Optimizing Basic COCOMO Model Using Simplified Genetic Algorithm

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Procedia Computer Science 89 ( 2016 ) 492 – 498

Peer-review under responsibility of organizing committee of the Organizing Committee of IMCIP-2016 doi: 10.1016/j.procs.2016.06.107

ScienceDirect

Twelfth International Multi-Conference on Information Processing-2016 (IMCIP-2016)

Optimizing Basic COCOMO Model using Simpliﬁed Genetic

Algorithm

Rohit Kumar Sachan

∗

, Ayush Nigam, Avinash Singh, Sharad Singh, Manjeet Choudhary,

Avinash Tiwari and Dharmender Singh Kushwaha

Motilal Nehru National Institute of Technology Allahabad, Allahabad 211 004, India

Abstract

The estimation of software effort is an essential and crucial activity for the software development life cycle. In recent years, many researchers and software industries have given significant attention on the estimation of software effort. In industry, effort is used for planning, budgeting and development time calculation. Therefore a realistic effort estimation is required. Many researchers have proposed various models for software effort estimation, such as statistical models, algorithmic models, machine learning based models and nature inspired models in the past. In this research paper, a simplified genetic algorithm based model is proposed. A simplified genetic algorithm is used for optimizing the parameters of the basic COCOMO model. The proposed approach is applied on NASA software project dataset. Experimental results show better realistic estimation over the basic COCOMO.

Peer-review under responsibility of organizing committee of the Twelfth International Multi-Conference on Information Processing-2016 (IMCIP-2016).

Keywords: COCOMO Model; Effort Estimation; Genetic Algorithm; Nature-inspired Algorithm; Optimization.

1. Introduction

Software effort estimation (SEE) has been an essential and crucial activity for the software development life cycle (SDLC). Effort estimation is used for planning, budgeting and monitoring the activities of software development. It is also used for on time and within budget delivery of software. It is a method for computing the most realistic and reliable value of required effort for developing or developed project. It is calculated in term of person-month. This effort is used for project plans, project budgets, investment analysis, resource allocation schemes, pricing process, etc. According to Standish Group Report1, in UK during the period of 2002–2003, out of 13522 projects only 33% projects were completed within time and budget, 82% projects were late, 43% projects were overrun their ﬁnancial plan and 20% projects were cancelled. According to another report2, 70–80% software projects were above their estimated plan and that average overrun is about 30–40%. Hence, there is a requirement of a more realistic and reliable software effort estimation model.

Several effort estimation methods have been proposed and improved by many researchers in the past. These methods are categorised into Expert judgement, Algorithmic method and Analogy based method. Expert judgment methods are

∗Corresponding author. Tel.: +91-9999434710; Fax: +91-532-254-5341.

E-mail address: [email protected]

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Table 1. Basic-COCOMO Models.

Model Name Project Size Effort Organic Model Less than 50 KLOC E= 2.4 (KLOC)1.05

Semi-Detached Model 50–300 KLOC E= 3.0 (KLOC)1.12

Embedded Model Over 300 KLOC E_{= 3.6 (KLOC)}1.20

Work Breakdown Structure (WBS) method and Delphi technique3_{. Algorithmic methods are Constrictive Cost Model}

(COCOMO)4, Function Point (FP)5method, Software Life Cycle Management (SLIM)6and Software Evaluation and Estimation of Resources-Software Estimating Model (SEER-SEM)7. The analogy based method is applied at a very early phase of SDLC. Early stage effort estimation methods are Improved Requirement Based Complexity (IRBC)8, Requirement Based Software Development Effort Estimation (RBDEE)9, 10and many others. Some researchers used Cognitive Information Complexity Measure (CICM)11, 12for effort estimation. Currently, many issues have arisen regarding the applicability of these methods to solve the software effort estimation. Heuristic techniques are used to overcome the limitation of these methods and improve the applicability.

Various heuristic optimization methods are used in optimization problems. These methods can be used in the software effort estimation also. These methods are Genetic algorithm13, Genetic programming14, Differential Evolution15_{, Particle Swarm Optimization}16_{and many others.}

This research paper provides a brief study of the Genetic Algorithms (GA) as an optimization algorithm. It is used for optimizing the parameter of the COCOMO model so that a more realistic effort can be estimated. The performance evaluation of the proposed method is analysed with the NASA software project dataset. The remaining research paper is organized as follows. Section 2 contains a concise description of background, proposed simpliﬁed genetic algorithm is explained in Section 3, Section 4 gives various evaluation criteria and dataset. Experimental results have been explained in Section 5. Finally, Section 6 concludes the proposed method with directions for future work.

2. Background

The concise description of the COCOMO model and Genetic algorithm is discussed in this section.

2.1 The Constructive Cost Model (COCOMO)

The Constructive Cost Model is a well documented and widely accepted algorithmic model for effort estimation. It was developed by Barry W. Boehm in 19814. Constructive Cost Model has three variants. These are basic, intermediate and detailed. The main parameter for the SEE is the size of the project. The size is represented in terms of lines of code (LOC) or a thousand-lines of code (KLOC). This model was built based on a historical dataset of 63 projects. The model deﬁnes mathematical equations for estimating effort, development time and the maintenance effort. The mathematical equation of a basic COCOMO model is deﬁned in Equation 1

E= A × (KLOC)B (1)

where KLOC is the size of the code (kilo-lines of code), E is the software effort computed in person-month and A, B are the COCOMO model parameters.

The value of A and B depend on the model of a software project. COCOMO model has three types, depending upon project size. These models are Organic, Semi-detached and Embedded model17, 18. Table 1 shows the basic COCOMO models.

The main issue with the COCOMO model is that it does not provide realistic effort in the current development environment. This limitation of the COCOMO model was overcome by exploration of the non-algorithmic technique like genetic algorithm or any other nature-inspired algorithms. Software effort estimation based on existing parameters

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does not always give precise result; due to that, we require the tuning of the parameters to get more accurate results. This paper optimizes the value of parameters A and B.

2.2 Genetic Algorithm (GA)

The genetic algorithm is an evolutionary search algorithm. It belongs to the ﬁeld of nature-inspired algorithms. In 1970s, John Holland and his collaborators proposed genetic algorithm at University of Michigan19. It is a global optimization method which is inspired from the abstraction of Darwinian evolution and natural selection of biological systems. GA20, 21uses mathematical operators such as selection of ﬁttest, crossover and mutation. The wide range of optimization problems have been successfully solved using genetic algorithms.

3. Proposed Method

In this research paper, the parameters of the basic COCOMO model are optimized using the simpliﬁed genetic algorithm. This shall ensure that complexity of the proposed algorithm remains low. We use the crossover and selection operator for calculating new value of parameters A and B.

The steps of the proposed simpliﬁed genetic algorithm are: 1. Randomly generate an initial population of A and B.

2. Calculate the ﬁtness of each chromosome using ﬁtness function. 3. Select parent chromosome from population.

4. Create new chromosomes by applying crossover for A after 8thbit to 17thbit and for B after 7thbit till 15thbit. 5. Compute the ﬁtness of new chromosomes.

6. Select the next population by selecting the best chromosomes.

7. Goto step 3, until max-generation is not reached else stop and return the best chromosome.

4. Evaluation Criteria and Data Set

We propose to use the absolute difference between effort and estimated effort (Manhattan distance (MD)) as the ﬁtness function for the proposed simpliﬁed genetic algorithm. The Manhattan distance is calculated by Equation 2

M D=

_n

i=1

|Efforti− Estimated Efforti|

(2) The other evaluation criteria may be used as ﬁtness function for evaluating the performance of the proposed model. They are22:

Mean Magnitude of Relative Error (MMRE): MMRE= 1

n

i=1

|Efforti− Estimated Efforti|

Efforti

(3) Variance-Accounted-For (VAF):

VAF=

1−var(Effort − Estimated Effort) var(Effort)

× 100% (4)

Root Mean Square (RMS):

RMS= 1 n n i=1

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Table 2. The NASA Software Project Dataset.

Project No. KLOC Methodology (ME) Measured Effort 1 90.2000 30.0000 115.8000 2 46.2000 20.0000 96.0000 3 46.5000 19.0000 79.0000 4 54.5000 20.0000 90.8000 5 31.1000 35.0000 39.6000 6 67.5000 29.0000 98.4000 7 12.8000 36.0000 18.9000 8 10.5000 34.0000 10.3000 9 21.5000 31.0000 28.5000 10 3.1000 26.0000 7.0000 11 4.2000 19.0000 9.0000 12 7.8000 31.0000 7.3000 13 2.1000 28.0000 5.0000 14 5.000 29.0000 8.4000 15 78.6000 35.0000 98.7000 16 9.7000 27.0000 15.6000 17 12.5000 27.0000 23.9000 18 100.8000 34.0000 138.3000

Table 3. Simpliﬁed GA Parameter Setting. Operator Type

Selection Mechanism Elitism Selection

Type of Crossover Two Point Binary Crossover Type of Mutation NA

Population Size 10 Maximum Generation 100 Domain of search for A 0:10 Domain of search for B 0.3:2

Euclidian Distance (ED):

ED= n i=1

(Efforti− Estimated Efforti)2 (6)

Performance evaluation of the proposed work is tested on well-known and public NASA project dataset. The NASA dataset23contains the size of project, Methodology (ME) and Measured effort of 18 software projects. These values are shown in Table 2.

5. Experimental Results

The proposed experiment applies simplified GA for optimizing the value of A and B of the basic COCOMO model given in Equation 1. This model allows us to estimate effort for the software development of the 18 projects of NASA dataset. The parameters of simplified GA are set as Table 3. The fitness function is shown in Equation 2. The computed parameters can significantly simplify the estimation of the software effort for all projects.

The computed values of effort are presented in Table 4. The model with the optimal set of parameter of A and B is presented in Equation 7. Figure 1 shows the measured effort comparison between NASA dataset, basic COMOMO and proposed simpliﬁed genetic algorithm. The result shows that effort estimated by the proposed simpliﬁed GA gives

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Table 4. Computed Effort Value by Basic COCOMO and Simpliﬁed GA. Basic COCOMO Simpliﬁed Project No. KLOC NASA Effort Effort GA Effort 1 90.2000 115.8000 271.1308 114.8510 2 46.2000 96.0000 134.3028 63.0152 3 46.5000 79.0000 135.2187 63.3821 4 54.5000 90.8000 159.7450 73.0839 5 31.1000 39.6000 88.6358 44.1810 6 67.5000 98.4000 199.9770 88.5476 7 1 2.8000 18.9000 34.8964 19.9217 8 10.5000 10.3000 28.3439 16.6782 9 21.5000 28.5000 60.1549 31.7247 10 3.1000 7.0000 7.8730 5.5821 11 4.2000 9.0000 10.8298 7.3303 12 7.8000 7.3000 20.7448 12.7740 13 2.1000 5.0000 5.2304 3.9359 14 5.000 8.4000 13.0055 8.5715 15 78.6000 98.7000 234.6414 101.5074 16 9.7000 15.6000 26.0808 15.5325 17 12.5000 23.9000 34.0382 19.5022 18 100.8000 138.3000 304.6805 126.8900

Fig. 1. Effort Graph for NASA, COCOMO and Proposed Simpliﬁed GA.

Table 5. Computed Manhattan Distance (MD).

Model Input Model Output Manhattan Distance (MD) Basic COCOMO Effort 48.8360 Proposed Simpliﬁed GA Effort 6.7125

better results as compared to actual NASA effort. The performance comparison of basic COCOMO and proposed simpliﬁed GA are shown in Table 5 and Fig. 2

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Fig. 2. Comparison of Manhattan Distance by COCOMO and Simpliﬁed GA.

6. Conclusions and Future Work

This paper proposes a software effort estimation (SEE) model using a simplified form of genetic algorithm. The simplified GA is used for optimizing the parameters of the basic COCOMO model. This is computationally cheaper also. The performance analysis of the proposed model is analysed on the well-known NASA dataset. We have used the simplified genetic algorithm for developing a model for the software effort calculation. The Manhattan distance of proposed simplified GA is 6.7125 which is better than basic COCOMO. COCOMO with simplified GA tuned parameters gives an improved estimation compared to basic COCOMO. In the future, we will extend this work to optimize the effort estimation model provided by Alaa F. Sheta13_{and intermediate COCOMO.}

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