Application of Chaotic Increasing Linear Inertia Weight and Diversity Improved Particle Swarm Optimization to Predict Accurate Software Cost Estimation

Application of Chaotic Increasing Linear Inertia Weight ░ ABSTRACT- Nowadays usage of software products is increases exponential in different areas in society, accordingly, the development of software products as well increases by the software organizations, but they are unable to focus to predict effective techniques for planning resources, reliable design, and estimation of time, budget, and high quality at the preliminary phase of the development of the product lifecycle. Consequently, it delivered improper software products. Hence, a customer loses the money, time, and not belief on the company as well as effort of teamwork will be lost. We need an efficient and effective accurate effort estimation procedure. In the past, several authors have introduced different methods for effort of estimation of the software. Particle Swarm Optimization is a most popular optimization technique. Maintaining diversity in particle swarm optimization is the main challenging one and in this paper, we propose chaotic linear increasing inertia weight and diversity improved mechanism to enhance the diversity. Seven standard data sets were employed to analyze of performance of the proposed technique, and it is outperformed compared to the previous techniques.


░ 1. INTRODUCTION
SCE is a challenging task in the software product development community. It is process of predicting required resources to complete the process within a time limit and budget. Nowadays usage of software products is increases exponential in different areas in society, accordingly, the development of software products as well increases by the software organizations, but they are unable to focus to predict effective techniques for planning resources, reliable design, time, budget and required quality at the early stages of the software product development lifecycle. As a result, an inaccurate software product is delivered to the customers. Hence, the consumer loses money, time, and trust in a company. Various methods have been examined for SEE; including conventional methods may be the Cost Construct Model [4], and, supplementary machine learning techniques such as Neural Networks (NN) [1], bagging predictors [2], and Support Vector Regression (SVR) [3]. Machine learning approaches built a model for analyzing old projects, and to estimate new projects effort. For these techniques, huge amount of data samples are required to predict accurate results, but SCE estimation data sample size is very small. Hence, machine learning techniques give inaccurate results. Evolutionary techniques are Genetic Algorithms (GA), PSO, and more optimization techniques available in the literature. PSO has more popularity in the evolutionary community due to easy implementation, yet effectiveness, and its performance is greatly relevant to the diversity of the particles, especially when trying to avoid premature convergence and to get away from local optima. Hence, preserving a high diversity in PSO is a vital task. In this paper, we propose combination of Chaotic Increasing Linear Inertia Weight and enhanced diversity technique of PSO to predict accurate Cost of the software at early stages of development. Remaining sections of the paper is structured in the following manner. Literature survey is presented in Section 2. In Section 3 Employed Techniques. Section 4 proposed mechanisms. Results and Discussions are presented in the Section 5. In Section 6 paper conclusion.

░ 2. LITERATURE SURVEY
The basic PSO was invented by Eberhart et al. in 1995 [5], it is a biological inspired evolutionary computation [6] and population-based stochastic search technique [7] start with an initial solutions of particles [8], required less memory, is computationally effective, and easier to implement [7]. For any search problem in Z-dimensional space, a particle can be represented by its position and velocity. Every particle is moved to its particle personal best (pb), and particle global Website: www.ijeer.forexjournal.co.in Application of Chaotic Increasing Linear Inertia Weight best (gb) during an exploration process as followed [8].
PSO is a familiar optimizer and has been widely used in many practical applications since it was invented. Past thirty-year PSO has several variants. Starts with a summary of these different versions are can be presented as follows. Yuhui et al. [9] a special kind of parameter is called inertia weight iw embedded to the original PSO. Participation of iw is an important because of make a balance search and convergence activities, iw value decreasing linearly was a good choice for the search process. Constriction factors originally introduced by Clerc [10, 11, and 12] were used to solve different applications. Finally, all were decided was improves convergence velocity.
Bergh et al. [13,15] highlighted in depth analysis of PSO parameters and provided mathematical evidence that each particle convenes to a check point. Kathrada [14] proposed flexible PSO (FlexiPSO) was including simple heuristics by which improves the flexibility of particle swarm. Lang et al. [16] introduced Comprehensive PSO (CPSO) which uses a novel learning mechanism is to gain knowledge from other particles in various dimensional to solve complex problems. Chen et al. [17] introduced another version of PSO was Dynamic Linkage Discovery to progress convergence rate of PSO, and is an effortless and successful linkage detection practice, and thereafter, a recombination operator that make use of dynamic linkage design to support the cooperation of PSO and Dynamic Linkage Discovery (DLD). Blackwell et al. [18] optimal values are obtained by dynamic function over the time period using a multi-swarm PSO. Li et al. [19] introduced adaptive learning PSO, which is a combination of its own personal best, nearest neighbor, and global best.
Khatibi et al. [20] proposed a hybrid mechanism which including PSO and analogy-based estimation to enhanced accuracy of SEE. Hassaniet al. [21] examined effects of the genetic algorithms, PSO algorithm and ant colony optimization, and presented comparative study of them. Shahpar et al. [22] proposed Polynomial Analogy Based Estimation (PABE) to improve the accurate prediction of the SCE. An analogy method is used to find out similarity property of the given project. Khatibi et al [23] proposed new service-oriented effort estimation is called global village service effort estimation which emphasizes an idea is think locally, operate globally. Khatibi et al. [24] propose a hybrid model which integrates Analogy Based Estimation (ABE) and Differential Evolution (DE) practice to predict software development services effort. Amid Khatibi Bardsiri [25] employed machine learning and statistical methods on different benchmark data sets to analyze data, build model and evaluate outcome. Venkataiah et al. [26] PSO to predict software cost estimation. K-means algorithms are used to frame the data of the cluster are given as input to PSO. The PSO is employed to determine the optimized result. But the major problem of PSO is suffering from the premature convergence means frequently struck at local minima.
In order to solve the diversity problem, number of methods was proposed. Standard PSO is used to test multi-model problems, which tend to suffer from the local minima and early convergence due to reduced diversity in a problem space.
In order to overcome this problem of PSO, S. Das et al. [27] proposed the attractive and repulsive two stage mechanism in PSO is called (ARPSO). In stage one every particle is attracting each other because of information flow is good between particles, and hence the diversity decreases. In stage two individual particles are no longer attracted which means repelled by global best position and local best position. When the diversity drops under a lower bound dlower in stage one, ARPSO switches to the repulse stage, and diversity reached is high dhigher, then ARPSO switches back to attraction stage. The entire search process of ARPSO exchanges between attraction stage and repulsion stage-lower and higher diversities. However, the search behavior cannot be changed by ARPSO when diversity remains between dlower and dhigher. According to the ARPSO, Pant et al. [28] proposed a new stage is called the positive conflict stage as the middle stage between attraction stage and repulsion stage. In this stage, attraction, and repulsion are not complete present. Every particle is paying attention by its earlier best position and is repelled by the best global particle.
Where y'ij is the i th position and j th dimension of vector, N is entire particles that participated in the computation of diversity measurement and Z is the dimension vector. Qingjianet al. [29] proposed three measurements for improvement of diversity in PSO. Jonathan et al. [30] presented measures used to quantify diversity, and how they can be utilized to quantify the dispersion of both the candidate solutions and find out optima. Cheng et al. [31] Population diversity of PSO is vital when measuring and regulating algorithms ability of exploration or exploitation dynamically.

Chaotic Linear Increasing Inertia Weight
Where iw is inertia weight, is maximum, and is minimum inertia weights, maxiter is maximum iterations and iter is iteration.

Diversity Improved Method
To improve the diversity between particles, for swarm diversity maintained, we offer a new diversity improved method. For every particle P1i (t), a new particle P1i (t+1) is created by the PSO position updating equation. By using the following question creating a trail particle P2i (t+1) = (TYi (t+1), TUi (t+1)) Where i=1 to N, j=1 to D, and rand () is a random function which generate random value within range of (0, 1). Every element of the new position in a vector is X1i (t+1) obtained from the equation (5) and (6).

░ 4. PROPOSED MECHANISM
In this paper, we proposed Chaotic Liner Increasing Inertia Weight and Diversity Improved Particle Swarm Optimization. Chaotic liner increasing inertia weight is used in a velocity update rule in each iteration generate to weight iw. DPSO which employs one strategy is particles are regularly moving same direction in a search process of PSO. It means that particles begin to be similar with the next iterations. When the trail P2i (t+1) is selected for next generation, the dissimilarities between P2i (t+1) and P1i (t+1) will find out, the dissimilarities among P1i (t+1), and remain particles of the swarm. High divergence in the swarm means high diversity and lower divergence in the swarm means lower diversity it leads to particles struck at local minima.

░ 5. RESULTS AND DISCUSSION
Seven datasets are used in experimentation to test the outcome of proposed method. Details about datasets were described in Table 1 with statistical information. These datasets are IBMDSP, CHINA, DESHARNAIS, MIYAZAKI, COCOMO81, ISBSG, and MAXWELL, and which are collected from the literature [31, 32, 33 34, 35, 36, and 37]. In all datasets, effort is considered as the targets attribute and remains of the attributes considered as input sources. Effort estimation can be calculated as follows.
Effort (E) = r*(size) s (10) Where effort can be measured in terms of PM (Person per month), r and s constants and size considered as Kilo Line of code. Min-Max normalization technique used to transfer larger data scale to small data scale because of to void the distortion in data. Normalized data is given as input to all proposed techniques. All the experimentation was conducted 20 times. According to the Table 2 first column shows that performance PSO with inertia weight w=0.9 over seven data sets. Second column illustrate best results of PSO with proposed inertia weight when compared to first column. Third column presents results of proposed PSO diversity enhanced with inertia weight w=0.9 and last column shows that proposed mechanism which including proposed inertia weight and diversity enhanced, and the results of proposed mechanism is outperformed compared to remaining columns. Table  3describesanalysis of comparison results between various inertia weights are used in PSO on over seven datasets. Proposed inertia weight accomplished best results compared to the linear decreasing, chaotic, random, and chaotic random inertia weights. Table4 presents a comparative study on proposed method, and with other five variants of PSO on 7 datasets which are summarized in Table 1. Comparison of the proposed technique with PSO, PSOW, PSOCF, UPSO and FIPSO achieved better results than other techniques on all datasets except for PSOCF, and FIPSO on COCOMO 81. We used seven effort estimation benchmark datasets to analyze the performance of the proposed technique. Out of seven datasets, the CHINA dataset achieved the best global optimum value by the proposed technique which means that gap between actual and estimated effort should be minimized and followed by DESHARNAIS, IBM DSP, MIYAZAKI94, and MAXWELL. Similarly, FIPSO compared to PSO, PSOW, PSOCF, and UPSO achieved better results on only two datasets are IBM DSP and CHINA and did not give impressive results on the remaining of the datasets. Likewise, USPO achieved better results only on the ISBSG dataset. Equally, PSOCF achieved better results only on the COCOMO81 dataset. Performance of the PSO and PSOW is almost equally over seven datasets. Finally, figure 1 Describes the root mean square error value over seven data sets by PSO, and proposed techniques. Figure  2 shows the comparisons of PSO variants with root mean square values.