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\title{Bayesian Regularization Based Neural Network Tool for Software Effort Estimation}
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\begin{document}

             \author[1]{Harwinder  kaur}

             \author[2]{Dalwinder Singh  Salaria}

             \affil[1]{  Lovely Professional University}

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\date{\small \em Received: 14 April 2013 Accepted: 5 May 2013 Published: 15 May 2013}

\maketitle


\begin{abstract}
        


Rapid growth of software industry leads to need of new technologies. Software effort estimation is one of the areas that need more concentration. Exact estimation is always a challenging task. Effort Estimation techniques are broadly classified into algorithmic and non-algorithmic techniques. An algorithmic model provides a mathematical equation for estimation which is based upon the analysis of data gathered from previously developed projects and Non-algorithmic techniques are based on new approaches, such as Soft Computing Techniques. Effective handling of cost is a basic need for any Software Organization. The main tasks for Software development estimation are determining the effort, cost and schedule of developing the project under consideration. Underestimation of project done knowingly just to win contract results into loses and also the poor quality project. So, accurate cost estimation leads to effective control of time and budget during software development. This paper presents the performance analysis of different training algorithms of neural network in effort estimation. For sake of ease, we have developed a tool in MATLAB and at last proved that Bayesian Regularization [20] gives more accurate results than other training algorithms.

\end{abstract}


\keywords{effort estimation, levenberg-marquardt (trainlm), back propagation, bayesian regularization (trainbr), gradient descent (traingdx), MATLAB.}

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\let\tabcellsep& 	 	 		 \par
effort estimation, levenberg-marquardt (trainlm), back propagation, bayesian regularization (trainbr), gradient descent (traingdx), MATLAB. 
\section[{I. Introduction}]{I. Introduction}\par
oftware effort estimate is one of the noticeable \& mind catching field. But since it was started, it is challenging factor for software industry and Academia to realize the exact estimation of software development. In today's fast changing world, success in managing projects is a critical factor for the success of the entire organization. Estimation that either overestimated or underestimated both is very critical. In case of Overestimating time and effort (or budget), due to a presumed lack of resources or because the projected completion is too late, can convince management not to approve projects that may otherwise contribute to the organization. On the other hand, underestimation may result in approval of projects that will fail to deliver the expected product within the time and budget available. There are many factors that influence the Software estimation, some of them are: uncertainty, level of detail of preparing the project plan, managerial factors, lack of past data, pressure to lower estimation and estimator experience \hyperref[b0]{[1]}. In spite of the critical role of accuracy, examples of incorrect estimation abound, especially in IT projects, resulting in enormous waste of time and money. Some techniques which were used in the past are not in use during present time, like SLIM \hyperref[b13]{[14]}, checkpoint \hyperref[b1]{[2]}, Seer \hyperref[b1]{[2]}. In all the way of work time, many of new advance roads have been suggested for effort estimation like Genetic programming \hyperref[b10]{[11]}, Fuzzy logic \hyperref[b9]{[10]}, Neural Network \hyperref[b14]{[15]}, data mining \hyperref[b8]{[9]}, etc.\par
One cannot state that one model give better accuracy above all. Each and every give different level of accuracy in different Environment. But in recent days, Neural Network gains main attention due to many flavor of algorithm available for it. The main focus of this paper is to investigate the accuracy of estimation using neural network approach based on three different training algorithms: Levenberg-Marquardt (trainlm) [20], Back propagation [20], Bayesian Regularization (trainbr)  {\ref [20]} and this has been done with the help of tool generated by us in MATLAB.\par
This paper comprises as follow: section II describes the some former effort estimation models and review of related work to Neural Network, section III includes introduction of Neural Network and training algorithms used for this paper, in section IV problem is stated, section V describes methodology used, section VI includes experimental results and comparisons. In last conclusion and future scope is given. 
\section[{II.}]{II.} 
\section[{Review of Literature}]{Review of Literature}\par
The period of Effort Estimation was started from the expert judgments, which is based on the experiences of experts. But it is only proceed as pillar when current project \& pertinent Past projects are similar. Choices of effort estimation techniques footstep from COCOMO \hyperref[b13]{[14]} to AI approaches \hyperref[b1]{[2]}. In 1970, Larry Putnam developed the method SLIM \hyperref[b13]{[14]}, based on the Rayleigh function and the influence used to Rayleigh curve was Manpower Buildup Index (MBI and Productivity Factor (PF) \hyperref[b1]{[2]}. Linear programming was key work to drive effort estimation in SLIM \hyperref[b13]{[14]} and depend upon the source line of code.\par
In of an easy going \& understandable model, could call the effort \& time period of project. Due to some problems and some misses found in COCOMO, later on Barry Bohem developed the advance road of this model i.e. COCOMO 2.0 \hyperref[b6]{[7]}. As growth of software industry rising tremendously and previous version was not up to need.\par
After that, Howard Rubin proposed the ESTIMAC model to estimate effort at conception stage \hyperref[b3]{[4]}. Equations used in this model are not available, because it was a proprietary model. ESTIMAC is high level model but doesn't provide accurate solution \hyperref[b2]{[3]}. Six critical estimation dimensions identified by Rubin for this model are: effort hour, staff size, cost, hardware resource requirement, risk, portfolio impact \hyperref[b1]{[2]}. But these methods (COCOMO, SLIM, ESTIMAC) are based on Line of code (LOC). The main problems in Line of Code methods are: lack of universally accepted definition for exactly what line code really is? Other side line of code is language dependence. So, in 1979 IBM, developer Allan Albrecht developed measurement method called Function point \hyperref[b2]{[3]} in order to reduce the issues related with LOC methods. Function point defines the complexity of software system in terms of functions that system delivers to user. It comprise linear combination of five basic software components (input, output, master files, interfaces, inquiries) consider to be low, average, high \hyperref[b2]{[3]}. In 1990, GC Low and DR. Jeffery also concluded in their paper that Function point method is more consistent then the line of code measure \hyperref[b5]{[6]}. But on the other side, function point method is unable to deal with Uncertain, imprecise and incomplete data. Many researcher's use different Neural Network with different datasets in order to generate more accurate result for effort estimation. The main advantage of neural network is its ability to handle non-linear data and confidence in decision making. In 1995, Krishna moorthy Srinivasan and Douglas Fisher applied the machine learning approach for Software Effort Estimation \hyperref[b15]{[16]}. They applied the Back propagation algorithm on COCOMO dataset, along with configuration of 33 neuron of input layer, 10 neurons for hidden layer and 1 output neuron. Actually they had done three experiments on different datasets. They concluded that Back propagation competitive again traditional approaches but quite sensitive.\par
In one paper written by Ali Idri, et al. \hyperref[b16]{[17]} in 2002, in which he uses COCOMO-81 dataset and three layered back-propagation ANN, concluded that accuracy provide by back propagation is acceptable.\par
In 2005, N Tadayon compares the three models COCOMO II, Neural Network and expert judgments to state the strength of different estimation techniques \hyperref[b12]{[13]}. In 2006, according to Barcelos Tronto et.al Neural Network approach provides better tune result than the linear regression \hyperref[b17]{[18]}. In his methodology, he used the Back propagation as training algorithm on COCOMO dataset.\par
In 2010, Iman Attarzadeh, proposed new model of COCOMO II using neural network, and comcluded that neural network approach gives best accuracy than COCOMO II.\par
Mrinal Kantri, et al. \hyperref[b18]{[19]} implemented a backpropagation ANN of 3-3-1 architecture on Lopez Martin dataset consist of 41 projects. There are many other techniques such as ordinary least square (OLS) \hyperref[b1]{[2]}, Case based reasoning \hyperref[b11]{[12]}, Date mining \hyperref[b8]{[9]}, Bayesian COCOMO II \hyperref[b1]{[2]}, Genetic Programming \hyperref[b4]{[5]} etc. also used for the effort estimation but not discussed in this paper. 
\section[{III. Introduction to Neural Network and Training Algorithms}]{III. Introduction to Neural Network and Training Algorithms}\par
A Neural Network is massively distributed processor made up of simple processing elements called neuron, which model some functionality like human brain \hyperref[b14]{[15]}. The use of Neural Network offers the some useful properties and capabilities: -Nonlinearity, Adaptivity, Evidential Response, Confidence in decision made. A primary advantage of learning systems is that they are nonparametric; predictive models can be tailored to, the data at a particular site \hyperref[b7]{[8]}. One of the problems that occur during above neural network training algorithms is over fitting. Due to this, error in early stage is very small, but, when new data is presented to the network the error is large. The solution to this problem is Bayesian regularization (trainbr)  {\ref [20]}. trainbr updates the weight and bias values according to Levenberg-Marquardt [20] optimization. It minimizes a grouping of squared errors and weights, and generates a network that generalizes well. The process is called Bayesian regularization. It is suitable method for estimation when large number of inputs is used for best output. Till now, Levenberg-Marquardt and Back-propagation algorithm used by many researchers for training phase. 
\section[{IV. Problem Statement}]{IV. Problem Statement}\par
The main aim of any software development organizations is to finish the project within acceptable or customary schedule and budget. Budget is mainly driven by labor cost and time and together they form a measure called effort. From quality point of view estimating effort is one of the major important factors. Because estimation either it be over estimate or under estimate, produces worst results. In case of over estimation of time and effort project completion is too late due to lack of resources, which refuses the management to approve that favored project. On the other hand, under estimation may result in approval of projects that will fail to deliver the expected product within the time and budget available \hyperref[b0]{[1]}. So, there is a need of accurate estimation effort technique at early stages of software development. In this research, the main aim is to improve software effort estimation by using different training algorithms of Neural network.\par
The main reason for using such a learning system for this problem is to keep the estimation process up-to-date by incorporating up-to-date project data. At last Comparison is drawn between training algorithms used in this research to state that Bayesian Regularization gives much accurate estimation. One algorithmic approach, COCOMO is also compared with all three algorithms.  For the sake of ease, tool is generated with the help of MATLAB. This has been shown in   
\section[{V. Proposed Methodology}]{V. Proposed Methodology} 
\section[{D}]{D}\par
For our work, we use feed-forward network with three different training algorithms: LM, BPA, BR. The Neural Network is implemented using 12 neurons for input layer, 12 for hidden layer and 1 for output layer. f) Performance Criteria Mean Magnitude Relative Error: MMRE is frequently used to evaluate the performance of any estimation technique. It seems obvious that the purpose of MMRE is to assist us to select the best estimation approach. It measures the percentage of the absolute values of the relative errors, averaged over the N items in the "Test" set and can be written as \hyperref[b17]{[18]}: MMRE = \{actual effort\} -\{estimated effort\}|\}\textbackslash  \{actual effort\} 
\section[{VI. Experimental Results and Comparison}]{VI. Experimental Results and Comparison}\par
Neural Network trained by three different training algorithms, with same dataset i.e. NASA93.    
\section[{Conclusion}]{Conclusion}\par
Effort Estimation is one of the crucial tasks in software project management. This simulation with NASA93 dataset has been carried out using tool created with the help of MATLAB. Neural Network is trained using "trainlm", "traingdx" and "trainbr" algorithm. The result from our simulation shows that Bayesian  
\section[{Year}]{Year}\par
Regularization gives the best performance, among the other training algorithms. We have experimented with 15 attributes of the COCOMO and further investigation can be done with other attributes and also concentration needed for process maturity.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
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\noindent\textbf{III}\includegraphics[]{image-7.png}
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\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{I} \par 
\begin{longtable}{P{0.25803571428571426\textwidth}P{0.07083333333333333\textwidth}P{0.14166666666666666\textwidth}P{0.048065476190476186\textwidth}P{0.09107142857142857\textwidth}P{0.13154761904761905\textwidth}P{0.10877976190476189\textwidth}}
Author's Name\tabcellsep Year\tabcellsep Dataset\tabcellsep Project\tabcellsep Training Algorithm\tabcellsep ANN Layers\tabcellsep Conference/ Journal\\
Krishnamoorthy et.al\tabcellsep 1995\tabcellsep COCOMO\tabcellsep 63\tabcellsep BPA\tabcellsep 33-10-1\tabcellsep IEEE\\
Ali Idri, et al.\tabcellsep 2002\tabcellsep COCOMO\tabcellsep 63\tabcellsep BPA\tabcellsep 13-13-1\tabcellsep IEEE\\
N Tadayon\tabcellsep 2005\tabcellsep -\tabcellsep -\tabcellsep BPA\tabcellsep -\tabcellsep IEEE\\
Barcelos Tronto et.al\tabcellsep 2006\tabcellsep COCOMO\tabcellsep 68\tabcellsep BPA\tabcellsep 1-9-4-1\tabcellsep IEEE\\
Attarzadeh\tabcellsep 2010\tabcellsep COCOMO, Ar tifical\tabcellsep 100\tabcellsep BPA\tabcellsep 24 input neuron\tabcellsep IEEE\\
Mrinal Kantri\tabcellsep 2011\tabcellsep Lopez martin\tabcellsep 41\tabcellsep BPA\tabcellsep 3-3-1\tabcellsep IEEE\end{longtable} \par
 
\caption{\label{tab_1}Table I :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.10119047619047618\textwidth}P{0.18853383458646614\textwidth}P{0.5283208020050125\textwidth}P{0.022368421052631576\textwidth}P{0.0021303258145363405\textwidth}P{0.007456140350877193\textwidth}}
\tabcellsep \multicolumn{3}{l}{Table II : Cost-drivers of COCOMO model}\tabcellsep \tabcellsep \\
Attribute\tabcellsep Type\tabcellsep \tabcellsep Description\tabcellsep \tabcellsep \\
RELY\tabcellsep Product\tabcellsep \multicolumn{3}{l}{Required system reliability}\tabcellsep \\
CPLX\tabcellsep Product\tabcellsep \multicolumn{4}{l}{Complexity of system modules}\\
DOCU\tabcellsep Product\tabcellsep \multicolumn{4}{l}{Extent of documentation required}\\
DATA\tabcellsep Product\tabcellsep \multicolumn{2}{l}{Size of database used}\tabcellsep \tabcellsep \\
RUSE\tabcellsep Product\tabcellsep \multicolumn{4}{l}{Required percentage of reusable}\\
\tabcellsep \tabcellsep \multicolumn{2}{l}{components}\tabcellsep \tabcellsep \\
TIME\tabcellsep Computer\tabcellsep \multicolumn{3}{l}{Execution time constraint}\tabcellsep \\
PVOL\tabcellsep Computer\tabcellsep \multicolumn{4}{l}{Volatility of development platform}\\
STOR\tabcellsep Computer\tabcellsep \multicolumn{2}{l}{Memory constraints}\tabcellsep \tabcellsep \\
ACAP\tabcellsep Personnel\tabcellsep \multicolumn{3}{l}{Capability of project analysts}\tabcellsep \\
PCON\tabcellsep Personnel\tabcellsep \multicolumn{2}{l}{Personnel continuity}\tabcellsep \tabcellsep \\
PCAP\tabcellsep Personnel\tabcellsep \multicolumn{2}{l}{Programmer capability}\tabcellsep \tabcellsep \\
PEXP\tabcellsep Personnel\tabcellsep \multicolumn{4}{l}{Programmer experience in project}\\
\tabcellsep \tabcellsep domain\tabcellsep \tabcellsep \tabcellsep \\
AEXP\tabcellsep Personnel\tabcellsep Analyst\tabcellsep experience\tabcellsep in\tabcellsep project\\
\tabcellsep \tabcellsep domain\tabcellsep \tabcellsep \tabcellsep \\
LTEX\tabcellsep Personnel\tabcellsep \multicolumn{4}{l}{Language and tool experience}\\
TOOL\tabcellsep Project\tabcellsep \multicolumn{2}{l}{Use of software tools}\tabcellsep \tabcellsep \\
SCED\tabcellsep Project\tabcellsep \multicolumn{4}{l}{Development schedule compression}\\
SITE\tabcellsep Project\tabcellsep \multicolumn{4}{l}{Extent of multisite working and}\\
\tabcellsep \tabcellsep \multicolumn{4}{l}{quality of inter-site communications}\\
d) Tool Generation\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{III} \par 
\begin{longtable}{P{0.05750528541226216\textwidth}P{0.10063424947145877\textwidth}P{0.19947145877378433\textwidth}P{0.1599365750528541\textwidth}P{0.16712473572938688\textwidth}P{0.1653276955602537\textwidth}}
\tabcellsep \tabcellsep \multicolumn{2}{l}{and COCOMO model}\tabcellsep \tabcellsep \\
Row No.\tabcellsep Expected\tabcellsep COCOMO\tabcellsep LM\tabcellsep BPA\tabcellsep BR\\
15\tabcellsep 48\tabcellsep 85.9557\tabcellsep 53.7929\tabcellsep 1737.61\tabcellsep 61.9294\\
40\tabcellsep 114\tabcellsep 66.9477\tabcellsep 186.747\tabcellsep 1702.08\tabcellsep 121.206\\
92\tabcellsep 240\tabcellsep 85.9557\tabcellsep 117.681\tabcellsep 1694.9\tabcellsep 85.847\\
74\tabcellsep 4178.2\tabcellsep 1649.24\tabcellsep 1730.38\tabcellsep 1843.92\tabcellsep 4058.46\\
91\tabcellsep 1772.5\tabcellsep 539.26\tabcellsep 1400.97\tabcellsep 1829.47\tabcellsep 2902.12\\
94\tabcellsep 1924.5\tabcellsep 393.61\tabcellsep 2524.9\tabcellsep 1830.02\tabcellsep 1201.62\\
5\tabcellsep 25.2\tabcellsep 38.2213\tabcellsep 260.445\tabcellsep 1731.69\tabcellsep 83.0016\\
80\tabcellsep 703\tabcellsep 904.279\tabcellsep 367.178\tabcellsep 1836.86\tabcellsep 562.929\\
59\tabcellsep 4560\tabcellsep 6718.84\tabcellsep 1347.35\tabcellsep 1945.73\tabcellsep 4471.23\\
64\tabcellsep 150\tabcellsep 115.445\tabcellsep 270.15\tabcellsep 1048.19\tabcellsep 61.3017\\
71\tabcellsep 72\tabcellsep 155.732\tabcellsep 85.29\tabcellsep 1759.78\tabcellsep 106.606\\
63\tabcellsep 160\tabcellsep 270.499\tabcellsep 294.428\tabcellsep 1056.21\tabcellsep 61.7749\\
38\tabcellsep 444\tabcellsep 463.311\tabcellsep 150.555\tabcellsep 1706.99\tabcellsep 338.233\end{longtable} \par
 
\caption{\label{tab_3}Table III :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{IV} \par 
\begin{longtable}{P{0.35172413793103446\textwidth}P{0.14655172413793105\textwidth}P{0.08793103448275862\textwidth}P{0.17586206896551723\textwidth}P{0.08793103448275862\textwidth}}
Performance Criteria\tabcellsep COCOMO\tabcellsep LM\tabcellsep BPA\tabcellsep BR\\
MMRE\tabcellsep 0.52\tabcellsep 1.23\tabcellsep 12.18\tabcellsep 0.48\\
\tabcellsep \tabcellsep \tabcellsep VII.\tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table IV :}\end{figure}
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