Estimating Redevelopment Costs for High-Risk Components Using a Genetic Algorithm
Subject Areas : Computer EngineeringZeinab Faraji 1 , Faraein Aeini 2 * , Homayun Motameni 3
1 - Department of Computer Engineering, Sar. C., Islamic Azad University, Sari, Iran
2 - Department of Computer Engineering, Sar. C., Islamic Azad University, Sari, Iran
3 - Department of Computer Engineering, Sar. C., Islamic Azad University, Sari, Iran
Keywords: Component-Based Software Engineering (CBSE), Component Selection, High-Risk Components, Genetic Coefficient, Software Cost Development.,
Abstract :
Efficient component selection is crucial in component-based software engineering. This selection involves optimally combining commercially available off-the-shelf (COTS) components and in-house components. COTS components are available in different varieties, including low-risk and high-risk components. Among the two, the latter requires significant modifications to be compatible with the system, which can impact productivity, cost, and execution time. This paper addresses the challenge of integrating commercially available off-the-shelf (COTS) and in-house components, with a particular focus on the cost implications of incorporating high-risk COTS components that necessitate significant adaptation. A genetic algorithm-based method is presented to calculate the cost coefficient for redeveloping these high-risk components, following an initial identification based on their reliability. The efficacy of this approach is supported by case study results, which reveal notable improvements in Intra-modular Coupling Density (ICD) and overall system functionality, highlighting its potential to optimize component selection.
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Journal of Applied Dynamic Systems and Control,Vol.8, No.2, 2025: 33-47
| 33 |
Estimating Redevelopment Costs for High-Risk Components Using a Genetic Algorithm
Zeinab Faraji1, Faraein Aeini2*, Homayun Motameni3
1 Department of Computer Engineering, Sar. C., Islamic Azad University, Sari, Iran. Email:zeinab.faraji84@gmail.com
2* Corresponding Author :Department of Computer Engineering, Sar. C., Islamic Azad University, Sari, Iran. Email: aeini@ iausari.ac.ir
3 Department of Computer Engineering, Sar. C., Islamic Azad University, Sari, Iran. Email: motameni@iausari.ac.ir
Received: 2025.05.08; Accepted: 2025.07.16
Abstract–Component selection is a key challenge in component-based software systems, particularly when integrating a mix of commercially available off-the-shelf (COTS) and in-house components. This study emphasizes the impact of high-risk COTS components, which often require extensive modification to align with system requirements, potentially affecting cost, efficiency, and performance. To address this, high-risk components are initially identified based on reliability, and a genetic algorithm is then employed to compute a cost coefficient for their redevelopment. The proposed method led to improved outcomes in component selection, as demonstrated in a case study that reported increases in Intra-modular Coupling Density (ICD) by up to 0.05 and functionality gains of up to 1.08—validating the effectiveness of this cost-aware optimization strategy.
Keywords: Component-Based Software Engineering (CBSE); Component Selection; High-Risk Components; Genetic Coefficient; Software Cost Development
1. Introduction
This article gives you guidelines for preparing papers Component-based software engineering (CBSE) is a prevalent approach to software development, utilizing pre-existing software components. These components are largely independent and replaceable, designed to perform specific tasks within well-defined contexts. Developers employ CBSE to mitigate software complexities, streamline change management, and enhance software reusability [1,2,3]. Reusable software components are generally classified into four categories [4,5]. The first category comprises ready-made components, also known as commercially available off-the-shelf (COTS) components. These are obtained from third-party sources or are integrated into existing projects and can be used in the software development process without modification. The second category consists of complete components, which closely resemble new project components in terms of specifications, design, code, and testing. Development teams are typically familiar with these components, considering them low-risk. The third category includes incomplete components, or high-risk components, which share similarities with a current project but require substantial adjustments. Due to limited team expertise, these components are deemed high-risk. The fourth category is new components, which must be developed by the team to fulfill specific project requirements. COTS components encompass ready-made, complete, and incomplete components, with incomplete components classified as high-risk. High-risk components are often selected for their initial low cost; however, they can exhibit low reliability and negatively impact quality attributes such as Intra-modular Coupling Density (ICD) and cohesion, ultimately increasing system complexity. Therefore, effective component selection necessitates identifying component types and accurately estimating the redevelopment cost of high-risk components. This paper presents a method using a genetic algorithm to calculate the development cost factor for high-risk components. The results demonstrate the efficacy of this optimization and calculation approach in determining the software redevelopment cost factor for component selection. The primary objective of this study is to differentiate component selection and ordering strategies to enhance system performance, minimize the inclusion of high-risk components, and reduce redevelopment costs. Following the recommendation in [3], we optimized ICD and a performance function as objective functions, subject to constraints related to cost, delivery time, reliability, and ICD. This research investigates the following hypotheses:
1. Selecting fewer high-risk components results in a more optimal set of components.
2. Employing a genetic optimization approach leads to a more precise evaluation of the redevelopment effort required for COTS components.
While genetic algorithms are frequently used for component selection, their potential for optimizing objective functions and constraints is often underutilized. The method proposed in this paper leverages a genetic algorithm to determine the optimal
coefficients for the cost constraint function, owing to its robust output and mathematical foundation. The data collection for this study includes components from various device versions and internal parts assigned to different software modules. Table 1 show A summary of the methods presented by researchers in optimal components selection of software and figure 1 is showing pie chart of distribution of methods optimization, cost criteria and optimization types adopt to table 1.
The remainder of this paper is organized as follows: Section 2 reviews related work on optimal component selection, with a focus on cost considerations. Section 3 details the proposed approach. Section 4 presents the optimization problem within the case study. Section 5 presents the experimental results of the case study. Section 6 compares the results with other methods from the literature. Finally, Section 7 concludes the paper and outlines directions for future research.
Table 1: A summary of the methods presented by researchers in optimal components selection of software
Optimization type | Optimization method | Cost criteria (objective/constraint) |
Single objective | Hierarchical clustering algorithms | Cost/budget in constraint |
Single objective | AHP based on the access frequencies of the modules | Cost/budget in constraint |
Single objective | fuzzy optimization model | Cost/budget in constraint |
Single objective | optimization model based on decision variables | Cost in objective function |
Multi objective | fuzzy mathematical programming | Cost in objective function |
Multi objective | goal programming approach | Cost/budget in objective and constraint |
Multi objective | Multi-criteria optimization approach in fuzzy environment | Cost in objective function |
Multi objective | fuzzy optimization model | Cost/budget in constraint |
Multi objective | fuzzy optimization model | Cost in objective constraint |
Multi objective | fuzzy optimization model | Cost/budget in constraint |
Multi objective | genetic algorithm (GA)-based hybrid approach with fuzzy exponential membership function | Cost/budget in constraint |
Fig. 1.the pie chart of distribution of methods optimization, cost criteria and optimization types adopt to table 1.
2. Related work
In research focused on selecting the best software components, cost frequently plays a key role as either a goal to minimize or a limitation within the optimization process. Table 1 provides an overview of how researchers have incorporated cost into their models. Table 2 presents statistical insights derived from analyzing approximately 40 common factors considered during software component selection for optimization [6]. As highlighted in Table 1, cost is the most prevalent factor in optimal component selection, appearing in 17.70 of the 130 studies that considered 41 different criteria. The data in Table 2 suggests that cost is a critical factor when deciding whether to acquire or develop components due to its impact on software development expenses. Consequently, software development organizations need to account for cost when choosing software components, potentially even making it the primary
goal of their optimization efforts for ideal selection. Various optimization techniques, including multi-objective, mathematical, and genetic algorithms, have been widely employed for optimal component selection [7,8,9,10,11,12,16]. Numerous researchers have reported successful outcomes using different heuristic methods, multi-objective optimization strategies, and genetic algorithms. Figure 2 is show Statistical results of the cost criterion according to the table 2.
Table 2: Statistical results on the practical use of the cost criterion in the problem of optimal selection of components
Criteria | NP | MPP | Ref |
Cost | 23 | 17.7 | [17, 4, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 ,29, 30, 31, 32, 33, 14, 34, 37, 38, 39, 41] |
Reliability | 12 | 9.23 | [32, 4, 20, 33, 14, 34, 23, 26, 35, 36, 37, 31] |
Number of components | 9 | 6.92 | [17, 18, 15, 21,23,25, 33, 34,35] |
Delivery time | 6 | 4.60 | [1, 14, 20, 23, 30, 31] |
Functionality | 6 | 4.60 | [1, 18, 21, 23, 30, 34] |
Number of modules in the software | 5 | 3.85 | [29,14 ,31, 32,36] |
Number of provide interfaces | 5 | 3.85 | [15,18 ,33, 37,38] |
Number of alternative COTS available | 5 | 3.85 | [29,31 ,36, 32,38] |
Coupling | 3 | 2.30 | [1 , 24,25] |
Other | 56 | 43.10 | [16, 21, 33, 18, 15, 33, 30, 31, 20, 14, 30, 31 , 14, 19, 28, 1, 14, 30, 31, 29, 36, 31, 35, 22 ,35, 17] |
| 130 | 100 |
|
Fig. 2.Statistical results of the cost criterion according to the table 2.
Gholamshahi et al. [20] categorized different approaches to component identification and selection. In [11], the authors introduced a Genetic Algorithm (GA)-based hybrid approach with a fuzzy exponential membership function to select the best COTS component. The researchers in [42] used genetic algorithms and fuzzy techniques to create an optimization model for component selection in credit models. They solved the problem using a single-objective optimization method with three objective functions: cost, size, and execution time. The optimal component was determined using GA. In [44], the authors developed a model to optimize the selection of COTS components in the process of developing modular software systems. In more recent studies, researchers have increasingly focused on multi-period, multi-objective optimization frameworks that combine cost with other real-world constraints such as outsourcing, redundancy, and integration [48, 49]. These newer models reflect a growing trend toward holistic evaluation strategies that account for dynamic and time-dependent factors in component selection.
For instance, Gupta et al. (2019) proposed a framework that integrates customer relationships and outsourcing dynamics into component evaluation decisions [49]. Mehlawat et al. (2020) extended this approach by addressing software maintenance and enhancement through an adaptive multi-objective model, taking into account long-term integration costs and performance metrics [48].
Additionally, Nabot (2024) presented an optimized component selection criterion specifically tailored to modern CBSE environments. This recent study introduced refined metrics for cost, cohesion, and risk that align closely with commercial software development constraints [16].Table 3 presents the statistical results obtained by analyzing 35 articles about the best way to select components. These results reveal a variety of methods proposed in the literature for solving optimization problems. Among all, the evolutionary method using the genetic algorithm was found the most popular. All of these methods provided a solution in the form of a single-objective system, but the genetic algorithm had a positive impact on optimizing objective functions. This can lead to better results when selecting the optimal components for both single and multi-objective problems. Figure 3 illustrates Frequency chart methods that applied to solving optimal component selection problem.
Method | NP | MPP | Reference |
Evolutionary MOO based on GA | 7 | 20 | [18,15 ,21,22,33, 34,39] |
Fuzzy mathematical programming (FMP) | 3 | 8.571 | [14,30,31] |
Customized MOO (used LINGO optimization model solver) | 2 | 5.714 | [21,41] |
Goal programming | 2 | 5.714 | [36,27] |
Both AHP and WSM | 2 | 5.714 | [19,45] |
Fuzzy clustering | 2 | 5.714 | [35,24] |
Integer Programming | 2 | 5.714 | [29,40] |
Customized GA | 1 | 2.858 | [17] |
Fuzzy MOO | 1 | 2.858 | [1] |
Other methods (Lexicographic, Lagrange, MCDM, Evolutionary and WSM, AHP, WSM, SIREN method, Neural network, C4.5, Ontology-based, XML Query, backtracking algorithm | 13 | 37.143 | [23, 46, 25, 26, 28 , 32, 37, 38, 44, 45, 47 ,42, 43] |
Total | 35 | 100 |
|
Table 3.Statistical results on applied methods in the problem of optimal selection of components
Fig. 3.Frequency chart methods to solving optimal component selection problem
3. Proposed approach: calculating the cost coefficients for the redevelopment of high-risk components using a genetic algorithm
Cost is a vital consideration for management and business in software development. Since it directly impacts their budgets, software companies must carefully consider cost when choosing software components. Cost can be factored into their decision-making as either a goal to minimize or a limitation they must stay within. In software systems built from components, overlooking compatibility, miscalculating extra costs, selecting unsuitable components, or choosing high-risk options can increase system vulnerabilities and threaten the stability of the underlying technology. Some inexpensive components available may also carry high risks due to a lack of extensive use and documented history. These might not integrate well and could require replacement to improve performance, ultimately driving up the system's cost. Therefore, a method to estimate the additional development costs associated with such components is necessary. After acquiring them, these components might need further development to function within the intended system, which increases the likelihood of selecting high-risk components when using optimization techniques. This can negatively affect the system's reliability and other related goals. To accurately determine the true cost of these components, this paper outlines a calculation method that considers both their initial purchase price and potential future development expenses. This will aid in selecting the most cost-effective option and improve the overall component selection process. The proposed technique employs genetic multi-objective optimization to estimate the cost of redeveloping components, specifically considering the impact of high-risk components on the total cost. Overall, this approach aims to provide a more precise cost calculation for component redevelopment, particularly for high-risk components, and enhance the system's reliability and other performance metrics. This paper proposes using cost coefficients and a genetic algorithm to more accurately assess the cost of high-risk components. Figure 4 illustrates the proposed approach, including the method for calculating the genetic cost of component redevelopment within a multi-objective optimization framework.
Fig. 4.The Schematic of the proposed approach with the approach of calculating the cost of genetics for the redevelopment of components in multi objective optimization.
3.1 Calculating the cost of components redevelopment
Component-based systems consist of two categories of components: build and buy. Choosing to use readily available COTS components from the market can shorten the system’s delivery time, but it may also compromise security and reliability because of compatibility concerns. On the other hand, designing in-house components may take longer and cost more, but it results in a more reliable and compatible system. When dealing with multi objective systems and constraints, it is important to choose the appropriate component that can achieve the system’s goals. When calculating costs, most references consider three factors. First, in [1,4] only COTS components are used, and the total cost is simply the cost of purchasing these components. This cost is determined by Equation 1, where 
equals the sum of all costs (k) of each component.
Second, in [1, 4], only components produced by the development team are used. The total cost is determined by Equation 2, where 
equals the sum of all costs (i) of each component ( j ):
Third, in [1,2,4], a combination of in-house and COTS components are used. This is determined by Equation 3
The final total cost is obtained by combining the buy-build expenditures of all modules in the build-or-buy strategy, as shown in Equation 4.
In Equation 4, the total cost is equal to the sum of all costs (i) of each component (j) and its manufacturing time (tij) plus any additional cost (τ(ij)) and quantity produced (Nijtot) multiplied by (yij) ), plus the sum of all costs (k) of each COTS component.
3.2 Proposed approach: Calculating the cost of redevelopment of components based on the optimal calculation of coefficients with the genetic algorithm
As previously stated, certain COTS components are not compatible with software systems and are considered high-risk components. To make them compatible, changes and redevelopment are necessary. In the case study performed for the purposes of this study, low-cost and unreliable components were classified as high-risk components because of their affordability and cost constraints. However, selecting these components may reduce the reliability of the system and, specifically, ICD, which is directly related to reliability. Therefore, the selection of components needs to be evaluated based on their impacts on the objectives and constraints of the problem. To determine the ideal components that meet the goals of the problem, there is a need for considering the influencing factors of other criteria, whether they have a direct or indirect effect. Equation 5 is used to calculate the cost of a system, which includes the cost of high-risk components, including any costs associated with developing or adapting the component. Therefore, the cost of the bought component should be calculated using the following Equations:
Total Cost = Cost In-house + Cost-COTS =
Cost In-house + (Cost-COTS + Cost-develop)=
Cost In-house + (Cost-COTS + w _GA* Cost In-house) (5)
The cost of the component is calculated using Equation5, which is derived from Equations 3 and 4 and then using Equation6, which is derived from Equation 5.
This study analyzed three factors that affect the cost of software development: development time, delivery time, and the number of interactive interfaces. The goal was to determine the coefficient (W) that represents the development cost of high-risk components. The amount of time spent on development equals the time spent on developing bought components (COTS). The number of interfaces is equal to the number of connections between high-risk components and other modules, and the cost of redevelopment increases as these connections increase. Delivery time is the sum of the development and buy times of the components. We used three input parameters as the chromosomes’ data structure and W, as the output’s development cost coefficient in the genetic algorithm. The findings showed that the proposed approach is effective in selecting a combination of elements that improve the objectives of the problem.
3.3. Genetic parameters
To find the weighting coefficients of high-risk component costs, this paper used GA with the following features:
Chromosome allocation: To determine the weighting coefficient for high-risk component costs, data structures should be created for the chromosomes that represent the parameters affecting the component’s cost. To do this, this study used an array with dimensions of m * n, where m represents the initial population of the algorithm and n represents the factors that affect software development costs. Because of the presence of three influencing parameters in this case (Develop time, Delivery time, and Number of interact), an array of 3 * 50 was designed. Finally, this variable was analyzed using the principle of maximization. Equation 7 is also defined for the cost influencing parameters variable as follows:
Where Yi denotes a component of the cost chromosome, and it is necessary to satisfy Equation 8 as well. To fulfill Equation 8, the average value of each row of chromosomes was calculated at every phase of the execution using Equation 9. Then, the number of chromosomes was replaced with this average value to normalize the random amounts of the chromosomes.
Fitness function: During each stage of the genetic algorithm, the cost of every chromosome is calculated based on the target functions defined in Equation 10.
At this stage, the chromosomes undergo evaluation through the cost function. In the proposed approach, the cost is a variable inversely proportional to the fitness function of the chromosomes. The presence of negativity in Equation 10 is a result of the potential for maximizing the function.
Selection: The selection operator improves the overall quality of chromosomes in the next generation by selecting the high-quality ones. This paper uses the tournament selection method [24, 25] because it is efficient and easy to implement.
Crossover: During the crossover operation, parts of the chromosomes are accidentally exchanged. This exchange results in children inheriting high-quality traits from either parent, which may lead to higher levels of confidence compared to both parents. To calculate the cost weight coefficient, a uniform composition for the intersection is used, which is called a comprehensive recombination intersection. In this approach, the chromosome points are selected as the intersection points. The procedure involves generating a random number between zero and one for each part of the chromosome. If this number is less than a constant value such as α, then the genes located after that point on the chromosomes will be displaced. The intersection rate in this paper is 1 [7].The comprehensive recombination intersection method was chosen due to its ability to explore a larger portion of the solution space, which increases diversity and helps avoid premature convergence. It is particularly effective in problems involving multiple influencing parameters, such as the cost-related coefficients in our model.
Mutation: To ensure diversity in the population after the intersection, a mutation threshold is established to calculate the best coefficients. The goal is to generate a random number between zero and one for every chromosome. If the number is less than a certain limit, a random number is generated for each gene, and the corresponding gene is mutated if the product number is smaller than a constant value β. The default mutation rate is 0.08, as mentioned in [7].
Termination criteria:Once the algorithm completes a certain number of iterations, it offers the optimal solution as an output. In this study, the number of repetitions is set to 100 [7].
Algorithm1: Initialize Population with Cost-Related Chromosomes
Input:
- Population size (P)
- Number of genes per chromosome (n = 3)
- Range of values for each gene:
DevTime∈ [t_min, t_max]
DelTime∈ [d_min, d_max]
Interfaces ∈ [i_min, i_max]
Output:
- Initialized population of chromosomes: Pop[P][3]
Begin
For i = 1 to P do
// Generate one chromosome with 3 genes
Chromosome[i][1] ← Random value in [t_min, t_max] // Development Time
Chromosome[i][2] ← Random value in [d_min, d_max] // Delivery Time
Chromosome[i][3] ← Random value in [i_min, i_max] // Number of Interfaces
// Normalize genes (optional step)
For j = 1 to 3 do
Chromosome[i][j]← Normalize(Chromosome[i][j])
End For
Pop[i] ← Chromosome[i]
End For
Return Pop
End
3.4. Application of proposed approach to a case study
This research conducted a detailed analysis to investigate the way high-risk components affect costs and to determine how accurately the suggested approach estimates costs, especially when high-risk components are involved [1, 4]. The cost function was considered a constraint in the optimization problem of the case study, and this paper aimed to demonstrate the positive role of calculating cost coefficients in achieving the objectives of the problem.
3.5. Case study and dataset
The present research used a case study of financial and accounting software [2] to evaluate the effectiveness of the proposed approach, in selecting the optimal combination of COTS and in-house components for CBSS development. The case study involved a software system consisting of three modules, M1, M2, and M3. We had access to 20 software components in the market, numbered SC1 to SC20, which could be used to create a set of ten components, S1 to S10. Ten components could additionally be developed in-house which were labeled SB1 to SB10. For each software module, one component was needed to be selected from the alternatives available to meet operational needs. For example, S1 could be made up of SC1, SC2
, SC3, SC4, or SB1. Therefore, we had to choose one of these five components to satisfy the operational requirements of S1. SC1, SC2, SC3, and SC4 were COTS components, while SB1 was developed in-house. A more detailed description of the case study and dataset is presented in [1, 2]. In addition, the tables related to the data of this case study are given in the appendices section.
4. Optimization problem
As mentioned earlier, a case study of financial and accounting software [2] was used to assess proposed approach effectiveness in the selection of the optimal component of COTS or in-house components for CBSS development. This case study is based on a case study that considers the goals of the multi-objective optimization model, such as ICD and functionality, as well as constraints like cost, delivery time, reliability, and ICD.
4.1 Objective functions and constraints
When dealing with a software system made of various components, the levels of their individual performance should be assessed. The components can either be bought from vendors or created in-house, and their functional performance can be tailored to meet the unique requirements of the organization or client.
First objective function – Functionality: The overall functional performance of the system depends on the functionality of each module, which is calculated using Equation 11 [1,2]. In essence, functionality is a crucial measure that determines the efficacy of a modular software system.
Second objective function – Intra-modular coupling density (ICD):
The intra coupling density is a measure of how coupling and cohesion of the modules are in a modular software system. Each module in a software system has multiple connections to other modules, and the ICD0s objective function is determined using Equation 12 based on both coupling and cohesion [1,2]. While Cohesion is the number of component interactions in the module, Coupling is the number of interactions between components in separate modules [1].
First constraints – Threshold on ICD: This constraint expresses the minimum threshold H on the value of ICD for each module using Equation 13:
Second constraints – Building decision versus buying decision: Developers can choose from multiple instances of COTS and one in-house example for each component, with a calculation of build and buy decisions included Equation 14.
Third constraints – Budget constraint: One of the most crucial considerations in system design is the cost constraint. It is determined by adding up all the costs associated with various modules of the build-or-buy strategy using Equation 15.
)≤B (15)
Fourth constraints – Delivery time constraint: When referring to a software component, the delivery time indicates the duration required to prepare and make the component available for use in a component-based software system. This includes the time taken for development, integration, and system testing. Commercially available components are represented by dij, while components developed in-house can be expressed as the delivery time of the ith component for the jth module using Equation 16.
component | High-risk Cost weight | ||||||||||||||||||||
8 | 9 | 12 | 13 | 14 | 19 | 21 | 22 | 23 | 24 | 33 | 38 | 41 | 43 | 45 | 46 | 48 | 49 | 50 | 54 | 60 | |
Cost weight | 0.9624 | 0.1768 | 0.122 | 0.948 | 0.2174 | 0.3125 | 0.2476 | 0.5963 | 0.7288 | 0.1606 | 0.5795 | 0.6187 | 0.8869 | 0.5905 | 0.1648 | 0.9055 | 0.9025 | 0.0896 | 0.9614 | 0.8533 | 0.7800 |
Table 4.cost coefficient for the high-risk components calculation by GA
Fifth constraints – Threshold on the reliability constraint: To calculate the likelihood of the ith component developed in-house for the jth module failing, we can use Formula 1. In addition, by applying Equation 17, we can determine the average number of failures for both the ith component and the jth module, which is represented as qij.
4.2. Results of the optimal components selection
The case study identified the components categorized as high-risk and low-risk, which included the following:
High-risk components: 8,9,12,13,14,19, 21, 22, 23, 24, 33, 38,41, 43, 45, 46, 48, 49, 50, 54, 60
Low-risk components: 1, 2, 3, 4, 5, 6, 7, 10, 11, 15, 16, 17, 18
The case study used low-cost and compatible components to identify high-risk components. By using Equation 18, the selection of such components during the optimum component selection process led to a lower ICD, which was owing to their reliability, cohesion, and affordability. The aim of this approach is to find components with low risk and high ICD (low cost). Therefore, the key issue in selecting components with the ICD objective function is to identify low-risk components with high ICD.
The redevelopment process is more time-consuming and expensive because high-risk components need modification to work with the intended software system. The suggested approach to calculate the cost of redevelopment involves the calculation of cost coefficients. Using the genetic algorithm with the settings mentioned in the previous section, the cost coefficients for high-risk components were determined in the case study. Table 4 shows the values of these coefficients.
Cost 
Reliability cohesion ICD (18)
So: Min number of high-risk component selected max ICD (19)
5. The experimental results
To select the best components, there are two main methods: single-objective and multi-objective. Single-objective methods, which often use genetic algorithms or fuzzy methods, focus on changing the objective functions to create a single goal. On the other hand, multi-objective methods, which use the NSGA method, keep the objective functions the same. To ensure the effectiveness of proposed approach in optimal component selection, both multi-objective and single-objective methods were tested in this paper. Despite a shortage of case studies in this research area, this paper managed to compare GA-ICD to two other methods. To compare the effectiveness of the proposed approach with other methods, we implemented our own proposed approach using three methods that other authors used in selecting the optimal component and compared the results of this implementation with the results of others' methods. Also, to create a comparative standard environment, in addition to the proposed approach, we also implemented and implemented normal conditions (other than the approach) with these methods and presented the results in the form of relevant tables.
5.1. Multi-objective optimal component selection by fuzzy logic
To solve the optimal component selection problem as explained in [1,2], the problem was formulated based on the Belman-Zadeh maximization principle. First, the objective functions and constraints were calculated using the proposed approach, for high-risk cost. Next, the values of X1 and X2 were calculated using the two objectives in the problem. Afterward, the Functionality and ICD objective function optimization problem was solved (see the results in Tables 5 and 6). Then, the optimal lower limit (l) and upper limit (u), as well as the worst-case scenarios for each, were determined by evaluating the functionality and ICD while taking into account the constraints of the optimization problem obtained. The number of restrictions considered is based on the information provided in Table 7.
The membership functions for ICD and functionality in the case study are equation as 20 and 21, respectively.
Table 5. Result of solving the optimization problem with the
objective of functionality in the case study
Functionality | ICD | Time | Budget |
5.40 | 0.8809 | 6s | 25 |
Table 6.Result of solving the optimization problem with the objective of ICD in the case study
Functionality | ICD | Time | Budget |
7.82 | 0.4940 | 6s | 24 |
Table7.Optimization solution set of the high-risk approach for the first and second objective function
| X1 | X2 |
ICD | 0.8809 | 0.4940 |
Functionality | 5.40 | 7.82 |
The fuzzy multi-objective optimization model for high-risk components, based on the principle of maximizing introduced by Bellman-Zade and the fuzzy membership functions, defined implementing. The results of this implementation are displayed in Table 8.
5.2. Single-objective optimal component selection by GA approach
To ensure the efficiency of the proposed high-risk component approach for optimal component selection, this paper used an evolutionary and single-objective method to select the optimal component. To transform the probleminto a single objective problem, both objective functions were checked to be in the direction of maximization and parallel. Finally, the first and second goals were defined in the form of Equation 22 by integrating Equation 11 and 12 [7]. To ensure that both objective functions have an equal impact on the final result, the coefficients of each function were set to 0.5 when converting the multi-objective problem to a single-objective one [7]. As a result, Equation22 was redefined as Equation 24 Subject to condition 23.
Thus:
In addition to the proposed risky cost approach, the component selection algorithm (GA) also formulated and solved the simple cost model presented in [1,4]. Table9 presents the results of both approaches in a comparative way.
5.3. Multi-objective optimal component selection by non-dominated sorting genetic algorithm (NSGA-II)
The process of selecting components using NSGA involves the following steps:
Step_1: An initial population of size N was randomly generated based on objective functions and constraints. The population of offspring Qt (t = 0) was generated from Ptusing GA operators such as selection, crossover, and mutation.
Step_2: Pt and Qt populations were combined to create a new population of size 2N. Non-dominant sorting of the population Rt was performed and classified into multiple classes (F1, F2, F3, etc.). Crowding distance was then calculated for a set of individuals in the population. Two fitness functions in the maximum state, the subject of equations 25 and 26, were defined for this problem.
Step_3: The best N individuals were selected according to the forward dominance order and crowding distance to form a new population Pt+1. Individuals from fronts with low mastery rank and high distance in the same front were chosen first.
Step_4: Selection, crossover, and mutation were performed on the population Pt+1 to create a new offspring Qt+1 of size N.
Step 5: If the termination criteria were met, the set of non-dominated solutions was considered as output and the process was stopped; otherwise, step2 would be repeated. The results of this implementation are shown in Table 10.
Table 8.The results of this implementation fuzzy component selection
approach | Functionality | ICD | Time | Budget | Module1 | Module2 | Module3 |
High-risk redevelop cost | 7.75 | 0.85 | 7.4s | 30 | SC5,SC6,SC17 | SC11,SC7,SC4 | SC14,SB7,SB9,SB10 |
simple cost [1] | 6.49 | 0.50 | 6s | 25 | SC5,SC6,SC17 | SC2, SC8, SB5 | SB9,SC14,SC15,SB10 |
Table 9.Optimal selection of components in the approach by the single-objective method of genetic
algorithm
approach | Functionality | ICD | Time | Budget | Module1 | Module2 | Module3 |
High-risk redevelop cost by GA | 7.1 | 0.68 | 6s | 30 | SC5,SC6,SC17 | SC8,SC7,SC4 | SC14,SB7,SB9,SC20 |
simple cost | 6.43 | 0.52 | 6s | 25 | SC4, SC5, SC6 | SC8, SC11, SB6 | SC15,SB8,SB9,SB10 |
Table 10.result of optimal components selection in the propose approach by the NSGA-II
approach | functionality | ICD | Time | Budget | reliability | Module1 |
High-risk redevelop cost | 7.13 | 0.76 | 7.1s | 30 | 0.99 | SC5,SC17,SC2, SC6,SC7,SC11,SC14,SC19,SC15,SC20 |
6. Results Comparison
The technique of Component-based software engineering (CBSE) involves using pre-made software components to develop software systems. These components can either be purchased as COTS or built from scratch by software developers. The use of high-risk components can lead to longer development time and increased costs. Given that cost is a crucial factor in software development, accurate computation is essential. This study used the genetic algorithm to determine the cost factor for redeveloping high-risk components. The results of the case study demonstrated that the genetic algorithm was effective in accurately estimating the cost of software redevelopment. Table 11 compares the proposed approach with other techniques used in the field for software system creation. According to the table, the proposed method selects an optimum component with a shorter execution time than that of others. Table 12 compares the unique features of the proposed method with the features of the other methods.
Table 11.The results of the optimal selection of the component using the multi-objective selection method based on the cost of redevelopment with the GA coefficient. Figure 5 demonstrate results to bar chart.
ref | Type of optimization | objective | constraint | approach | Novelty |
[4] | Multi objective | Fuzzy-ICD, Functionality | Fuzzy-ICD, reliability, Cost, Delivery time | Fuzzy approach | Compute coupling and cohesion in Mayer’s classification by fuzzy method for calculate ICD |
[2] | Multi objective | ICD, Functionality | ICD, reliability, Cost, Delivery time | Fuzzy approach | Fuzzy optimization |
[5] | single objective | Quality | ICD, reliability, Cost, Delivery time | GA approach | Joint objective using GA |
[56] | Multi objective | ICD, Functionality | Cost, Consistency | Fuzzy approach | Weighted objective |
Proposed method | Multi objective | ICD, Functionality | ICD, reliability, high-risk Cost, Delivery time | GA approach | Joint constraint (cost) using GA weight |
Table 12. Comparison between the presented method and other previous methods in the field of optimal component selection and their innovation aspect
approach | Functionality | ICD | Time | Budget | Module1 | Module2 | Module3 |
High-risk redevelop cost + NSGA-IIselection method | 7.75 | 0.85 | 7.4s | 30 | SC5,SC6,SC17 | SC11,SC7,SC4 | SC14,SB7,SB9,SB10 |
simple cost + NSGA-II selection method | 6.49 | 0.50 | 6s | 25 | SC5,SC6,SC17 | SC2, SC8, SB5 | SB9,SC14,SC15,SB10 |
High-risk redevelop cost + fuzzy component selection | 7.13 | 0.76 | 7.1s | 30 | SC5,SC17,SC6 | SC2, SC7, SC11 | SC14,SC19,SC15,SC20 |
simple cost + fuzzy component selection [1] | 6.61 | 0.82 | 6s | 24 | SC5,SC17,SB6 | SC1, SC7, SC11 | SC14,SC15,SC19,SC20 |
High-risk redevelop cost + GA component selection | 7.1 | 0.68 | 6s | 30 | SC5,SC6,SC17 | SC8,SC7,SC4 | SC14,SB7,SB9,SC20 |
simple cost + GA component selection | 6.43 | 0.52 | 6s | 25 | SC4, SC5, SC6 | SC8, SC11, SB6 | SC15,SB8,SB9,SB10 |
Fig. 5. The bar chart for results of optimal component selection by proposes approach and other method.
7. Conclusion and future work
When optimizing a component-based problem, it is important to consider various objective functions such as cost, reliability, and delivery time. This is because different types of components exist in optimization-related problems. These include COTS components such as ready, complete, incomplete, and new components. The aim of this study was to improve the optimization of software systems while reducing the developer's involvement in the calculation process. By improving cost calculations within the constraints, this study succeeded in reducing the selection of high-risk components with higher costs. As a result, the final value of performance significantly improved. The Strengths of proposed approach is accurate cost estimation for high-risk components, improved ICD and functionality, integration of real-world constraints in a multi-objective framework. The Weaknesses of proposed approach is Performance may depend on proper parameter tuning in GA; the method has been tested on a single case study and needs broader validation.
Future studies could conduct a more thorough analysis of high-risk components, along with evaluating the cost of other effective parameters, such as time and efficiency. They could also explore different types of evolutionary methods to optimize objective functions and constraints of the problem.
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