Over the past years, various heuristic-based RNP approaches have been developed to address different challenges. For example, Gupta and Iyer [14] proposed two heuristic-based RNP models to incorporate driver design, antenna range calculations, and a reader emulator for coverage optimization in obstacle-free environments. Mysore et al. [15] utilized a geometry-driven Graham scan to achieve complete coverage with the minimum number of readers. Liu et al. [16] introduced a federated framework to coordinate readers, mitigating reader-tag and reader-reader collisions. Qu et al. [17] integrated RFID with Markov chain models to improve equipment access and management within supply chains, and Tsai et al. [18] proposed a real-time tracking system for mobile healthcare assets. Moreover, Nhat [19] presented a Hopfield Network for RNP Optimization (HNRNPO) specifically for space-constrained clinical settings.

Metaheuristic approaches have been widely used to address different RNP challenges [20]. For instance, Dimitriou et al. [21] utilized Particle Swarm Optimization (PSO) to improve network coverage, limit interference, and cut overall costs. Shi et al. [22] utilized Chicken Swarm Optimization (CSO) to determine optimal antenna placement, while Cuckoo Search (CS) was applied to distribute reader loads efficiently and reduce energy consumption [23]. An evolutionary-based Genetic Algorithm (GA) has also been applied to optimize networks with both directional and omnidirectional antennas [24], and a hybrid GA-PSO model was developed for planning readers to track predictable mobile tags [25]. Xu et al. [26] integrated Monte-Carlo simulations into PSO to improve robustness under uncertainty, while Yuan et al. [27] presented a multi-objective Bacterial Foraging Optimization (BFO) combining adaptive search strategies, multi-cell communication, and indicator-based preference metrics.

Recent studies have further advanced RNPs. Shokouhifar [28] developed a hybrid RNP solution method using Simulated Annealing (SA) and Whale Optimization Algorithm (WOA). Mohammed et al. [29] combined Birch clustering with Chaotic PSO to achieve a balance between coverage and interference. Knapp and Romagnoli [30] applied GAs to reduce the number of antennas without compromising accuracy, while Zheng et al. [31] utilized multiple local search operators to improve convergence. Abdulbaqi and Abdullah AL-Khalidi [32] tackled RNP from a topological perspective using PSO, and Maimouni et al. [33] developed a neural-inspired metaheuristic, named IRAENNA, to optimize antenna deployment.

There are also some hybrid metaheuristic-based approaches. For instance, Ma et al. [34] integrated a fuzzy model to select appropriate solutions from Pareto Fronts in a multi-criteria RNP. Lu and Yu [35] formulated RNP as a constrained optimization problem using a fuzzy k-coverage model, ensuring that each tag is monitored by at least k readers, and solved it with the Plant Growth Simulation Algorithm (PGSA), which separates the treatment of objectives and constraints to enhance convergence stability. Hosseinzadeh et al. [36] employed a Takagi-Sugeno-Kang (TSK) fuzzy model for the deployment of RFID antennas, complemented by an offline hyper-parameter tuning phase using Greylag Goose Optimization (GGO). Additionally, Lamin et al. [37] introduced a fuzzy-guided Ant Colony Optimization (ACO) approach for sequential RFID network design in hospital environments, utilizing heterogeneous multi-port readers equipped with directional antennas.

An examination of the existing RNP approaches indicates that heuristic-based methods are preferred due to their simplicity and rapid execution, which makes them well-suited for real-time applications. However, they often lack global search capability and deliver suboptimal performance. In contrast, metaheuristic-driven methods provide greater flexibility and stronger exploration mechanisms, enabling more efficient optimization of the conflicting objectives inherent in multi-criteria RNP problems. From a network modeling perspective, the use of omnidirectional antennas typically results in excessive interference, while studies employing directional antennas often assume homogeneous antenna characteristics, overlooking variations in coverage behavior.

To address these limitations, the proposed KBGWO-RNP model embeds knowledge-based heuristic information (from structural and environmental factors) into the search process of the metaheuristic-driven GWO algorithm. By incorporating heuristic local search operators based on the network structure, the proposed model effectively guides the metaheuristic algorithm toward high-quality solutions with faster convergence. Furthermore, through supporting directional RFID antennas with heterogeneous configurations in terms of gain, read range, and beam width, the KBGWO-RNP framework achieves high coverage with minimal interference and deployment cost.

As illustrated in Fig. 3, a feasible solution, denoted as Sol (i.e., a grey wolf), is represented by four direct and four indirect vectors, each of length A_max. Specifically, each solution is encoded using four direct sub-structures: a binary vector Sol.S, which indicates the selection or exclusion of antennas for deployment within the hospital layout, and three integer vectors Sol.G, Sol.T, and Sol.D, representing the grid location, antenna type, and orientation of each antenna, respectively.

Based on the selected antenna types (Sol.T) and their corresponding specifications listed in Table 2, the indirect variables including antenna gain (Sol.Ga), read range (Sol.R), beam width (Sol.B), and deployment cost (Sol.C), can be simply derived. These indirect variables are therefore implicitly determined by the direct encoding and do not require independent optimization variables. Accordingly, the direct variables used to encode each feasible solution in the KBGWO-RNP framework can be expresses as:(1)Sol.S(i)={1if antenna iis selected0otherwise, (2)Sol.P(i)=selected grid for placement of antenna i:Sol.P(i)∈G, (3)Sol.T(i)=selected type for antenna i:Sol.T(i)∈T, (4)Sol.D(i)=selected direction for antenna i:Sol.D(i)∈D.

The fitness function is designed to maximize the total criticality-weighted coverage (F₁) while minimizing the criticality-weighted interference (F₂) and the total deployment cost including reader and antenna costs (F₃). Generally, Pareto-based multi-objective optimization and weighted-average single-objective optimization are two common methods for handling multiple objectives, each with its own advantages and limitations depending on the problem requirements and decision-making context. In this paper, we utilize the weighted fitness formulation to provide controllable prioritization among the competing objectives while maintaining algorithmic simplicity and computational efficiency. Accordingly, objectives F₁, F₂, and F₃, are combined into a single-objective fitness function as follows:(5)Fitness=maximize{w1×F1+w2×F2+w3×F3},where w₁, w₂, and w₃ ∈ [0, 1] (w₁ + w₂ + w₃ = 1) are the relative weights of the coverage, interference, and cost, within the total fitness function, respectively. These weights can be adjusted by the hospital decision-maker according to the specific application requirements and deployment priorities. Furthermore, the three sub-objectives F₁, F₂, and F₃ can be calculated as:(6)F1=∑g=1GCg×COV(g)∑g=1GCg, (7)F2=1−∑g=1GCg×INT(g)∑g=1GCg, (8)F3=1−∑i=1I∑gGSol.C(i)×PA(i,g)+∑j=1J∑gGCR×PR(j,g)max(C)×Amax+CR×Amax,

Subject to:(9)F1≥Covmin, (10)Sol.S(i)≤1∀i∈I, (11)∑g=1GPA(i,g)≤1∀g∈G, (12)∑g=1G∑i=1IPA(i,g)≤Amax, (13)∑j=1JPR(j,g)≤1∀g∈G, (14)∑i=1IPA(i,g)≤4∀g∈G.

Eq. (9) enforces that the total coverage meets the minimum acceptable level. Eq. (10) specifies whether an antenna i is selected for deployment, while Eq. (11) ensures that each selected antenna is assigned to a specific grid location. Eq. (12) limits the total number of deployed antennas across the hospital layout to the maximum allowable value A_max. Eq. (13) restricts each grid location to at most one specific reader. Finally, Eq. (14) constrains the number of antennas placed at any reader (grid) to 4, supporting single-, two-, and four-port reader configurations.

Grey Wolf Optimizer (GWO) is a population-based metaheuristic that has proven effective for continuous optimization tasks by striking a strong balance between global exploration and local exploitation, while also exhibiting rapid convergence toward near-optimal solutions. GWO is characterized by a small number of control parameters, straightforward implementation, and competitive convergence speed [38,39], which make it attractive for complex optimization problems such as RNPs.

In the proposed KBGWO-RNP framework, the optimization process begins with a random initial population of grey wolves, where each wolf encodes a feasible RFID network design through four sub-solution components, namely Sol.S, Sol.P, Sol.T, and Sol.D, as depicted in Fig. 3. During each iteration of the algorithm, all candidate solutions are evaluated using the fitness function and then ranked in descending order. Then, the three highest-quality grey wolves are identified as the X_α (alpha), X_β (beta), and X_δ (delta) wolves, as follows:(15)X1(k)=Xα−A1⋅|C1Xα−XOLD(k)|, (16)X2(k)=Xβ−A2⋅|C2Xβ−XOLD(k)|, (17)X3(k)=Xδ−A3⋅|C3Xδ−XOLD(k)|.

The remaining wolves update their positions based on the guidance of these three leaders using the position update rule in Eq. (18). In this mechanism, the coefficient vectors A_1,2,3 and C_1,2,3 are calculated as A = 2a·r₁ − a and C = 2r₂, respectively, where r₁ and r₂ are random vectors with values within [0, 1], and a is a linearly decreasing parameter that transitions from 2 to 0 throughout the optimization process. (18)XNEW(k)=(X1(k)+X2(k)+X3(k))3.

Based on these update equations, wolves move toward promising regions of the search space when |A| < 1 (attacking prey), corresponding to exploitation, and explore new regions when |A| > 1 (search for prey). With the progression of iterations and the gradual decrease of a, the search shifts from exploration to exploitation, enabling efficient solution refinement and convergence to high-quality RNP configurations.

To strengthen the search capability of GWO within the KBGWO-RNP framework, a KBH-based local search improvement phase is applied to each grey wolf. The proposed KBH is considered knowledge-based because it integrates multiple sources of domain-specific and structural knowledge (i.e., coverage demand, interference interactions, and environmental constraints) and aggregates them into a multi-criteria heuristic model that dynamically adapts to the current state of the network. Although the KBH introduces a guided local search mechanism, it does not lead to premature convergence due to the concurrent exploration capability of the GWO population. The hybrid design preserves diversity while enabling informed refinement, thereby mitigating the risk of stagnation in local optima.

As illustrated in Pseudo-code of Algorithm 1 and Fig. 4, the KBH algorithm exploits structural and environmental knowledge through three context-aware input parameters to assess the suitability of candidate modifications for a randomly selected antenna in each solution. The first input H1(i,g,t,d) represents the coverage density obtained by placing antenna i at grid g with type t and direction d to cover currently uncovered grids. This metric evaluates the concentration of critical grids within the coverage footprint of the antenna and favors antenna configurations that maximize coverage of high-priority or densely populated tag areas. By steering directional beams toward regions with greater unmet demand (non-covered grids), this input promotes efficient utilization of antenna resources. It is formulated as follows:(19)H1(i,g,t,d)=∑h∈H(g)(Ch×(1−COVh)×Vi,g,t,d,h)∑h∈H(g)Ch.

The second input H2(i,g,t,d) denotes the inter-antenna interference associated with antenna i when deployed with type t and direction d. This parameter enables a balanced trade-off between coverage expansion and interference mitigation by penalizing configurations that introduce excessive overlap with already deployed antennas. Consequently, antenna placements with lower mutual interference are preferred to be selected. This input can be computed as follows:(20)H2(i,g,t,d)=∑h∈H(g)(Ch×COVh×Bi,g,t,d,h)∑h∈H(g)Ch.

The third input H3(i,g,t,d) captures the directional distance to walls for antenna i located at grid g under a given type and orientation. It measures the proximity of the main lobe of the antenna to the closest wall, reflecting the impact of physical obstructions on signal propagation. Since walls act as natural boundaries that can limit effective coverage and cause energy loss, antenna orientations pointing directly toward nearby walls are penalized. This encourages beam directions that better exploit effective open spaces and improve coverage efficiency in indoor hospital environments. The formulation is given by:(21)H3(i,g,t,d)=minw(di,g,t,d,w)Rt.

After calculating the three input parameters for all candidate modifications for antenna i, the KBH-based score of each candidate is calculated. The higher values of H₁ and H₃ increase the score, whereas lower values of H₂ are favored to reduce interference. Since all three inputs are normalized within the range [0, 1] using Eqs. (19)–(21), they can be merged to calculate the KBH-based score as follows:(22)S(i,g,t,d)=α1×H1(i,g,t,d)+α2×(1−H2(i,g,t,d))+α3×H3(i,g,t,d),where α₁ to α₃ are weighting coefficients in [0, 1] satisfying α₁ + α₂ + α₃ = 1, allowing flexible control over the relative importance of coverage, interference, and wall-awareness in the local search decision process, while considering the correlations with already deployed antennas.

The time complexity of the KBGWO-RNP model can be analyzed by considering its two main components: the knowledge-based heuristic (KBH) and the Grey Wolf Optimizer (GWO). The KBH module performs local search refinement on each solution at every iteration. As illustrated in Fig. 4, it evaluates T × D candidate situations, resulting in a time complexity of O(T × D). Furthermore, the overall complexity of the GWO-based optimization process can be represented as O(PopSize×MaxIter×(DGWO+DKBH)), where PopSize and MaxIter are the population size and the maximum iterations of GWO, respectively. Since the GWO-related complexity can be defined based on the number of grids and maximum deployable antennas as DGWO=G×Amax, the total time complexity of KBGWO-RNP is O(PopSize×MaxIter×(G×Amax+T×D)).

Typically, both G and A_max are much larger than T and D, leading G×Amax>>T×D. It means that the computational cost of the KBH module per iteration and per solution can be dominated by that of the GWO component. Therefore, the overall time complexity of KBGWO-RNP can be reasonably simplified to O(PopSize×MaxIter×G×Amax). This analysis shows that, despite its effectiveness in improving solution quality and convergence speed, integrating the KBH module into the GWO search process adds only marginal overhead and does not significantly affect the overall computational complexity.

To evaluate the performance of the KBGWO-RNP model, we applied it to a hospital plan, with randomly assigned criticality levels across the grid. The hospital plan, shown in Fig. 5, reflects an indoor healthcare environment characterized by corridors, walls, and heterogeneous patterns of medical asset occurrence. To assess the performance of the KBGWO-RNP framework, a simulated indoor workspace was configured as summarized in Table 3. The environment covers an area of 40 m × 20 m, discretized into 1 m × 1 m grid cells, resulting in a total of 800 grids. Within this space, up to 50 directional RFID antennas can be deployed at accessible grids. As described in Section 3, a library of 20 heterogeneous antenna types is used, each characterized by different gain, read range, beam width, and cost. The read ranges are from 2 to 10 m, while the beam widths span 40° to 90°, offering flexible options to meet the different coverage requirements.

Furthermore, Table 4 lists the controllable parameters of KBGWO-RNP. The population size of GWO is set to 20, and the number of iterations is 300. The three KBH input parameters are assigned equal influence. For the fitness function, the weights are set to w₁ = 0.25, w₂ = 0.25, and w₃ = 0.5, assigning half of the total weight to deployment cost and the remaining half to balancing performance metrics: i.e., coverage and interference. Moreover, the minimum acceptable coverage rate is set to 60%, 75%, and 90%.

In Section 5.2, the performance of the KBGWO-RNP model is evaluated under different scenarios with varying values of COV_min, while keeping the fitness function weights fixed at w₁ = 0.25, w₂ = 0.25, and w₃ = 0.5. In Section 5.3, the KBGWO-RNP approach is compared against existing methods reported in the literature to demonstrate its relative effectiveness. Sections 5.4, 5.5, and 5.6 present a series of sensitivity analyses to investigate the impact of key parameters, including the minimum acceptable coverage rate, the fitness function weights, and the structure of the criticality maps, respectively. In Section 5.7, a statistical analysis is conducted using randomly generated criticality maps to assess the robustness and stability of the proposed approach under varying spatial conditions. Finally, an ablation study is presented in Section 5.8 to evaluate the contribution of the individual components of the KBGWO-RNP framework.

It should be noted that the main comparative results presented in Sections 5.2 to 5.5 correspond to representative executions under the same reference map configuration (as seen in Fig. 5), while the analyses reported in Sections 5.6 to 5.8 primarily evaluate robustness against spatial criticality variability across different generated maps.

In this section, the results of the KBGWO-RNP framework for three scenarios considering COV_min as 60% (Scenario C1), 75% (Scenario C2), and 90% (Scenario C3), are reported. The results obtained for Scenario C1 (COV_min = 60%) demonstrate the capability of KBGWO-RNP to achieve acceptable coverage with a very compact and cost-efficient deployment. As shown in Fig. 6, the algorithm rapidly converges to a stable solution, reaching a fitness value of 0.824 within 200 iterations. As shown in Table 5 and Fig. 7, only six antennas and four readers are deployed, while maintaining extremely low interference. This behavior reflects the effectiveness of the KBH component in guiding antenna placement toward high-criticality regions while avoiding unnecessary overlaps. In this scenario, the optimizer prioritizes strategic placement rather than extensive deployment, resulting in a low normalized cost and a high overall fitness value.

As COV_min increases to 75% in Scenario C2, the algorithm naturally shifts toward a denser deployment strategy. The number of antennas and readers increases to satisfy the stricter coverage requirement, as reflected in Table 6 and Fig. 8. Importantly, the growth in interference remains controlled, which highlights the role of directional antennas and interference knowledge-based rules embedded in KBH. Instead of uniformly increasing transmission power or beam width, the algorithm selects heterogeneous antenna types and orientations to selectively expand coverage while limiting overlap.

Scenario C3 (COV_min = 90%) represents a more challenging planning condition, requiring near-complete coverage of the hospital space. The results in Table 7 and Fig. 9 show that KBGWO-RNP meets this requirement by deploying 21 antennas across 14 readers, achieving over 90% coverage. As expected, higher coverage leads to increased interference and cost. These results confirm that KBGWO-RNP adapts its deployment strategy based on coverage demands, rather than relying on uniform or overly conservative configurations.

To evaluate the performance of the proposed KBGWO-RNP model, its results are compared against those obtained using HNRNPO [19], RNPPSO [32], and I-RAENNA [33]. All methods are evaluated under the same experimental environment, including the same hospital layout, discretized grid representation, grid resolution, and criticality map #1 (as illustrated in Fig. 5). All approaches employ the same antenna library consisting of 20 heterogeneous directional antenna types, as well as identical deployment cost parameters for antennas and readers, as specified in Table 3. Furthermore, all compared metaheuristics were executed using the same population size of 300 and the same maximum number of iterations of 20.

It should be noted that the proposed KBGWO-RNP framework explicitly incorporates a strict minimum coverage constraint (COV_min = 90% in Scenario C3), whereas the compared baseline methods were not originally designed with native hard-constraint handling mechanisms for minimum coverage enforcement. Therefore, exact equivalence between the constrained optimization formulation of KBGWO-RNP and the unconstrained behavior of the baseline methods cannot be fully guaranteed. To maintain approximate functional comparability among the evaluated methods and avoid clearly infeasible low-coverage deployments, only baseline solutions achieving coverage levels close to 90% were considered in the comparative analysis. It should be noted that this filtering criterion was introduced as a practical approximation rather than a strict equivalence condition.

Despite these methodological differences, the comparative results in Table 8 and Fig. 10 show that the proposed KBGWO-RNP framework achieves a more balanced trade-off among coverage, interference, and deployment cost. Although all methods produce relatively high coverage levels close to 90%, KBGWO-RNP achieves this performance with significantly lower cost and competitive interference levels. This improvement is primarily attributed to the integration of knowledge-based local refinement with the global exploration capability of GWO, in addition to the explicit modeling of heterogeneous directional antennas and multi-port reader deployment.

The improvement rates of the KBGWO-RNP model over the compared techniques are summarized in Table 9, where “+” indicates improvement and “−” denotes that the compared method performs better for the corresponding metric. Although KBGWO-RNP achieves slightly lower coverage than IRAENNA and slightly higher interference than HNRNPO, the proposed framework consistently provides the best overall fitness performance. Specifically, it achieves fitness improvements of up to 29.3% over HNRNPO, 27.0% over RNP-PSO, and 15.4% over IRAENNA. The comparative analysis suggests that embedding heuristic knowledge within a metaheuristic optimization framework can effectively guide the search toward more balanced and computationally efficient RNP configurations.

In this section, a sensitivity analysis is conducted to evaluate the impact of the minimum acceptable coverage rate on the system’s performance. Specifically, COV_min is varied across three levels as 60%, 75%, and 90%, corresponding to Scenarios C1, C2, and C3, respectively. This variation allows for a systematic examination of how stricter or more relaxed coverage requirements affect the resulting deployment strategy and overall solution quality. In addition, the analysis highlights the trade-offs that emerge among key performance dimensions, including coverage, interference, and cost, as the constraint becomes more demanding.

The sensitivity analysis presented in Table 10 and Fig. 11 provides an insight into how increasing the minimum acceptable coverage constraint (COV_min) impacts the trade-off between coverage, interference, and cost. It should be mentioned that the fitness function values are computed using the formulation defined in Eq. (5), where the overall fitness is expressed as a weighted sum of three sub-objectives: coverage, interference, and cost. Specifically, coverage is directly considered as a normalized fraction (F₁), while interference (F₂) and cost (F₃) are transformed into maximization terms by taking their complements, i.e., F₂ = 1 − Interference (%) and F₃ = 1 − Cost (%), since lower values are preferred for both metrics. After converting all percentage values into normalized form, the corresponding weights are applied to each component, and the final fitness value is obtained accordingly.

As the required coverage rises from 60% to 90%, the model responds by gradually increasing the number of deployed antennas and readers. This behavior is consistent with fundamental RFID planning principles: higher coverage in indoor hospital environments requires more spatially distributed antennas to overcome walls, obstructions, and corridor segmentation. A key observation is the nonlinear increase in interference as coverage constraints become stricter: it is negligible in Scenario 1 but rises in Scenarios C2 and C3 due to denser deployments and overlapping radiation footprints. This growth is effectively moderated by the use of directional antennas and the interference-aware KBH parameter (H₂), which adapt beamwidths, directions, and gains to limit overlap and maintain acceptable signal quality even at higher coverage levels. It should be mentioned that the decreasing trend of the overall fitness value with higher coverage constraints does not indicate poorer performance, but rather reflects the stricter optimization conditions from Scenario C1 to Scenario C3.

In this subsection, the sensitivity of the KBGWO-RNP model to different configurations of the fitness function weights is analyzed for Scenario C2 (COV_min = 75%), with a detailed focus on their impact on coverage, interference, cost, and the resulting fitness value. This analysis provides insight into how shifting the relative importance of the objectives influences the deployment strategy and overall solution quality.

Table 11 summarizes the results obtained under various weight combinations. Under the default configuration (w₁ = 0.25, w₂ = 0.25, w₃ = 0.5), the model achieves a well-balanced solution with 77.5% coverage, 5.9% interference, and 35.9% cost, resulting in a fitness value of 0.749. This confirms that prioritizing cost while maintaining moderate emphasis on coverage and interference leads to a strong overall trade-off. When the importance of interference is increased (w₂ = 0.5), the model reduces interference to 4.5%, indicating effective avoidance of overlapping coverage regions. However, this reduction comes at the expense of slightly lower coverage (76.2%) and higher cost (37.5%), leading to a decrease in fitness (0.728). This reflects the trade-off between minimizing interference and maintaining efficient coverage. In the next case, increasing the weight of coverage (w₁ = 0.5) improves coverage to 80.9%, but also results in higher interference (9.2%) and cost (39.1%). In this case, the fitness value rises to 0.758, suggesting that moderate emphasis on coverage can improve overall performance when balanced against the other objectives.

When cost is heavily prioritized (w₃ = 0.8), the deployment cost is reduced to 33.1%, but coverage drops to 75.8% and interference increases slightly to 6.8%. This configuration yields a fitness value of 0.733, indicating that excessive cost minimization may compromise solution quality. In contrast, strongly emphasizing interference minimization (w₂ = 0.8) leads to the lowest interference level (3.8%), but also reduces coverage (75.1%) and increases cost (39.5%), resulting in the lowest fitness value (0.699). This suggests that aggressively minimizing interference alone is not sufficient for achieving an optimal solution. Finally, assigning a dominant weight to coverage (w₁ = 0.8) produces the highest coverage (82.2%), but also leads to the highest interference (11.2%) and cost (42.2%). Nevertheless, this configuration achieves the highest fitness value (0.784), indicating that under this scenario, improving coverage has a stronger positive impact on the overall objective despite the associated penalties.

The sensitivity analysis results of the fitness function weights in this section demonstrate that the KBGWO-RNP model effectively adapts to different optimization priorities. However, extreme weight settings tend to amplify trade-offs among objectives, whereas balanced or moderately coverage-oriented configurations provide more efficient solutions for RNP. It should be emphasized that all results in this section are obtained under Scenario C2, where the minimum coverage constraint (COV_min) is set to exceed 75%. Any variation in this constraint would significantly influence the results, potentially leading to more pronounced differences than those reported in Table 11.

In this subsection, the robustness of the KBGWO-RNP model is evaluated using 10 different randomly generated criticality maps on the hospital plan of Fig. 5. This analysis introduces variability in spatial criticality distributions to simulate asset importance as non-uniform. Each map assigns different criticality levels to grid cells, while preserving the same physical layout (walls, corridors, and accessible areas). The model is executed independently on each map under the three scenarios C1, C2, and C3.

Table 12 summarizes the overall fitness function values obtained across all maps. The results demonstrate that KBGWO-RNP maintains consistent performance across varying criticality patterns. Although slight fluctuations are observed, the variance remains limited, indicating that the model effectively adapts antenna placement strategies based on spatial importance distributions.

To evaluate the robustness and statistical reliability of the KBGWO-RNP model, a comprehensive statistical analysis is performed using the results obtained from the 10 different criticality maps reported in Table 12. In addition to descriptive statistics, dispersion measures and inferential tests are employed to assess the consistency and significance of the model’s performance. It should be noted that the statistical analysis evaluates variability across different criticality-map realizations (reported in Section 5.6), rather than repeated stochastic executions over a fixed map configuration.

Table 13 presents the mean, standard deviation, coefficient of variation, and 95% confidence interval of the fitness values for each scenario. The results show that KBGWO-RNP maintains a high level of stability across all scenarios. The standard deviation values are low (approximately 0.010), and the coefficient of variation remains close to 1%–1.5%, indicating limited sensitivity to variations in the criticality maps. Scenario C1 exhibits slightly higher variability due to the more flexible solution space under relaxed constraints, whereas Scenarios C2 and C3 show comparable and stable behavior despite stricter requirements. The relatively narrow confidence intervals confirm the statistical reliability of the obtained mean values.

To examine the statistical significance of performance differences, a non-parametric Friedman test is conducted across the three scenarios using the results from Table 12. The test indicates statistically significant differences among the scenarios (p < 0.05), which is consistent with the increasing coverage constraints. Furthermore, post-hoc Wilcoxon signed-rank tests confirm that all pairwise differences between scenarios are statistically significant (p < 0.05). Overall, these results demonstrate that the KBGWO-RNP model provides not only strong optimization performance but also consistent and statistically reliable results under varying spatial conditions.

To assess the contribution of each component in the proposed KBGWO-RNP framework, an ablation study is conducted by comparing three configurations:

KBH-only (heuristic-based placement without metaheuristic search): For the KBH-only configuration, an initial solution is randomly generated. Then, the KBH-based improvement procedure (as seen in Fig. 4) is applied iteratively to all deployed antennas i across all grid locations g.

The ablation study results over the 10 criticality maps, are presented in Table 14. The KBH-only configuration, which serves as the baseline heuristic method, achieves the lowest fitness values across all scenarios. Its main advantage lies in computational efficiency, as reflected in its very low running times (0.12–0.15 s). However, this efficiency comes at the cost of limited exploration capability and reduced robustness. This behavior is reflected in the relatively high standard deviation values (0.0283, 0.0270, and 0.0266), which indicate strong sensitivity to map variations and inconsistent convergence behavior across different deployments. In contrast, the GWO-only configuration improves fitness performance across all scenarios, achieving values of 0.798, 0.720, and 0.595. This improvement is attributed to the stronger global search capability of the GWO, which enables broader exploration of the solution space than a heuristic search method. Moreover, the standard deviation values decrease significantly to 0.0092, 0.0096, and 0.0087, showing that the metaheuristic search provides more stable solutions and better adaptability to varying criticality maps. However, this comes with a significant computational cost, as reflected in the substantially higher running times (74–83 s).

The proposed KBGWO-RNP hybrid model consistently achieves the best fitness performance across all scenarios, with values of 0.821, 0.747, and 0.627. This improvement comes with a slight increase in computational cost compared to GWO-only, with running times of 78–90 s. More importantly, the hybrid model achieves the lowest standard deviation values (0.0031–0.0034), indicating highly stable and consistent performance across all tested maps. The very small variance demonstrates that the integration of knowledge-based refinement with global optimization not only improves solution quality but also enhances convergence reliability and robustness against environmental variations.

These results highlight a clear trade-off between computational efficiency and solution quality across the three methods. KBH provides extremely fast execution but suffers from weak exploration capability and high variability. GWO significantly improves solution quality and stability but at a high computational cost. In contrast, the proposed hybrid KBGWO-RNP framework achieves the best balance between these two extremes by combining strong global exploration with informed local refinement, resulting in superior fitness performance, lower variability, and more reliable convergence behavior.