Optimizing SVR using Local Best PSO for Software Effort Estimation

. In the software industry world, it’s known to fulfill the tremendous demand. Therefore, estimating effort is needed to optimize the accuracy of the results, because it has the weakness in the personal analysis of experts who tend to be less objective. SVR is one of clever algorithm as machine learning methods that can be used. There are two problems when applying it; select features and find optimal parameter value. This paper proposed local best PSO-SVR to solve the problem. The result of experiment showed that the proposed model outperforms PSO-SVR and T-SVR in accuracy.


Introduction
Software effort estimation needs techniques to make the approximate in an attempt to improve accurately all requirements.Some projects are proved to have problems at the time of completion and costs swell, i.e. around 43% till 59% of the incident (information from Standish Group).It is heavily influenced by the strategies and considerations used in the initial process [1].The issue is highly developed and must be resolved, because so far mostly relied on the help of an expert assessment, but the results will be very biased, because it looks less objective, which will have an impact on the value of the results of the final evaluation of the estimate is not good [2].
Clever algorithm as machine learning has many help in overcoming the problem of engineering [3].The advantage of machine learning is able to learn from previous data patterns adaptively and provide models and the results are consistent and stable [4].For example, SVM which well known as a robust machine learning [5].A form of development SVM is SVR that is designed specifically for producing optimal performance machine prediction/ forecasting.The machine's main problem is the difficulty of determining the optimal parameter values and the difficulty of determining the selection of optimal features as well [6], [7], [8].Previously, Braga has tried using GA and Hu technique with PSO to obtain the optimal SVR results [9], p-ISSN: 2540-9433; e-ISSN: 2540-9824 [10].The result, PSOs provide the excellent performance and effective in finding the most optimal solutions, rather than GA and others [11].PSO improvements have been made to deal with premature convergence (local optimum), although the time it takes a little longer, but can still be tolerated and comparable to the best optimization results obtained, the name of the method is the Local best PSO utilize ring topology that illustrated in Fig. 1 [12], [13].Thus, based on that reason, ring topology-based local best PSO-SVR is proposed in our paper.and output (scalar value as target).Other forms of alternative for bias to calculation f(x) is can be build solution like bias as follows [14]: (1) xi is support vector where |αi -αi * | isn't zero.Equation f(x) can be write as follows: (2) Lambda (λ) is scalar constant, with it's an augmented factor defined as follows [15]: (3)

2.1.1
Sequential Algorithm for SVR Vijayakumar has made tactical steps through the process of iteration to obtain the solution of optimization problems of any nature by way of a trade-off on the values of the weights xi, or called αi to make the results of the regression becomes closer to actual value.The step by step as follows: p-ISSN: 2540-9433; e-ISSN: 2540-9824 for i,j = 1,…,n 2. For each point, do looping, i=1 to n:

Particle Swarm Optimization
This algorithm defined solution as each particle for any problem in dimension space j.
Then, it's extended by inertia weight to improves performance [16], [17].Where xid, vid, yid is position, velocity, and personal best position of particle i, dimension d, and Ŷi is best position found in the neighborhood Ni.Each particle's neighborhood at ring topology consists of itself and its immediate two neighbours using euclidean distance.
(11) ( 12) is velocity and position of particle i in dimension j=1,...n at time t, c1 and c2 are cognitive and social components, r1j and r2j are rand[0,1].yi and ŷ is obtained by The inertia weight w, is follows equation

Local best PSO SVR Model 2.3.1 Particle Representation
In this paper, SVR nonlinear is defined by the parameter C , ε , λ, σ , cLR.The particle is consisted of six parts: C, ε, λ, σ, cLR (continuous-valued) and features mask (discrete-valued).Table 1 shows the representation of particle i with dimension nf+5 where nf is the number of features.

Objective Function
Objective function is used to measure how optimal the generated solution.There are two types of objective function: fitness and cost.The greater fitness value produced better solution.The lesser cost value produced better solution.In this paper, cost-typed is used as objective function because the purpose of this algorithm is to minimize the error.To design cost function, prediction accuracy and number of selected features are used as criteria.Thus, the particle with high prediction accuracy and small number of features produces a low prediction error with set weights value WA = 95% and WF =5% [7].
where n is number of data, Ai is actual value and Fi is prediction value for data, fj is value of feature mask.
where x is the original data from dataset, x min and x max is the minimum and maximum value of original data, and xn is normalized value.8.If stopping criteria is satisfied, and then end iteration.If not, repeat step 2. In this paper, stopping criteria is a given number of iterations.

Experimental result
Fig. 3 illustrates the correlation between optimal cost and number of particle in 5 simulations.It showed that optimal cost is decreased while number of particle is being increased.From this chart, we can conclude that the more number of particles can provide more candidate solution so model can have more chance to select optimal solution.However, computing time is also increased because model spent much time to find solution among many particles and it is illustrated by Fig. 4. It happened because model must perform solution searching in many particles and it compromised computing time.In the experiment, we discovered that 20 particles could obtain the most optimal cost, but we can't use it as optimal parameter since spending much computing time.Thus, we decided to use 15 particles under consideration that it has less computing time but still obtain optimal cost.p-ISSN: 2540-9433; e-ISSN: 2540-9824  5 illustrates the correlation between optimal cost and number of iteration in 5 simulations.It showed that optimal cost is decreased while number of iteration is being increased.For the example, in 4 th simulation, optimal cost remained steady until 4 th iteration and move down until 8 th iteration.From 8 th iteration until 40 th iteration, optimal cost didn't perform any change and it means that model converged and found optimal solution.

Conclusion
This paper examined the implementation of local best particle swarm optimization for optimal feature subset selection and SVR parameters optimization in the problem of software effort estimation.In our simulations, we used Desharnais dataset.We compared our results to PSO-SVR and T-SVR.From the experiment results, using local best version can improve performance of PSO.For further research, we suggest to use different topologies e.g.Von Neumann, pyramid, wheel and four clusters, to give more perspectives about effect of social network structures to PSO for selecting optimal number of feature and optimizing SVR parameters combination in the

2 .
Dividing data into k to determine training and testing data.

3 .
Initializing a population of particle.

4 .
Calculating cost by averaging error over k SVR training.5. Updating individual and local best position of each particle.p-ISSN: 2540-9433; e-ISSN: 2540-9824 6. Updating inertia weight.7. Updating velocity and position of each particle.

Fig. 5 .
Fig. 5. Convergence during process Table 3 showed the comparison of the experiment results.The experiments showed that the proposed model outperforms T-SVR and PSO-SVR in optimizing SVR.Local best PSO SVR obtained lowest error among three models.It is observed that PSO-SVR spent less computing time because of fast convergence.Local best PSO-SVR model has slow convergence because it finds optimal solution in its neighborhood.

TABLE I .
PARTICLE I IS CONSISTED OF SIX PARTS: C, Ε, Λ, Ε, CLR AND FEATURE MASK