A Hybrid AI Approach for Intelligent Group Buying and Digital Marketing Strategy Optimization Based on Machine Learning and Evolutionary Algorithms

Abstract

This study considers the digital transformation of Kazakhstan’s agro-industrial complex, which has created an urgent need for scientifically grounded methods that can optimize marketing strategies under conditions of resource limitations, production seasonality, and heterogeneous consumer behavior. This study proposes a hybrid decision-support framework integrating a modified NSGA-III algorithm with machine learning techniques for optimizing digital marketing strategies in the agro-industrial complex of Kazakhstan. The model considers three objectives: maximizing channel efficiency and audience reach while minimizing marketing costs. Experimental results based on a dataset of N = 1200 observations demonstrate that the proposed approach improves the composite performance indicator by 12.4% compared to baseline single-objective optimization methods. Pareto front analysis reveals three distinct clusters of strategies, corresponding to (1) high-impact integrated digital TV strategies, (2) cost-efficient traditional channel strategies, and (3) high-risk high-return allocations. The clustering validity is confirmed by a silhouette score of 0.624, indicating strong separation between strategy groups. The results highlight the practical significance of adaptive budget allocation and demonstrate the effectiveness of combining evolutionary optimization with machine learning for decision support in complex marketing environments.

1. Introduction

The contemporary agro-industrial complex (AIC) of the Republic of Kazakhstan is confronted with challenges arising from the need to optimize marketing strategies in an environment characterized by resource constraints and highly competitive pressure [1,2,3]. Digital marketing today is an integral part of the economic activity of enterprises, playing a key role in forming stable relationships between producers and consumers [4,5,6]. Computerization and digitalization of marketing [7,8,9,10] have made it possible not only to optimize promotion processes but also to use a systematic method for selecting marketing strategies. Traditional methods of marketing budget allocation, based on empirical experience and simplified analytical models, demonstrate limited effectiveness when working with multi-criteria problems [11,12], typical of the agricultural market. In the context of product competition in the agricultural market, the development of scientifically based decision-making methods that take into account the specifics of the AIC in Kazakhstan, including the seasonality of production, the geographic dispersion of consumers, and the heterogeneity of distribution channels, is becoming increasingly relevant. Current agricultural reforms in Kazakhstan are accompanied by a significant reduction in agricultural land and a decline in the agro-industrial complex’s productive potential. This is due to a combination of factors, including soil degradation, declining humus content, and deteriorating forage quality. In the context of the digital transformation of the economy, the development of scientifically based marketing strategies capable of offsetting these negative trends is particularly relevant [3]. The livestock sector in Kazakhstan continues to face systemic problems associated with the insufficient use of digital technologies in breeding, forage management, and veterinary services. Analysis shows that the introduction of modern marketing tools could significantly improve product positioning in the market, despite existing production constraints. The crop production industry in Kazakhstan also faces challenges requiring comprehensive marketing solutions, from supply chain optimization to product promotion on digital platforms. The development of adaptive marketing strategies that take into account the seasonality of production and regional specifics is of fundamental importance. The processing sector of Kazakhstan’s agro-industrial complex demonstrates a pressing need to digitalize marketing processes, which would improve the competitiveness of products in both domestic and foreign markets. A key aspect is the implementation of intelligent systems for demand analysis and optimization of distribution channels. Existing infrastructure limitations in the agro-industrial complex highlight the need to develop digital marketing platforms capable of compensating for the shortcomings of traditional distribution channels. Particular attention should be paid to the creation of integrated marketing systems uniting producers, processors, and end consumers. Given limited funding, the development of cost-effective digital marketing strategies is becoming crucial for the sustainable development of Kazakhstan’s agricultural sector. However, this will require the implementation of modern analytical tools and methods for optimizing marketing budgets, taking into account the specifics of agricultural production.

This study proposes a hybrid approach that combines modern digital marketing methods with multi-criteria optimization and machine learning (ML) algorithms. The methodological basis of the study is a modified NSGA-III (Non-dominated Sorting Genetic Algorithm III) [13,14], supplemented by cluster analysis methods [15,16] to identify patterns in the solution space. This synthesis allows for the simultaneous consideration of three key criteria characteristic of digital marketing methods [17,18], namely, the effectiveness of distribution channels, target audience reach, and the level of marketing expenditures.

The relevance of this study is driven by several fundamental factors. First, the digital transformation of Kazakhstan’s agro-industrial complex requires scientifically sound approaches to allocating marketing resources between traditional and digital channels. Second, existing optimization methods often fail to account for nonlinear relationships between marketing campaign parameters. Third, the specifics of Kazakhstan’s agro-industrial market, including patterns of agricultural consumption and regional differences in purchasing power, require adaptive solutions. The scientific novelty of this study lies in the development of a hybrid algorithm that combines the advantages of evolutionary computation for multi-criteria optimization with machine learning methods for analyzing and interpreting results. The composite performance indicator proposed in this study will enable quantitative evaluation of trade-offs between conflicting objective functions, facilitating the rationale for management decision making under conditions of uncertainty. The practical significance of this study is confirmed by the potential for the direct implementation of the developed approach in the operations of Kazakhstan’s agro-industrial enterprises. The results will not only optimize marketing budget allocation but also identify consistent patterns in the interaction of various channels for promoting agricultural products in both Kazakhstan and international markets. The proposed approach provides the basis for developing a scientifically sound marketing strategy tailored to the specifics of Kazakhstan’s national agro-industrial complex.

Despite the extensive use of optimization and machine learning techniques in digital marketing, existing models exhibit several limitations. Most approaches either focus on single-objective optimization or fail to account for nonlinear interactions between marketing channels. Additionally, current models rarely incorporate sector-specific constraints such as seasonality, regional heterogeneity, and resource limitations inherent in the agro-industrial complex.

This study addresses these gaps by proposing a hybrid framework that integrates multi-objective optimization (NSGA-III) with machine learning-based interpretation, enabling both optimal decision making and a practical decision-support framework that helps managers select optimal marketing strategies under constraints.

2. Literature Analysis

As new information and communication technologies develop, approaches to marketing in the agro-industrial complex are also radically changing. Modern methods of digital marketing (DM) optimization in the agro-industrial complex include the use of analytical tools, personalized advertising campaigns, and strategies based on data mining. A review of existing scientific research allowed us to identify key areas that determine the trends and challenges in the field of digital marketing for the agro-industrial complex. Thus, in [19], the authors examine the optimization of digital marketing strategies, emphasizing the use of search engine optimization (SEO). The study in [20] focuses on various aspects of marketing strategies, including the integration of new technologies and the use of analytical data to improve customer interactions and increase sales. The authors of the [21] emphasize the optimization of online marketing strategies to increase sales and develop e-commerce. In [22], the authors analyze the prospects of using big data and ML for digital marketing optimization. The study in [23] examines the role of ML technologies in digital marketing and personalization. This study presents a description of the ways in which ML can be used to create personalized marketing offers and improve their effectiveness. In [24], the use of deep learning and swarm methods for effective customer segmentation in digital marketing is investigated. The study in [25] is a systematic review analyzing the evolution of artificial intelligence and ML in digital marketing over the past two decades. The paper in [26] studies the application of ML to building response models for direct marketing using Bayesian networks with evolutionary programming, and the authors consider how these methods can be used to more accurately predict consumer responses and optimize marketing strategies. The paper [27] is devoted to multi-criteria grammatical evolution of decision trees for predicting user conversion in mobile marketing. The authors propose a new approach to improve user behavior predictions and increase the effectiveness of marketing campaigns in a mobile environment through the use of evolutionary algorithms and decision trees. The paper [28] proposes a fuzzy hybrid approach for analyzing digital marketing strategies in tourism. The paper [29] focuses on best practices in hybrid marketing. The authors explore ways to integrate traditional and digital marketing methods to improve performance.

However, despite the clear need for integrated approaches aimed at the efficient allocation of marketing resources in the context of digital transformation, the scientific literature still lacks research focused on the application of hybrid methods in digital marketing for the agro-industrial sector. In particular, hybrid approaches combining multi-criteria optimization algorithms with machine learning methods remain understudied in the context of the specifics of the agro-industrial sector. Despite a significant number of studies devoted to specific aspects of digital marketing optimization and the application of machine learning methods, there are very few comprehensive models that take into account all the specific features of both the agro-industrial sector and modern digital marketing strategies. All of the above motivated our interest in research in this area.

While the reviewed studies provide valuable contributions to digital marketing optimization, several important limitations can be identified. First, many existing approaches focus primarily on single-objective optimization or simplified multi-criteria models, which do not adequately capture the complex trade-offs between efficiency, reach, and cost. Second, most studies do not consider sector-specific constraints of the agro-industrial complex, such as production seasonality, regional heterogeneity, and limited resource availability. Third, although machine learning techniques are widely used for prediction and personalization, their integration with multi-objective optimization for decision support remains limited.

In contrast to these approaches, the proposed method combines a multi-objective evolutionary algorithm (NSGA-III) with machine learning techniques to enable both the optimization and interpretation of results. Unlike traditional models, the proposed framework incorporates domain-specific constraints and applies clustering and XGBoost-based analysis to extract actionable insights from the Pareto-optimal solution space. This allows not only identifying optimal solutions but also understanding their structural patterns, thereby improving decision making in practical applications.

As shown in

Table 1. Comparative analysis of the NSGA-II and NSGA-III algorithms for the five-criteria problem of optimizing marketing strategies.

Comparison Criterion	NSGA-II	NSGA-III	Applicability Analysis
Convergence at m = 5	Local optima (dominance of random solutions)	Global convergence (systematic search)	According to [30] (3045–3052), for m ≥ 4, NSGA-III demonstrated 18–22% better coverage of the solution space than NSGA-II.
Solution distribution	Clustering in narrow regions of the frontier	Uniform hyperplane coverage	According to [30] (3045–3052); [31] (20), NSGA-III provides 35–37% better distribution (spatial metric) for m = 5 than NSGA-II.
Limitations	Effective only for m ≤ 3	Optimal for 3 ≤ m ≤ 15	For m = 5, the density of reference directions in NSGA-III should be ≥12 partitions, according to [30] (3045–3052).

, existing approaches either focus on optimization (NSGA-II, NSGA-III) or prediction (machine learning models) but lack integration between these components. The proposed hybrid framework addresses this limitation by combining multi-objective optimization with machine learning-based interpretation, thereby providing both optimal solutions and actionable insights for decision makers in the agro-industrial sector.

3. Problem Statement and Objectives

Kazakhstan’s agro-industrial complex faces the need to optimize marketing strategies in the face of limited resources and intense competition from both domestic agricultural producers and foreign producers. Traditional methods of marketing and advertising budget allocation, based on empirical experience and simplified analytical models, are ineffective in solving the multi-criteria problems typical of the agricultural market. Nonlinear relationships between marketing campaign parameters, as well as the specific nature of Kazakhstan’s agro-industrial complex, including seasonality of production and regional differences in purchasing power, pose significant challenges. Existing approaches fail to comprehensively consider these factors, necessitating the development of new methods that combine optimization algorithms and machine learning.

The objective of this study was to develop and implement a hybrid method for optimizing marketing strategies in the agro-industrial complex, combining a modified NSGA-III algorithm and machine learning methods. The key objectives included formalizing a multi-criteria problem taking into account the specifics of the agro-industrial complex in Kazakhstan, developing a mathematical model for budget allocation between digital and traditional channels, implementing a cluster analysis of Pareto-optimal solutions, and evaluating their effectiveness using a composite indicator.

4. Materials and Methods

4.1. Mathematical Model

Let us consider a formal formulation of the problem of optimizing marketing strategies for the agro-industrial complex. Let us assume a set of marketing channels $K=\left\{1,\dots ,m\right\}$, where $m=5$ corresponds to digital (Digital), television (TV), radio (Radio), print (Print), and event (Events) channels, respectively. For each channel, $k\in K$ the following three key parameters were identified: efficiency $e_k\in \left[0,1\right]$, which characterizes the conversion of a digital channel; reach $c_k\in {\mathbb{R}}^{+}$, measuring the channel’s audience; cost $s_k\in {\mathbb{R}}^{+}$, which determines the unit costs. The optimization vector $x={\left(x_1,\dots ,x_m\right)}^T\in {\mathbb{R}}^m$ represents the distribution of the budget across channels, where $x_k\in \left[l_k, u_k\right]-$ share of the budget allocated to the channel $k$, with the lower ones $l_k$ and upper $u_k$ borders.

In this study, we will limit ourselves to only three target functions.

Maximizing overall efficiency:

$$f_1\left(x\right) = {\displaystyle \sum _{k=1}^m{e}_k\cdot x_k}\to max$$

(1)

Maximizing overall reach:

$$f_2\left(x\right) = {\displaystyle \sum _{k=1}^m{c}_k\cdot x_k}\to max$$

(2)

Minimize total cost:

$$f_3(x)={\displaystyle {\sum }_{k=1}^m}\sum s_k\cdot x_k\to min$$

(3)

Relative cost effectiveness. This is essentially a variation of the ROI metric.

$$f_4(x)={\displaystyle \frac{-E(x,s) }{\left(C\right(x)+\epsilon )}}\to max$$

(4)

where ϵ epsilonϵ is a small constant to avoid division by zero. This function reflects cost-adjusted performance.

In the agro-industrial complex, both the breadth of reach and also the depth of engagement are often crucial. Therefore, to select the optimal strategy, we introduce a fifth objective function into the model:

The depth of engagement with the audience, which must be maximized.

$$f_5(x,s)=-{\displaystyle {\sum }_{i=1}^n}{x}_{\mathrm{i}} · v_{\mathrm{s},\mathrm{i}}$$

(5)

where $v_{\mathrm{s},\mathrm{i}}$ assessment of the involvement of channel i in segment s.

We believe that $v_{\mathrm{s},\mathrm{i}}$ the parameters are set based on expert assessment or data on conversions, clicks, event participation, etc. We collect data using the following systems:

click data using Google Analytics and Yandex.Metrica;

CRM systems using Salesforce and HubSpot;

Marketing Automation Tools—Mailchimp and ActiveCampaign.

Let us set the following constraints:

Total budget limit: $g_1\left(x\right) ={\displaystyle \sum _{k=1}^m{x}_k-B\le 0,} \mathrm{where} B=1.5$.

Minimum channel shares: $g_{2k}\left(x\right) =l_k-x_k\le 0, \forall k\in K$.

Maximum channel shares: $g_{3k}\left(x\right) =x_k-u_k\le 0, \forall k\in K$.

Combined restrictions: $g_4\left(x\right) =\mathrm{\Theta }-(x_1-x_5)\le 0, \mathrm{where} \mathrm{\Theta }=0.3$.

It should be noted that the formalized system of constraints in the proposed hybrid model reflects the fundamental economic and technological characteristics of the agro-industrial complex. For example, the budget constraint takes into account the specifics of financial planning in the agro-industrial complex, where exceeding the nominal budget by up to 150% through seasonal credit lines is permissible, thereby aligning with the practice of financing agricultural enterprises. The thresholds for distributing funds across channels are driven by the need to maintain a minimum presence in all market segments—from digital platforms to traditional printed catalogs. The limit on the minimum share of digital marketing channels reflects the strategic priority of digitalization of the agro-industrial complex, enshrined in state programs for the development of agriculture in Kazakhstan. The combined limit on the sum of the shares of digital and event channels ensures a balance between new and traditional methods of promoting agricultural products, considering the need to combine online sales with participation in traditional agricultural exhibitions and fairs. The upper limit for event marketing was introduced to control costs associated with the high cost of organizing events and their limited scalability in the context of the low rural population density in Kazakhstan. For print channels, this threshold is set as a minimum (to ensure presence in the B2B segment through specialized publications).

The hybrid algorithm first uses a modified NSGA-III algorithm because the modified NSGA-III differs from the standard version by incorporating the following:

Latin Hypercube Sampling for improved population diversity

Adaptive mutation rate

Integration with clustering-based post-analysis. The population size (100) and number of generations (50) were selected based on empirical convergence analysis, balancing computational cost and solution quality.

The first step is to generate reference directions using the Das–Dennis method [32,33] for uniform coverage of the unit simplex in the criterion space. For three objective functions and N partitions: $W=\left\{w\in {\mathbb{R}}_{+}^3\left|{\displaystyle \sum _{i=1}^3{w}_i=1, w_i=\raisebox{1ex}{$k$}\!\left/ \!\raisebox{-1ex}{$N$}\right., k\in N_o}\right.\right\},$ where w is reference directions in the objective function space. These vectors define a uniform distribution of points on the unit simplex to ensure representative coverage of the Pareto front. And each direction $w\in {\mathbb{R}}_{+}^3$ is a normalized vector of weighting coefficients. Geometrically, they determine the direction of the search for optimal solutions in the space of criteria considered in this study.

Next, evolutionary operators are used. First, the SBX crossover with probability was applied $p_c=0.9$ and the distribution parameter η = 20. Let us write it like this $x_i^{\left(new\right)}={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\left[\left(1+\beta \right)\cdot x_i^{\left(1\right)}+\left(1+\beta \right)\cdot x_i^{\left(2\right)}\right], where \beta \sim U{\left[0,1\right]}^{{\eta }_{c^{+1}}}.$ And for a polynomial mutation, according to [26,27], so $x_k^{\prime }=x_i+{\delta }_i, {\delta }_i\sim N\left(0,{\sigma }_i^2\right), {\sigma }_i={\displaystyle \raisebox{1ex}{$\left(u_i-l_i\right)$}\!\left/ \!\raisebox{-1ex}{${\eta }_m$}\right.}$.

Next, we implement a cluster analysis of the solutions. For the Pareto frontier analysis, we use the k-means method with a Euclidean metric. We write it as follows: $\underset{{\left\{{\mu }_j\right\}}_{j=1}^3}{\min }{{\displaystyle \sum _{i=1}^N\underset{j}{\min }{\displaystyle \Vert }f\left(x_i\right)-{\mu }_j{\displaystyle \Vert }}}^2, j=1\dots k,$ where $f(x) = (f_1(x),f_2(x),f_3(x)) -$ vector of criteria, $k=3 -$ number of clusters.

The number of clusters (k = 3) was determined using the silhouette method, which indicated optimal separation at k = 3 compared to k = 2 and k = 4.

The weights α₁ = 0.6 and α₂ = 0.4 reflect a managerial preference for efficiency over reach.

The smoothing parameter ε = 0.1 prevents division instability.

The composite quality indicator was defined as follows: $\mathrm{\Phi }\left(x\right)={\displaystyle \left({\alpha }_1\cdot f_1\left(x\right) + {\alpha }_2\cdot f_2\left(x\right)\right)}/{\displaystyle \left(f_3\left(x\right)+\epsilon \right)},$ where the weights ${\alpha }_1=0.6, {\alpha }_2=0.4$ reflect the priorities of decision makers, $\epsilon =0.1 -$ smoothing parameter.

Then, the solution $x^{*}\in X$ is called Pareto optimal if $\nexists x\in X$: $f_i\left(x\right) \ge f_i{\displaystyle \left(x^{*}\right)} \forall i\in \left\{1,2,3\right\}$ and $\exists j: f_j\left(x\right) > f_j\left(x^{*}\right)$, where $X = \{x\in {\mathbb{R}}^m | g_j\left(x\right)\le 0, j=1..p\}-$ admissible set.

The computational complexity of the modified NSGA-III is $O\left(M{N}^2\right)$, where $M-$ number of targets, $N-$ population size.

Channel efficiency forecasting using XGBoost was defined as follows. Let us assume there is a historical data sample for a specific region or agricultural enterprise: $D = {\left\{\left(x^{\left(i\right)}, y^{\left(i\right)}\right)\right\}}_{i=1}^N,$ where $x^{\left(i\right)}\in {\mathbb{R}}^m-$ budget distribution vector, $y^{\left(i\right)}\in {\mathbb{R}}^m-$ observed performance. The XGBoost model [32] builds an ensemble of K decision trees. For XGBoost, $\widehat{y}\left(x\right) \to E\left[y\left|x\right.\right]> npu N\to \infty , K\to \infty$ (according to the boosting convergence theorem) [34].

The XGBoost model was trained using a train–test split (80/20). Key hyperparameters include the following:

max_depth = 5

learning_rate = 0.1

n_estimators = 100

Model performance was evaluated using RMSE and R² metrics.

The presented model was implemented in the Python version 3.11 algorithmic language. The results of the computational experiments are presented below.

4.2. Methodology for Conducting Numerical Experiments

The methodology for conducting numerical experiments is presented in pseudocode format. The initialization of the problem parameters includes (lines 1–8) a matrix of channel characteristics (efficiency/coverage/cost), constraints on the minimum/maximum channel shares, a system of budget constraints, and support directions for NSGA-III. The optimization phase (lines 9–18) implements a modified NSGA-III algorithm with Latin Hypercube Sampling for the initial population, SBX crossover and polynomial mutation, and a stopping criterion per generation (50 iterations). The decision analysis (lines 20–24) included Pareto front clustering using the k-means method, calculation of the silhouette score metric for assessing the quality of clustering, and ranking by a composite indicator $\mathrm{\Phi }\left(x\right)$. The interpretation of the obtained results (lines 25–27) included the construction of an XGBoost model to predict the composite indicator, followed by a SHAP analysis of the channel importance (Algorithm 1).

Algorithm 1. Multi-objective optimization based on the Pareto frontier approach.

1: procedure OPTIMIZE_MARKETING_STRATEGIES 2: Input: 3: channels ← {Digital, TV, Radio, Print, Events} 4: params ← {e_k, c_k, s_k} ∀k ∈ channels (Effectiveness, coverage, cost) 5: bounds ← [l_k, u_k] ∀k ∈ channels (Lower/upper bounds) 6: constraints ← {g_1,...,g_6} (Budget and channel limits) 7: ref_dirs ← Das-Dennis(3, 12) (3D reference directions) 8: 9: #Phase 1: Multi-objective optimization 10: algorithm ← NSGA-III( 11: pop_size = 100, 12: ref_dirs = ref_dirs, 13: sampling = LHS(), 14: crossover = SBX(prob = 0.9, η = 20), 15: mutation = PM(η = 20) 16: 17: results ← minimize(problem, algorithm, termination(‘n_gen’, 50)) 18: P ← non_dominated_sorting(results.F) (Extract Pareto front) 19: 20: #Phase 2: Solution analysis 21: clusters ← KMeans(n_clusters = 5).fit(P) 22: silhouette ← calculate_silhouette(P, clusters) 23: top_solutions ← rank_by_composite(P) (Eq. (0.6f1 + 0.4f2)/(f3 + 0.1)) 24: 25: #Phase 3: SHAP interpretation 26: model ← XGBoost().fit(P, composite_scores) 27: shap_values ← KernelSHAP(model).explain(P) 28: 29: Output: {P, clusters, top_solutions, shap_values} 30: end procedure

The proposed framework in the Figure 1 integrates data-driven modeling and evolutionary optimization. The input dataset is first processed using machine learning models (e.g., XGBoost) to estimate performance indicators such as efficiency, reach, and engagement. These outputs are then used within a multi-objective optimization framework based on NSGA-III, which generates a set of Pareto-optimal solutions. Finally, clustering techniques (K-means) are applied to identify distinct groups of marketing strategies, enabling interpretable decision making.

4.3. Evaluation Protocol

To ensure a fair and reliable evaluation of the proposed model, we replaced the random train–test split with a k-fold cross-validation protocol. Specifically, a five-fold cross-validation strategy was employed, where the dataset was randomly partitioned into five equal subsets. In each iteration, four subsets were used for training, and one subset was used for testing, ensuring that each sample was used for validation exactly once.

This approach mitigates the risk associated with a single random split and provides a more robust estimation of model performance. The final results are reported as the average values across all folds, along with standard deviation to reflect variability.

In addition, the same cross-validation protocol was consistently applied to all baseline methods to ensure a fair comparison.

5. Results

The experimental evaluation was conducted on a dataset of N = 1200 observations Kazakhstan Republic Inf https://drive.google.com/file/d/1uLp0nEJv2yfeh-beir9voYsxR0j1YJQj/view?usp=sharing (accessed on 27 January 2026), including real data from the Republic of Kazakhstan in the agricultural sector, to ensure sufficient variability in marketing scenarios. Here, we used the metrics discussed above, such as channel effectiveness (TV, digital, radio, etc.), audience reach, costs, and engagement metrics. The proposed hybrid NSGA-III structure was compared with baseline methods.

The main results of the modeling are presented in Table 1 and Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6. The conducted optimization of marketing strategies revealed a number of significant patterns in the distribution of resources between channels for promoting agricultural products. The analysis of Pareto-optimal solutions in Figure 2 demonstrates a pronounced dichotomy in the effectiveness of various channels, which was confirmed by the cluster structure of the solution space. The three-dimensional visualization of the Pareto front, presented in Figure 2, clearly shows the existence of three qualitatively different groups of strategies, differing in the balance of efficiency, coverage, and costs.

The three identified clusters have clear practical interpretations: (1) high-impact integrated strategies, (2) cost-efficient traditional strategies, and (3) high-risk high-return strategies. This classification enables decision makers to select optimal marketing strategies based on budget constraints and performance priorities.

The most promising strategies (cluster 1, blue dots in Figure 2) are characterized by the dominance of the television channel (39.8–69.5% of the budget), with a significant share of digital technologies (20.4–21.1%) and event marketing (26.4–30.0%). This configuration provides the maximum values of the composite indicator (0.815–0.820) presented in

Table 2. Optimal digital marketing strategies.

Digital (%)	TV (%)	Radio (%)	Print (%)	Events (%)	Efficiency	Coverage	Cost	Composite	Cluster
20.41	39.82	11.74	39.77	29.99	1.101	0.950	1.169	0.820	1
21.14	69.52	10.17	5.50	29.85	1.182	1.024	1.264	0.820	1
22.48	59.70	13.96	19.51	26.37	1.134	0.986	1.219	0.815	1
22.21	28.26	10.29	38.39	28.11	0.994	0.857	1.057	0.812	2
41.51	57.24	11.87	14.85	24.40	1.233	1.077	1.342	0.812	1

due to the optimal combination of efficiency (1.101–1.182) and coverage (0.950–1.024) at controlled costs (1.169–1.264), see Figure 3. Mathematically, this corresponds to solutions located in the region of maximum values of the objective functions $f_1\left(x\right)$ and $f_2\left(x\right)$ at moderate values $f_3\left(x\right)$.

Alternative strategies (cluster 2 in Figure 3, yellow dots) demonstrate a different balance, with an increased share of print channels (38.4%) and a reduced contribution of television (28.3%). Despite lower absolute values of efficiency (0.994) and reach (0.857), these solutions remain Pareto optimal due to significantly lower costs (1.057), reflecting the compromise nature of the solution space. Of interest was the strategy with an extreme budget distribution (41.5% digital, 57.2% TV), achieving maximum efficiency (1.233) at comparatively high costs (1.342). Mathematical analysis shows that such solutions become optimal with an increase in the weighting coefficient $\left({\alpha }_1\right)$ in the composite indicator $\mathrm{\Phi }\left(x\right)$, which corresponds to the priority of efficiency over coverage in the decision maker’s criteria (see Figure 3, Figure 4, Figure 5 and Figure 6). For ease of understanding, the clustering of solutions in 2D is shown in Figure 5. Note that a comprehensive Pareto front visualization was used to analyze the optimal solutions (see Figure 2 and Figure 5). The three-dimensional representation (see Figure 2) clearly demonstrates the spatial structure of trade-offs between the criteria of efficiency, coverage, and cost, revealing three characteristic clusters of solutions. An additional two-dimensional projection (see Figure 5) provided a more detailed interpretation of the identified patterns, emphasizing the key relationships between the target indicators of efficiency and cost of digital marketing in the agro-industrial complex.

Correlation analysis, see Figure 6, confirms a stable positive relationship between the share of the television channel and the values of the objective functions (0.74 for efficiency, 0.51 for coverage), while digital channels demonstrate a more pronounced impact on efficiency (0.65) than on coverage (0.52). The results obtained are statistically significant (p < 0.01, Pearson correlation), indicating a strong relationship between the analyzed variables. The high silhouette score (0.624) indicates clear differentiation between the clusters, thereby confirming the existence of fundamentally different approaches to marketing budget allocation in the agro-industrial complex. The presence of such clusters is mathematically explained by the nonlinear relationships between the model parameters and the presence of local optima in the solution space.

The XGBoost model achieved:

RMSE = 0.084

R² = 0.87

Analysis (Figure 7) shows that TV and digital channels have the highest importance. Print and radio have lower marginal contributions.

The proposed method outperforms baseline approaches: +12.4% improvement in composite score, −8.7% reduction in cost, +10.2% increase in reach.

6. Discussion

To ensure the robustness and reliability of the proposed approach, the experimental evaluation was conducted using multiple independent runs. Specifically, the NSGA-III algorithm was executed 10 times with different random seeds to account for stochastic variability inherent in evolutionary optimization.

The stability of the results was assessed by calculating the mean and standard deviation of the composite performance indicator across all runs. The obtained results demonstrate low variability, with a standard deviation not exceeding 0.018, indicating consistent convergence behavior of the proposed method.

Additionally, the hypervolume (HV) metric was computed for each run to evaluate the quality of the Pareto front. The average hypervolume value was 0.742 ± 0.015, confirming both stability and high solution quality.

Statistical Significance Testing

To provide a fair comparison with baseline methods, a paired t-test was conducted between the proposed NSGA-III-based method and the baseline approaches (single-objective optimization and NSGA-II).

The results indicate the following:

• Improvements in the composite performance metric are statistically significant (p < 0.01)
• Improvements in hypervolume and diversity metrics are also statistically significant (p < 0.01)

These findings confirm that the observed performance gains are not due to random variation but reflect the superiority of the proposed method.

The results obtained in this study confirm the effectiveness of the proposed hybrid framework that integrates the NSGA-III evolutionary algorithm with machine learning techniques for optimizing digital marketing strategies in the agro-industrial complex (AIC). Compared to traditional single-objective optimization approaches, the proposed method provides a more comprehensive exploration of the solution space and enables the identification of Pareto-optimal trade-offs between efficiency (f₁), reach (f₂), cost (f₃), relative efficiency (f₄), and engagement depth (f₅). The consistent formulation of these five objective functions ensures a clear interpretation of optimization results and eliminates ambiguity in the mathematical model.

A key strength of this study lies in the improved dataset design. The dataset consists of N = 1200 observations, combining real-world marketing data (Google Analytics, CRM systems such as Salesforce and HubSpot) and synthetically generated samples to ensure coverage of rare but realistic scenarios. Feature variables include channel efficiency, audience reach, cost coefficients, and engagement metrics. Preprocessing steps included normalization (min–max scaling), outlier removal (IQR-based filtering), and feature consistency validation. This ensures the robustness and reliability of the experimental results.

The clustering results (K-means, silhouette score = 0.624) further validate the structural consistency of the solution space, revealing three distinct strategy groups. This supports the hypothesis that marketing optimization in AIC is inherently multi-modal and requires adaptive decision-making frameworks.

However, several limitations remain. First, although synthetic data enhance coverage, they may not fully capture all real-world dynamics. Second, the computational complexity of NSGA-III may limit real-time applications. Third, behavioral and socio-economic factors were not explicitly modeled.

Future research should focus on dynamic optimization models, integration of real-time data streams, and expansion of the feature set (e.g., social networks and IoT).

7. Conclusions

This study confirmed the effectiveness of the proposed hybrid method for optimizing marketing strategies in the agricultural sector. A Pareto front analysis revealed three clusters of solutions reflecting various trade-offs between efficiency, reach, and cost. The most promising strategies are characterized by the dominance of television and digital channels with a balanced budget allocation for digital marketing of agricultural products. The results demonstrate a stable positive correlation between the television channel share and the objective function values, consistent with the theoretical assumptions of the model outlined in this study. The developed approach provides a tool for making informed management decisions under uncertainty and can be adapted to other industries facing similar challenges.