via Flask. The server computes optimized mixture proportions and returns both the mix design and predicted compressive strength to the user interface. This practical implementation demonstrates the usability of the framework even for non-expert users, supporting data-driven decision-making in construction material design.

An important advantage of the proposed framework lies in its adaptability to real-world economic conditions. In scenarios where market prices of materials fluctuate, the system can seamlessly adjust optimization results according to updated unit prices. Similarly, when project budgets vary – ranging from generous allocations to highly cost-sensitive cases – the framework can readily adapt to provide optimized designs that meet the specified financial constraints. This flexibility makes the proposed approach highly practical and valuable for real construction applications where both material costs and budget availability are inherently dynamic.

Moreover, unlike multi-objective approaches that typically generate a large set of non-dominated solutions (Pareto front), which may cause confusion for practitioners in selecting the most suitable mix design, the single-objective formulation adopted here provides a unique optimal solution. This simplifies the decision-making process by directly identifying the best mix design under the specified budget, thereby enhancing the usability of the framework in practical scenarios.

Workability, commonly quantified by slump, is a critical performance requirement for concrete mixtures, as it directly affects placing, compaction, and overall constructability, particularly in high-strength concrete. Future work may extend the proposed framework by incorporating concrete workability as a constraint rather than as an additional optimization objective. This can be achieved by developing a dedicated machine learning model to predict slump based on mixture proportions. During the optimization process, the objective function would remain the maximization of compressive strength, while a minimum target slump value would be imposed as a constraint. Such a constrained optimization strategy would ensure that the optimized concrete mixtures achieve high strength while maintaining adequate workability, thereby enhancing the practical applicability of the proposed framework.

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