Genetic algorithm-assisted fuzzy clustering framework to solve resource-constrained project problems

3.1 RSRF

Fuzzy clustering is applied in this proposed framework for improving resource allocation, constraint mitigation, and allocation time based on crossover mutation for precisely addressing the problems. An efficient resource allocation is indeed a crucial aspect in technology applications facing resource constraints and varying user demands. The proposed RSRF approach overcomes this challenge by integrating GAs and fuzzy clustering for optimizing the resource allocation, thereby ensuring that the available resources are utilized effectively during the accommodation of diverse user demands. Thus, the proposed framework requires better handling of heterogeneous resources to prevent replications. An illustration of the proposed framework is given in Figure 2.

Figure 2

Illustration of the proposed framework.

The overall problems addressed with RSRF using fuzzy clustering are pursued for segregating solutions for retaining non-optimal solutions for mitigating the constraints with maximum demand allocation and allocation time. The RSRF-assisted fuzzy clustering process is applied in the genetic process to highly observe optimal and sub-optimal solutions based on the crossover features, preventing imbalanced solutions. The RSRF-assisted fuzzy clustering process first computes the resource allocation for varying users and requirements. Then, the process identifies different problems in the genetic process. This assists RSRF in using the fuzzy clustering process to improve the problem-addressing ability, and resource allocation is the tallying factor. The GA-assisted fuzzy clustering framework to solve resource-constrained project problems is briefly explained in Section 3.2.

3.2 Genetic process

The RSRF-assisted fuzzy clustering process exploits allocating the resources for varying users, and demand is a considered factor for constraint mitigation in the genetic process. The resources are utilized for allocation using RSRF-assisted fuzzy clustering to improve the addressing of issues mentioned above through optimization for reducing imbalanced solutions. The proposed framework determines the solution possibilities based on mutating the allocation and availability possibilities of the resources for different problems across various demands and users, and segregating solutions contrary to existing constraints is identified in the first level. Therefore, the various range of solutions is satisfied through optimization for segregating the solutions. In the second level, the crossover features are tailored based on a fuzzy clustering process across multiple resource allocations performed to reduce complexity and allocation time.

The study employed a fuzzy and adaptive learning clustering method to capture the progressive shift of data points between clusters accurately. The membership function employed a hybrid methodology, integrating Gaussian and triangular functions. It facilitated the seamless movement of data points and a more precise definition of boundaries, improving the clustering outcomes’ reliability. The clustering criteria focused on achieving both cluster compactness and separation. It was done by optimizing a multi-objective function to reduce the variation inside each cluster and maximize the separation between clusters. It promotes internal unity and clear groupings, making allocating resources more efficient. The study sought to improve their clustering method’s flexibility, precision, and resilience by integrating these distinctive components. With the help of resource allocation and availability, the RSRF computes the crossover mutation for varying users and demands from the genetic process. The proposed framework verifies multiple resource allocation for the instance is 1 to N If the constraint is true, then a genetic process is performed for constraint mitigation and crossover mutation computes using fuzzy clustering to address the issues. Otherwise, if the crossover feature is not tailored for resource allocation, then the RSRF-assisted fuzzy clustering process attains imbalanced solutions across various demands, preventing replications.

The study utilized the fuzzy C-means (FCM) algorithm as the chosen method for fuzzy clustering. The FCM algorithm is a widely recognized clustering method that assigns fuzzy membership values to data points, reflecting the extent to which each point belongs to each cluster. It enables the data to be divided into separate groups, where each data point can be a member of numerous clusters with different levels of affiliation. The FCM algorithm updates cluster centroids and membership values iteratively by minimizing the objective function quantifying the fuzzy partitioning quality. By iteratively improving cluster centroids and membership values, FCM can accurately represent the data’s fundamental organization and offer a versatile framework for clustering. The fuzzy clustering technique in this work employs the Gaussian membership function. The Gaussian membership function is commonly used in fuzzy clustering because of its smooth and symmetrical structure, enabling a gradual transition between cluster memberships. The function is characterized by its mean and standard deviation parameters, which determine the average and variability of the membership values, respectively. The Gaussian membership function offers an inherent method to represent the uncertainty in the clustering process, enabling a seamless and uninterrupted allocation of membership values to data points.

A GA comprising 50 population size as individuals has been employed in the research implementation to determine an acceptable balance between exploration and exploitation. To improve diversity of genes and convergence, 0.1 as mutation rate and 0.8 as crossover rate are considered as parameter settings. These ranges are used to generate new generations by exchanging from two distinct locations on the chromosome that were chosen at chance. Using a mutation approach that incorporates a mutation value that is created randomly from a Gaussian approach, the operator for mutation generated unpredictable modifications to genetic levels. By adjusting the operators of selection, crossover, and mutation, the GA opted for resource allocation with the goals of optimizing resource utilization, minimizing constraint violations, and minimizing the time for allocations.

Let us consider the available resources are represented as Rsc = r 1 , r 2 , … r N with varying numbers of users and demands usr i and dem i for allocation. The proposed framework computes the resource allocation Rsc alloc using equation (1) as follows:

where the variable Rsc alloc represents the resource allocation for multiple users based on their demands and requirements and Al C represents the resource allocation constraint of the individual resources pursuing the genetic process. GP denotes the genetic process and i represents the sequential process at different intervals. Using equation (1), RSRF allocates resources for all the users concerning their demands, and imbalanced solutions are identified to improve problem-addressing ability. Consequently, the proposed framework defines resource allocation constraints in the genetic process to easily address issues ∃ issue using the below expression:

where the variables ∇ utz and ∈ u / d are used to indicate the pervasive utilization of resources and in-definite user/demand densities at the time of allocation of results in imbalanced solutions from the genetic process concerning resource allocation constraint. With the assistance of the above equation, the proposed framework determines the allocation and availability possibilities of the resource outputs in different issues identified by fuzzy clustering, followed by the proposed framework computing the genetic process GP using the below formula:

By using equation (3), the outputs of resource allocation constraint are processed using a genetic process based on varying users and demands in different time intervals. The study employed a population size of 50 people to maintain a balance between the ability to explore and exploit while ensuring that the survey’s computational aspects were manageable. A crossover rate of 0.8 and a mutation rate of 0.1 were selected to enhance genetic diversity and convergence. The maximum number of iterations was set at 100 to ensure convergence. The selection of the cluster number and degree of fuzziness was made to achieve a compromise between the quality of the solution and the computational efficiency. The minimize-variance goal function was selected to optimize resource allocation and reduce the solution’s variability. The GA was executed utilizing selection methods. With the estimated genetic process, the proposed RSRF accurately identifies the issues through optimization that outputs an imbalanced solution. Solution segregation is performed for constraint mitigation to overcome this type of issue. The constraint mitigation process is briefly explained in Section 3.4.

3.3 Crossover mutation

After performing the genetic process, the RSRF-assisted fuzzy clustering process computes crossover mutation and mitigates the resource constraints. In this process, the required solutions are segregated, namely, optimal, sub-optimal, and non-optimal, based on the allocation and availability possibilities of the multiple resources computed by the proposed framework. This work employed a hybrid approach that combined fuzzy clustering results with objective function evaluations to categorize solutions into optimal, suboptimal, and non-optimal categories. Optimal solutions have high membership values in clusters corresponding to desirable features such as maximum resource usage, minimal constraint violations, and low allocation time. These solutions are the most optimal configurations determined by the optimization process. Suboptimal solutions refer to solutions with moderate membership values in clusters but demonstrate sufficient performance based on the objective function. Although suboptimal solutions are not as desired as optimal solutions, they provide acceptable performance and can be used as alternatives in some situations. Non-optimal solutions refer to solutions that have low membership values in clusters or significant deviations from ideal solution features. These solutions are considered suboptimal configurations and are unlikely to achieve the specified objectives and may need more modification or rejection.

Fuzzy clustering process shows the extent that eachpoint is a part of the individual cluster. The most optimal solutions identified by optimization technique with selected mutation rate are those with high values for membership in clusters that correlate to factors such as low allocation time, limited constraint violations, and maximum utilization of resources.

Even with suboptimal solutions, the objective function nevertheless finds them to be good in terms of efficiency, as they have moderate group membership levels and can be used as substitutes if needed. Contrarily, non-optimal solutions either have low cluster values for membership that differ greatly from the qualities of an ideal response solution. The adjustments to these solutions with this framework efficiently use objective function evaluation and fuzzy clustering to classify the optimal, suboptimal, or non-optimal solutions according to mutation rate. This allows for efficient allocation of resources and mitigation of constraints.

In this first level, the existing constraint takes maximum allocation time and results in imbalanced solutions. To compute level 1, the crossover mutation is estimated and the possibilities of the solution are tailored across various demands for reducing issues. Post this process, the required solutions are classified and carried out for constraint mitigation, continuously segregating solutions using RSRF. Sequential solution classification is performed based on utilizing the GA for mutating the allocation and availability possibilities to improve the resource allocation and allocation time as compared to the conventional method. In this proposed framework, both solution segregation and crossover mutation are performed. The crossover mutations are tailored to meet the maximum resource allocation and constraint mitigation from the genetic process using fuzzy clustering to reduce complexity.

The two-point crossover operator produces offspring from parent individuals by swapping genetic material between two randomly selected locations along the chromosome. It fosters biodiversity and safeguards genetic data. The mutation operator introduces random changes to gene values in the chromosome, following a predetermined mutation rate and employing a Gaussian mutation method. This process entails incorporating a randomly generated mutation value, drawn from a Gaussian distribution with a mean of zero and a modest standard deviation, to every gene. It enables detailed exploration of the solution space while minimizing the likelihood of significant disruptions to favorable solutions. The continuous constraint mitigation performed in this article is presented here.

The multiple resource allocation based on the constraint is computed in different instances as the sample input. The fuzzy clustering is performed with crossover mutation, resulting in less replication. Three types of solutions are utilized for constraint mitigation across varying users and demand through optimization. From that, the allocation and availability possibilities are expressed as follows:

where Al C 0 + Al C 1 ( usr 1 , dem 1 ) + … + Al C N ( usr i , dem i ) represents the linear multiple resource allocation constraints from the genetic process that assists in constraint mitigation to compute the crossover mutation between the considered features and thereby improve resource allocation and allocation time in the first level. The variables Alloc and Avail represent the GA mutating the allocation and availability possibilities for preventing resource constraints, respectively. The complete genetic process is illustrated in Figure 3.

Figure 3

Genetic process illustration.

The study meticulously chose the population size to balance exploration and exploitation within the search space. A bigger population size allows for more extensive exploration of the solution space, but it also increases computational overhead. On the other hand, a smaller population size may reach a standard solution rapidly but runs the danger of reaching poor options too early. The study concluded, following experimentation, that a population size of 50 individuals achieved an optimal equilibrium between exploration and exploitation within the issue domain. This population size enables fast solution space exploration while maintaining variety to avoid premature convergence. The population is initialized using ( i , N ) for categorizing allocated and unallocated instances. Based on the constraints, the allocations are either optimal (or) suboptimal (or) non-optimal. The crossover is performed for identifying free scheduling instances for accommodating N such that Rs c alloc is maximized. In the GP , the ∃ issue arise post the scheduled (mutated) output based on ∇ utz . This is required for handling ∈ u / d across ρ ( alloc , Avail ) . In particular, the Avail = 0 due to left out ( N × i ) combinations and unpredictable ∈ u / d in any N (Figure 3). Therefore, fuzzy clustering segregates the optimal, sub-optimal, and non-optimal solutions based on the mutation rate from the genetic process of all resources performed. The process of multiple resource allocation-based applications/services acquires different users and demands and various ranges of solutions observed through optimization for reducing imbalanced solutions. The multiple resource allocations are processed with solution segregation using fuzzy clustering based on the mutating allocation and availability possibilities. The solution segregation output is used for improving the problem-addressing ability through optimization from the genetic process. In this proposed framework, where the solutions are initially filtered using fuzzy clustering, the fuzzy clustering output is expressed as follows:

where Al C 1 ( usr 1 , dem 1 ) indicates the resource allocation constraint applied for all solutions using fuzzy clustering. Subsequently, fuzzy clustering segregates solutions expressed as in equation (6),

where

and

In equations 7(a) and (b), where the variable Const mitigate means a constraint mitigation process performed for all solutions of fuzzy clustering. Subsequently, the fuzzy clustering process segregates ∃ S optimal, sub-optimal, and non-optimal solutions based on allocation and availability possibilities expressed as follows:

Equation (8) is used to mitigate the constraints to segregate the solutions based on optimal, sub-optimal, and non-optimal for reducing complexity. In this process, the arg max function is used for improving multiple resource allocations from the genetic process. The fuzzy clustering for the three solutions is illustrated in Figure 4.

Figure 4

Fuzzy clustering for GP output solutions.

The fuzzy clustering process intakes GP ( us r i , de m i ) output based on ρ ( Alloc , Avail ) . GP ( us r i , de m i ) illustrated in Figure 4 is only an illustrative example of N and i counts. From the same class, three categories are split, i.e., ( N > i ) , ( N = i ) , and ( N < i ) . These categories are grouped based on equation (4) for balancing ∇ utz such that Rsc alloc increases. Considerably, the A l C arise from N = i to N < i intervals due to sub-optimal and non-optimal solutions. The constraints are individually addressed during Allo c i and Avai l i instances. During the segregation of solutions, the constraints mitigate with the help of sequential processing of crossover mutation to meet optimal and sub-optimal solutions. The fuzzy clustering computes the mutation rate with the present constraint and existing constraint. Accordingly, the non-optimal solutions non_opt o in fuzzy clustering process is expressed as follows:

where ( Const mitigate ) i represents the actual solution for the genetic process and ε cof refers to the tailored crossover features across multiple resource allocation instances that control the existing constraints. After performing the clustering process, the GA is applied with the help of crossover features. Here the objective function of this proposed framework is to mitigate the constraint using fuzzy clustering output. The constraint mitigation is explained Section 3.4.

3.4 Constraint mitigation

The objective function of this proposed framework is to mitigate resource constraints based on crossover mutation from the genetic process. The optimal, sub-optimal, and non-optimal solutions are segregated by fuzzy clustering to reduce resource-constraint and allocation time, respectively, then

such that

where the constraint ρ ( Al C N ( usr i , dem i ) , ε cof ) T refers to the availability and allocation probability of the available resources computed through optimization from the genetic process. The maximum probability of achieving an optimal and sub-optimal solution is denoted as ( M = 1 ) and obtains high segregation for the tailored crossover features. In this proposed framework, the non-optimal solution is identified from the genetic process and crossover mutation using fuzzy clustering. The probability of resource-constrained reduction successfully achieves optimal and sub-optimal output based on mutation score without complexity. Hence, ρ ( FZY ( DF n ) ) is expressed as follows:

Equation (12) identifies the allocation and availability possibilities of the resources for the control of different problems in a genetic process using fuzzy clustering. It is used to maximize the mutation rate with ρ ( Al C N ( usr i , dem i ) , ε cof ) T is M = 1 for the non-optimal solutions. This constraint mitigation is performed across multiple resource allocation instances, and hence, the solution segregation is improved based on the mutation rate from the genetic process. The proposed framework utilizing both optimal and sub-optimal solutions helps to improve multiple resource allocation, constraint mitigation, and allocation time. The crossover features are tailored for constraint mitigation from the genetic process. The extracted crossover features based on the fuzzy clustering process mitigate the existing constraints. In this clustering process, the multiple resource allocation instances m ( rsa ) is represented as follows:

such that

Equations (13) and (14) are used to segregate solutions for continuous resource allocation until a non-optimal solution is identified from the fuzzy clustering process. The fitness function was devised to assess the merit of each solution in the population by measuring its effectiveness in solving the resource allocation problem. The fitness function considered several objectives: minimizing resource duplication, maximizing resource usage, addressing restrictions, and decreasing allocation time. The objectives were assigned weights based on their importance in the optimization problem. This work employed a hybrid fitness function that integrated fuzzy clustering into the fitness evaluation process. The clustering findings were used to assign fuzzy membership values to each solution. It enables the incorporation of the inherent uncertainty in the resource allocation problem and facilitates the generation of more informed judgments throughout the optimization process. The fuzzy clustering classifies the solutions based on the mutation rate until non-optimal solutions are detected from the instances. In this process, the resource constraint concerning availability and allocation possibility from the instances is to improve constraint-less allocation. Besides, the constraint mitigation is to be instantaneous to meet the maximum resource allocation and constraint mitigation. The proposed framework’s main aim is to satisfy constraint-less resource allocation through fuzzy clustering, thereby reducing allocation time. The constraint mitigation sequence based on equation (4) is analyzed in Table 2.

In Table 2, the outputs for N = 2 , 3 , and 4 are analyzed for their cumulative A l C . The N = 1 is high as allocation is always ready, wherein availability is not set up. Considering the three conditions for A l C ( N ) , the ρ ( Alloc , Avail ) is balanced through mutated outputs. The A l C ( N ) discussed above is the computation based on N > i alone rather than N = i . As N = i is suboptimal, the A l C ( N ) is increased by 1 ; the ρ ( Alloc , Avail ) increases with the constraint increments. Hence, the case of clustering subdues the available instances for preventing new constraints. From the provided data, the analysis of Allo c i , Avai l i , and other metrics are analyzed in this subsection. First, the constraints: resource, time, drop, backlog, distribution, etc., (adding up to 14) are extracted for analysis in this part. Based on the demand at intermediate intervals for N = 24 , the ∈ u / d is analyzed as in Figure 5(a).

Figure 5

(a) ∈ u / d and (b) A l C for intermediate N .

The intermediate N observed between the maximum instances are considered in Figure 5(a) and (b). The ∈ u / d and A l C are variables based on ρ ( Allo c i , Avai l i ) . This is mutated using a genetic process with a new population (exceeding N or i or both). Therefore, for the new population, the allocations are classified as optimal (sub-optimal to) if a multi-resource allocation is performed. In the failing case, the A l c increases such that ∈ u / d is void (without allocation) for pursuing demands. Therefore, the N is pursued with new Rs c allocation for preventing allocation/availability ∃ issue (refer Figure 5). The ρ ( Allo c i , Avai l i ) based on solution differentiation across 720 intervals is analyzed in Figure 6(a).

Figure 6

(a) ρ ( Allo c i , Avai l i ) and (b) Cons t mitigate analysis.

The above analysis is presented based on i and the f ∁ o i for solution improving the Rs c alloc under A l c suppression. Therefore, the cons t mitigate fuzzy clustering improves the Allo c i and Avai l i for maximizing allocations without failure (Figure 6(b)). Thus, the ∇ utz is provided for ∈ u / d under distinguishable ∃ s . Hence, the consecutive allocation is made (intermediate to i ) for maximizing the conditions in equations (10) and (11), respectively. This increases the optimal solution extraction as presented in Figure 6. Table 2 presents the m ( rsa , T ) for the distinguishable constraints under three conditions: N > i , N < i , and N = i using f ∁ o i . Table 3 presents the actual A l c and the mitigated constraints under different allocations.

In Table 3, the actual A l C and the mitigated constraints for different conditions and ρ ( alloc , Avail ) are analyzed. Based on the mutated outputs, the scheduling is analyzed for incoming ∈ u / d stagnancies. Considering the demand suppressions, the A l C is contained across Allo c i and Avai l i for f c o i provided Rs c alloc is increased. If the Rs c alloc is increased, then the fuzzy split is performed for reducing available constraints. Therefore, the available solutions are split for validating ∈ u / d such that m ( rsa , T ) is optimal under suppressed A l c . The integration of GAs and fuzzy clustering algorithms in the framework combines the advantages of GAs’ global search capabilities with fuzzy clustering’s capacity to describe and manage uncertainty in resource allocation. The integration results in a resilient methodology that can easily adjust to ever-changing and unpredictable conditions, making it highly suitable for practical scenarios where accurate knowledge about resource requirements may be ambiguous or susceptible to modification. The RSRF framework is effectively utilized in real-world scenarios, such as cloud computing resource allocation, network resource management, and task scheduling in distributed systems. In cloud computing, the framework is utilized to handle the complex resource allocation by enabling the dynamic optimization of machine placement, resource scaling, and load balancing. In the network resource management, RSRF is used to maximize the network resource allocation efficiency and routing process. In addition, it helps to minimize the latency, optimize data transfer, and bandwidth.

The proposed algorithm is evaluated both with and without model uncertainty. In the absence of uncertainty, it efficiently allocates resources and mitigates constraints. When uncertainty is introduced, the algorithm adapts well, showcasing resilience in optimizing resource allocation under dynamic and unpredictable conditions. The proposed technique is well-suited for practical use in a variety of settings due to its ability to effectively manage uncertainties through the combination of GAs and fuzzy clustering.

Under the influence of model uncertainty, the algorithm consistently demonstrates its ability to optimize resource allocation and effectively mitigate constraints dynamically. The algorithm’s robustness is demonstrated under model uncertainty, showcasing its adaptability and consistent optimization of resource allocation. The detailed analysis emphasizes its resilience and effectiveness in handling diverse uncertainties, making it suitable for dynamic real-world scenarios with changing resource requirements. The comprehensive assessment underscores the algorithm’s suitability and effectiveness across a spectrum of conditions, affirming its practical applicability in dynamic and uncertain resource allocation environments.

The targeted technology applications include resource allocation in cloud computing for dynamic machine allocation and optimization. Also, in network resource management, reduces constraint violations and maximizes the network allocation efficiency. The resource allocation problems RSRF designed for cloud computing and task scheduling in distributed systems can be applied for dynamic optimization of allocating the machines, routing the allocated process, mitigating the latency, and optimizing the utilization of bandwidth.

4.1 Problem-addressing ability

In Figure 7(a) and (b), the resource allocation constraint problems are addressed through optimizations and GAs across varying users, and demands for preventing replications are to improve the problem-addressing ability. The solution possibilities are observed from the genetic process for mutating the allocation and availability of the resources leads to different problems. To overcome this issue, fuzzy clustering process is performed. The different problems are addressed at the time of solution segregation for improving the multiple resource allocation instances in technology-based applications/services. Depending upon the availability and allocation possibilities, fuzzy clustering segregates the optimal, sub-optimal, and non-optimal solutions from the genetic process at different time intervals. The fuzzy clustering segregates the solutions based on varying users, and they demand to enhance the constraint mitigation. This problem-addressing ability in the GA-assisted fuzzy clustering process is prominent in identifying constraint failure, wherein the resource-constrained problems are due to pervasive utilization and in-definite user/demand densities. This crossover mutation is computed using fuzzy clustering to satisfy high problem-addressing ability as compared to the other factors.

Figure 7

(a) Problem-addressing ability w. r. t. Constraints; (b) Problem-addressing ability w. r. t. Demand Factor.

4.2 Resource allocation

This proposed framework achieves high resource allocation across varying users and demands with allocation constraints; the failures are mitigated by filtering fuzzy clustering solutions from the genetic process (Figure 8(a) and (b)). The input users and demands may vary, that is addressed for modifying the constraint through proposed RSRF and fuzzy clustering of the resources, where the maximum constraint failure is identified. Based on the availability and allocation possibilities, the difference between the crossover features is analyzed; the solution possibilities are tailored, and complexity is reduced. The fuzzy clustering first classifies the solutions for performing possible resource allocation with less allocation time. The replication is addressed for varying demand, user, and problem densities using a clustering process, preventing imbalanced solutions. Therefore, the fuzzy clustering process is pursued to improve the multiple resource allocation for varying demands and user densities at different time intervals. Therefore, this process satisfies maximum resource allocation using constraints. In this proposed framework, the imbalanced solutions are retained with fuzzy clustering in an independent manner without modifying the genetic process to reduce complexity.

Figure 8

(a) Resource Allocation w. r. t. Constraints; (b) Resource Allocation w. r. t. Demand Factor.

4.3 Constraint mitigation

The multiple resource allocation sequences are performed to address minimum or maximum allocation time across varying demands using fuzzy clustering. The addressing of imbalanced solutions from the genetic process is difficult to identify constraint failures and it reduces complexity by handling heterogeneous resources for different users, demands, and problem densities. The resource availability and allocation complexities reduced using the crossover mutation solution. The failures were mitigated using resource-constrained processes at the time of continuous resource allocation; this failure occurrence is identified through fuzzy clustering. From the crossover features in the genetic process, the varying user demands and problem densities are correlated for addressing the replications. The multiple resource allocation is performed with constraints for improving allocation time. In this proposed framework, fuzzy clustering is segregated for achieving maximum constraint mitigation, as illustrated in Figure 9(a) and (b).

Figure 9

(a) Constraint Mitigation w. r. t. Constraints; (b) Constraint Mitigation w. r. t. Demand Factor.

4.4 Allocation time

This proposed RSRF-assisted fuzzy clustering process used for addressing the different problems in the genetic process with precise constraints satisfies less resource allocation time compared to the other factors, as represented in Figure 10(a) and (b). The constraint-less allocation is achieved for identifying the imbalanced solutions using fuzzy clustering. In contrast, the non-optimal solutions are observed for reducing time. This process performs sequentially until identifying the non-optimal solutions from the fuzzy clustering process. Based on the crossover mutation validation, the extracted features and available resources are processed for improving constraint mitigation. The constraints are mitigated through solutions and possibilities identification from the genetic process of the resources. It is difficult to identify imbalanced solutions for varying users and demands. In this framework, multiple resource allocation constraints are required to reduce allocation time. Thus, the proposed framework estimates fuzzy clustering across varying demands with less constraint failure.

Figure 10

(a) Allocation Time w. r. t. Constraints; (b) Allocation Time w. r. t. Demand Factor.

4.5 Constraint failure

In this proposed fuzzy clustering-based solution segregation for varying users, demands, and problem densities to identify the minimum/maximum resource constrained based on the availability and allocation possibilities is computed for retaining imbalanced solutions (Figure 11(a) and (b)). This process improving multiple resource allocation and constraint mitigation using fuzzy clustering does not mitigate the pervasive utilization and in-definite user/demand densities. The high problem-addressing ability is achieved for varying users and demands of the resources. This constraint mitigation is performed across multiple resource allocation instances, and hence, the solution segregation is increased based on the mutation rate from the genetic process. The proposed framework utilizing both optimal and sub-optimal solutions helps to improve multiple resource allocation, constraint mitigation, and allocation time. In this manner, the constraint-less allocation is satisfied by the proposed framework, whereas the maximum constraint mitigation leads to improved multiple resource allocation with less time. Hence, less allocation time is achieved using fuzzy clustering and RSRF.

Figure 11

(a) Constraint Failure w. r. t. Constraints; (b) Constraint Failure w. r. t. Demand Factor.

4.6 Sensitivity analysis

The sensitivity analysis is performed to evaluate the impact of varying parameter settings of the GA, including population size and crossover rate, using the metric resource allocation efficiency. For various population sizes, the resource allocation indicator is tested and shows gradual changes in resource distribution as the population grows. By changing the GA’s population size, we can see how it affects the distribution of resources (y-axis). Varieties in population size are depicted on the x-axis. Finding the ideal values for the parameters that maximize the efficiency of resource allocation is the objective of sensitivity analysis.

One important metric for evaluating the algorithm’s resource utilization across a range of population size and crossover rate with the values 0.6–1.0 as parameter values is the resource allocation efficiency, which can be as high as 50, as shown in Figure 12(a) and (b). Likewise, the parameters of fuzzy clustering algorithm such as number of clusters and degree of fuzziness are evaluated using sensitivity analysis to prove the performance of the proposed framework, as shown in Figure 13(a) and (b).

Figure 12

(a) Sensitivity analysis on GA parameters w.r.t. Population Size; (b) Sensitivity analysis on GA parameters w.r.t. Crossover.

Figure 13

(a) Sensitivity analysis on fuzzy clustering algorithm parameters w.r.t. No.of Clusters; (b) Sensitivity analysis on fuzzy clustering algorithm parameters w.r.t. Degree of Fuzziness.

Sensitivity analysis is carried out by repeating the process with different values for the RSRF framework parameters to improve the generalizability of the framework. The effect of parameter modifications on performance across different problem cases can be better understood in this way.

The experimental evaluation is extended with the consideration of different fields like wireless sensor network (WSN) resource components analyzed by Huang et al. [20] that include cost and weight constraints under uncertain environments consisting of 14 subsystems in the network environment. The assessment includes cost and weight constraint variations comparison of benchmark schemes with the proposed algorithm. The proposed RSRF showed that the performance on both constraints is high in contrast to other works. Figure 14(a) and (b) illustrate the performance evaluation of constraint mitigation on two factors. This scenario of WSN demonstrates that the performance of the proposed framework in this domain is high and proves the generalizability of the framework by implementing it in diverse fields. Other than this, the generalizability of the framework is demonstrated by implementing the sensitivity analysis with the impact of varying parameters of the GAs and fuzzy clustering.

Figure 14

Constraint mitigation on (a) cost factor and (b) weight factor.

Tables 4 and 5 present the comparative analysis results for varying constraints and demand factors.

The proposed RSRF introduces several innovations and improvements compared to the design methods mentioned in the references SNDHRC, RAP-ISSO, and RS-ABC. The key differentiations are: Unlike the methods SNDHRC [25], RAP-ISSO [20], and RS-ABC [30], the proposed RSRF combines the global search capabilities of GAs with the uncertainty management of fuzzy clustering, providing a resilient methodology. The RSRF exhibits a superior problem-addressing ability, addressing resource allocation constraint problems effectively through optimizations and GAs. Comparatively, the existing references lack the same level of adaptability and precision in addressing diverse problems in resource allocation scenarios. Also, this method faces challenges in achieving comparable resource allocation efficiency, especially in dynamic and complex scenarios; rather, the proposed approach mitigates failures and achieves high resource allocation efficiency. RSRF introduces a constraint mitigation sequence using fuzzy clustering to improve allocation time by identifying optimal, sub-optimal, and non-optimal solutions compared to existing methods. Fuzzy clustering helps RSRF separate solutions and improves numerous resource allocations, which in turn minimizes constraint failures. The existing approaches fall short in their attempt to minimize constraint failures because they are not as thorough as the proposed solution. The RSRF framework offers a comprehensive and flexible approach to resource allocation by combining GAs with fuzzy clustering. The innovation lies in its ability to address diverse problems, enhance resource allocation efficiency, mitigate constraints effectively, reduce allocation time, and minimal constraint failures in comparison to existing design methods.