A two-stage differential optimally driven analog-based effort metric method

Abstract

The application relates to a two-stage differential optimization driving analog-based work quantity measurement method, comprising the following steps: receiving a new project; determining historical projects similar to the new project; calculating feature differences of the new project and the historical projects; constructing an objective function based on the feature differences; solving the objective function by using a BA algorithm to obtain optimal parameters; and weighting work quantities of each historical project participating in calculation based on the optimal parameters to obtain the work quantity of the new project. Compared with the prior art, the application has the change relationship between the feature differences and the work quantity differences, so that the calculated work quantity is more accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of software project management, and particularly to a two-stage differential optimization driven analogy-based effort estimation method. BACKGROUND

[0002] Software development estimation (SDE) is one of the most important steps in the software development process, and plays a vital role in the success of software projects. It not only includes predicting the effort, time and staff required to develop software, but also includes the effort required for software maintenance. In recent decades, various methods have been proposed to estimate SDE, which can be divided into algorithm-based and non-algorithm-based effort estimation techniques. One of the most widely used methods is the case-based reasoning (CBR) proposed by Shepperd in 1979. Although many SDE estimation methods have been introduced so far, the ease of use and simplicity make CBR widely used. The CBR method emphasizes the use of knowledge of past projects, and is therefore called an analogy-based estimation (ABE) method.

[0003] The background theory of the ABE method is that software development projects with similar characteristics have similar effort. The number of similar projects is a factor that affects the accuracy of SDE in the ABE method, and the number of projects involved in the estimation will affect the accuracy of the effort estimation. Different algorithms select projects differently, and fixedly selecting K nearest neighbor projects and flexibly determining the size of K using adaptive rules are two common methods. In the ABE method, the similarity of a new software development project to previous projects is measured by a similarity function. The similarity function is used to compare the characteristics of two projects and determine the degree of similarity between them, and it plays an important role in the ABE method. Since the importance of all original features (attributes) is not the same when estimating SDE, different features may have different weights when calculating the similarity between projects, and feature selection and feature weighting techniques can be used to optimize the influence of different features on the similarity function.

[0004] Currently, there are four commonly used advertising attribution algorithms: first-touch attribution, last-touch attribution, average attribution, and time decay attribution. First-touch attribution attributes the conversion revenue to the first touch on the conversion path, and the contribution of the first touch is 100%, while the rest is 0%. Last-touch attribution is the opposite of first-touch attribution, and it believes that conversion is only related to the last touch on the conversion path, so the contribution of the last touch on the conversion path is 100%, and the rest is 0%. Average attribution is to allocate the contribution of conversion to each touch point equally. Time decay attribution is to allocate the contribution to each touch point according to the time interval from the conversion time point, and the farther the touch point is from the conversion time point, the smaller the contribution.

[0005] The primary task of the ABE algorithm is to find a suitable similar item. Researchers have proposed various methods to specify this number: 1) using a fixed number selection (i.e. , etc.); 2) dynamic selection based on clustering; 3) selection based on similarity threshold. However, most studies use the same value for all new items, but such an approach does not necessarily produce the best match for each individual item; or only predict the best value based on the structure of the data set, without considering the adjustment workload. In order to more finely find the best similar item value for each item, Azzeh et al. use the bee algorithm to propose an optimized analogy-based estimation (OABE), which searches for the optimal value and the weight factor of each feature difference for each item at the same time.

[0006] The method of adjusting the workloads of new projects based on historical projects mainly studies similarity functions. A large number of adjustment methods are included in the existing researches, and the most widely used strategy includes: Walkerden and Jeffery proposed a linear size adjustment (LSE) method based on size extrapolation. Mendes et al. proposed a multiple linear feature extrapolation (MLFE) method to include all relevant size features. Jorgenson et al. proposed a regression towards the mean (RTM) to adjust the project according to the productivity value of the project. Chiu and Huang proposed a genetic algorithm (GA) based adjustment, which optimizes the coefficients of summarizing the distance of each feature on the basis of minimizing the performance metric. Recently, Li et al. proposed to use a neural network (NN) to learn the differences between projects and reflect the differences in the final estimate.

[0007] In summary, the analogy-based effort estimation method is popular in the software engineering community due to its excellent prediction performance. The idea behind this method is to estimate the workload of a new project by minimizing the error between the new project and the historical projects when the new project comes. There are two important steps to minimize the error, the first step is to determine the most similar projects to the new project, and the second step is to adjust the feature difference between the new project and the historical projects. However, for the process of adjusting the feature difference, the existing researches do not explicitly define the relationship between the feature difference and the workload difference, but assume that the two are equal changes, which leads to low accuracy of the measurement of the workload of the new project. SUMMARY

[0008] The purpose of the present application is to overcome the defects of the prior art and provide an analogy-based effort estimation method driven by two-stage difference optimization.

[0009] The purpose of the present application can be achieved by the following technical solutions:

[0010] An analogy-based effort estimation method driven by two-stage difference optimization, comprising the following steps:

[0011] receiving a new project;

[0012] determining historical projects similar to the new project;

[0013] calculating the feature difference between the new project and the historical projects;

[0014] constructing an objective function based on the feature difference;

[0015] Solving the objective function using the BA algorithm to obtain the optimal parameters;

[0016] Based on the optimal parameters, the workloads of each historical project participating in the calculation are weighted to obtain the workload of the new project.

[0017] Further, the feature difference refers to the feature difference between the new project and the historical project , that is:

[0018]

[0019] The feature difference includes positive feature difference and negative feature difference.

[0020] Further, the relationship between the positive feature difference and the negative feature difference and the workload is inconsistent, and the positive feature difference has a stronger correlation with the workload difference;

[0021] The correlation between the feature difference and the workload difference is defined as the workload elasticity l, The adjustment factor is called, and has:

[0022]

[0023] In the formula, Δe + is the workload difference, that is, the difference between the workload of the new project and the workload of the historical project ,

[0024] Further, when linear fitting is adopted, there is: is the positive adjustment factor, is the negative adjustment factor; each feature in the project has a corresponding

[0025] Further, the construction of the objective function includes the following steps:

[0026] The feature weight matrix is constructed as:

[0027]

[0028] In the formula, is the number of historical projects similar to the new project, is the feature weight, and m represents the number of features of each project; Each row in the matrix represents the weight corresponding to each feature in a similar historical project;

[0029] The adjustment factor function is constructed as:

[0030]

[0031] wherein, is a positive adjustment factor, is a negative adjustment factor,

[0032] Based on the feature weight matrix and the adjustment factor function, an average feature difference of each item is constructed

[0033]

[0034] By a target function to be solved is constructed

[0035]

[0036] Further, the feature weight needs to satisfy:

[0037] Further, solving the target function using the BA algorithm includes the following steps:

[0038] BA algorithm initialization solutions, the value of each solution is randomly generated under the condition of ensuring no repetition, and the value of each solution is also randomly initialized under the condition of meeting the constraint condition;

[0039] From solutions, select candidate solutions for neighborhood search, evaluate according to value, and sort the solutions in ascending order to obtain best solutions from small to large;

[0040] For these solutions, each solution is searched for neighborhood solutions, and for the remaining solutions selected, each solution is searched for neighborhood solutions

[0041] The solutions not selected are randomly searched in the solution space;

[0042] Repeat the above steps until the minimum value or the maximum number of iterations is met.

[0043] Further, the optimal parameters include optimal historical project participation number, positive adjustment factor of each feature, negative adjustment factor of each feature, and weight coefficient of each feature in each historical project.

[0044] Further, the weighting of the workloads of each historical project participating in the calculation to obtain the workload of the new project includes the following steps:

[0045] Based on the optimal parameters, the optimal average feature difference of each project is calculated.

[0046] For each project, the workload of the historical project is estimated according to the optimal average feature difference of the new project workload , which is expressed as:

[0047]

[0048] The estimated values of each historical project participating in the calculation are aggregated to obtain the workload of the new project.

[0049] Further, the aggregation of the estimated values of each historical project participating in the calculation is specifically the aggregation according to the similarity ranking, including the following steps:

[0050] According to the optimal average feature difference of each project from small to large, the similar historical projects are ranked;

[0051] The ranking result of the first project is represented by a label ,

[0052] The finally calculated workload of the new project is obtained according to the following formula

[0053]

[0054] Compared with the prior art, the present application has the following beneficial effects:

[0055] ​The application proposes a new analogy-based effort estimation method in the case of finding that feature difference and effort difference are not equal changes, defines positive feature difference and negative feature difference to represent different functional relationships with effort change respectively, and adopts two-section linear relationship to describe feature difference and effort difference. Compared with the prior art, the experimental results of different indexes on four disclosed data sets show that the algorithm proposed in the application has certain superiority and can more accurately measure the effort of new projects. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 Flowchart of effort estimation based on ABE method;

[0057] Figure 2 Flowchart of algorithm of the application;

[0058] Figure 3 Schematic diagram of relationship between average feature difference and effort difference on different data sets;

[0059] Figure 4 Schematic diagram of relationship between positive and negative feature differences and effort on different data sets. DETAILED DESCRIPTION

[0060] The application will be described in detail below in combination with the drawings and specific embodiments. The embodiments are implemented on the premise of the technical solution of the application, and detailed implementation and specific operation processes are given, but the protection scope of the application is not limited to the following embodiments.

[0061] The flow of the ABE-based effort measurement method is shown in Figure 1 The analogy-based effort measurement method is popular in the software engineering community due to its excellent prediction performance. The idea behind this method is that when a new project comes, the effort of the new project is estimated by minimizing the error between the new project and the historical projects. There are two important steps to estimate the minimum error, the first step is to determine the most similar project to the new project, and the second step is to adjust the feature difference between the new project and the historical projects.

[0062] The application proposes a two-section difference optimization algorithm to adjust the feature difference, and the main inspiration comes from the following two points: the application finds that the feature difference increment and the effort difference increment are not equal, and they have a multiple relationship; in addition, the positive and negative feature difference increments have different effects on the effort difference increment, and the positive feature difference increment has a stronger effect on the effort difference increment than the negative feature difference increment.

[0063] Based on the above two findings, this application employs the bee algorithm to find the optimal adjustment factor for the positive and negative difference increments of each feature. Experimental results on four publicly available datasets generally outperform other excellent algorithms used for comparison.

[0064] The algorithm flow proposed in this application is as follows: Figure 2 As shown. First, calculate the new project and... The feature differences of each historical project are then used to construct the objective function. After the objective function is constructed, the Base Algorithm (BA) algorithm is used to solve it. The optimal number of participants in each historical project can be obtained after the BA algorithm completes its iterations. The positive and negative feature difference fitting coefficients for each feature and the weight coefficients for each feature in each historical project.

[0065] Given the aforementioned optimal parameters, this embodiment calculates the workload of the new project by weighting the workload of each historical project involved in the calculation.

[0066] Specifically, this application mainly includes the following steps:

[0067] Step 1: Calculate the feature difference and workload difference;

[0068] Feature difference refers to the features of a new project. and historical projects The characteristic difference, i.e. Workload differential refers to the workload of a new project. and historical projects The difference in workload, i.e.

[0069] The characteristic difference and the workload difference have always been assumed to change by an equal amount, that is... However, experiments conducted in this embodiment on four publicly available workload metric datasets—Albrecht, Cocomo81, Kemerer, and Maxwell—revealed that this assumption does not appear to hold true.

[0070] Each dataset contains multiple project features. To study the relationship between feature differences and workload differences, this embodiment calculates the average feature difference for each project. The average feature difference is defined as:

[0071]

[0072] Where m represents the number of features for each item in the dataset. Since the amount of data in each dataset is very limited, this embodiment calculates the features for any two items in each dataset. and Δe, the average feature difference and effort difference, respectively, on the dataset Albrecht, Cocomo81, Kemerer and Maxwell are shown in Fig. 1, Fig. 2, Fig. 3 and Fig. 4, respectively. Figure 3

[0073] The dashed line in the figure is the linear fitting result, and the solid line is the fitting result by the two-stage fitting method. It can be seen from the figure that the change of feature difference is not equal to the change of effort difference. Therefore, it cannot be simply assumed that the change of feature is equal to the change of effort.

[0074] The feature difference and effort difference are not equal in change, so it is very important to explore the internal relationship between them for effort estimation tasks, Figure 4 The relationship between feature difference and effort of this embodiment is shown in Fig. 5. This embodiment adopts two-stage fitting because the relationship between positive and negative feature difference and effort difference can be well described by the following piecewise linear function:

[0075]

[0076] Figure 4 The solid line in the figure is the fitting result by the piecewise linear fitting method of this embodiment, and the fitting results on Albrecht, Cocomo81, Kemerer and Maxwell are 0.93, 0.44, 0.68, 0.77, respectively. Figure 4 It can be seen that the positive feature difference and the negative feature difference are indeed inconsistent with the relationship with effort. Moreover, it can be obviously observed that the positive feature difference and effort difference show a faster change rate than the negative feature difference. In fact, this phenomenon actually accords with the cognition of this embodiment, because increasing the intensity of a feature usually has a more severe impact on effort than reducing the intensity of the feature by the same amount. This phenomenon is defined by this embodiment as the effort elasticity l, which is called the adjustment factor, so there is:

[0077]

[0078] When using linear fitting, there is:

[0079] The parameters and ​​​​​is the unknown parameter to be solved in the subsequent algorithm of this embodiment, which is a parameter related to the feature and irrelevant to the specific project, so each feature has its own set of What this embodiment needs to do is to assume their two-stage linear relationship, and the specific solving method is to search and optimize them as the position parameters of the bee algorithm.

[0080] Step two: target function construction;

[0081] This embodiment first searches for the optimal number of similar projects and feature weights The structure of the feature weight matrix is as follows:

[0082]

[0083] Each row in the feature weight matrix represents the weight of each feature corresponding to a similar project, and the feature weight needs to satisfy:

[0084] As described in the above formula (1), this embodiment arranges a two-stage adjustment function for each feature Each function contains two adjustment factors and Both adjustment factors need to satisfy: Therefore, for all adjustment functions is expressed as follows:

[0085]

[0086] Based on the above feature weight and adjustment factor function, this embodiment first constructs the average feature difference of each project

[0087]

[0088] Through This embodiment constructs the target function to be solved for the entire problem

[0089]

[0090] The BA algorithm is used to solve the above minimization target function. Through sensitivity analysis on the data set used, this embodiment determines the parameters that need to be set for the initialization of the BA algorithm, and determines appropriate values for each parameter. Table 1 shows the BA parameters used in this study, their abbreviations and initial values. The following this embodiment briefly describes the process of BA finding the optimal value, weight and adjustment factor for each new project.

[0091] Table 1 Main parameters of BA algorithm and their initial value settings

[0092]

[0093] The BA algorithm initializes solutions, and the value of each solution is randomly generated under the condition of ensuring no repetition, and the matrix of each solution is also randomly initialized under the condition of meeting the constraint condition. The solution iteration process is as described in the foregoing BA algorithm: first, select candidate solutions from solutions for neighborhood search, then evaluate according to the value, sort the solutions in ascending order, and in turn obtain solutions from small to large, and for these solutions, each solution is searched for neighborhood solutions, and for the remaining solutions selected, each solution is searched for neighborhood solutions The solutions not selected are randomly searched in the solution space. The purpose of the above arrangement is that a large number of solutions are searched in the vicinity of promising solutions, and the steps are repeated until the stopping criterion (minimum MR) or the maximum number of iterations is met.

[0094] Step three: workload calculation;

[0095] After the above optimization objective function completes iteration, the unknown parameters in the objective function all obtain optimal values, at this time the embodiment can calculate the optimal average feature difference estimation of each project according to the optimal values The method of the present application is to estimate on the basis of the floating of the feature difference, and each similar project has an estimation of , which is denoted by , as follows:

[0096]

[0097] may be greater than or less than , which depends on the average feature difference

[0098] With the estimation of each similar project on , the next step is how to reasonably estimate the value of each project ​Aggregation. There are many methods for aggregation, such as mean aggregation, median aggregation, percentage aggregation, maximum and minimum aggregation, etc. By comparing several aggregation methods, the present embodiment finds that the method of aggregation according to the similarity ranking has better advantages. Therefore, the present embodiment adopts the method of similarity ranking aggregation, and the specific process is as follows: first, the similar projects are ranked from small to large according to the formula ; then the ranking result of the first project is represented by a label ; and finally the final workload is synthesized according to the formula

[0099]

[0100] The meaning of this estimation method is to weight according to the similarity of the projects, and the weight of the more similar projects is larger.

[0101] Up to now, all the processes of estimating the workload in the present embodiment have been introduced, from the feature difference calculation to the objective function construction and solving, and then to the workload aggregation. The present embodiment describes the calculation process of the method of the present application in three parts. It should be noted that the measurement method of the present embodiment is a data set dependent method, because the number of features and the number of projects of each data set is different. Therefore, before actually applying the method of the present application, a usable data set should be selected according to experience, and the workload of the new project is measured according to the calculation process described in the present application.

[0102] Step four: evaluation index

[0103] The standard for evaluating the workload measurement method is whether the error between the actual workload and the predicted workload is small enough. The commonly used evaluation indexes of the workload measurement method are the relative magnitude error (MRE), the mean magnitude relative error (MMRE), the median magnitude relative error (MdMRE), and the prediction performance (PP). The calculation formulas of them are as follows:

[0104] MRE calculates the percentage of the deviation of the estimated value from the true value, and its calculation method is as follows:

[0105] ​​​

[0106] MMRE is the mean of MREs of the designed methods

[0107] MdMRE is the median of MREs of the designed methods

[0108]

[0109] PP is the percentage of the number of projects whose MREs are not more than 25% after multiple predictions

[0110]

[0111] It is noted that MMRE is considered as a biased indicator of under- or over-estimation, but it is still used in this embodiment because it is widely used in the field of effort estimation.

[0112] Step five: evaluation of experimental results

[0113] Five classical ABE methods, LSE, MLFE, RTM, GA, NN, OABE are selected in this embodiment to compare with the method of the present application. The best value of the method of the present application is dynamically selected, and does not need to be set in advance. In contrast, the best value of other algorithms must be found almost suitable for their own model, so this embodiment tries different settings from 1 to 5 on each data set, and balances the differences of each data, and selects the best value of the average performance for other methods.

[0114]

[0115] In order to ensure the stability and fairness of the experimental results, the experimental method of this embodiment is to randomly divide the data set into training set and test set according to the ratio of 80%:20% on each data set, and the test set is executed on the training set for the effort estimation algorithm of the present application, and the three evaluation indicators of MMRE, MdMRE and PP are recorded. The above process is repeated 100 times on each data set, and then the average value of all test sets of the 100 times is taken as the final experimental result.

[0116] In summary, the present application first studies the relationship between feature difference and effort difference, and the experimental results show that feature difference and effort difference are not the equal change relationship of the potential assumption in the prior art, i.e. ​​​​​​​And the embodiment finds that the influence of positive and negative feature difference on the change of work load difference is not consistent, the influence of positive feature difference on the change of work load difference is obviously greater than that of negative feature difference, that is This phenomenon is also fully consistent with the cognition of the embodiment, because the influence of project increase unit strength on work load is definitely more significant than that of decrease unit strength. Accordingly, the application proposes a two-section fitting method to fit the change relationship of positive and negative feature difference and work load difference respectively, so that the work load can be more accurately estimated. In summary, the contributions of the application are as follows:

[0117] 1) It is found that the feature difference and the work load difference are not in a proportional change relationship.

[0118] 2) The influence of positive feature difference on work load is obviously stronger than that of negative feature difference, and this feature is considered in the work load measurement.

[0119] 3) Algorithm verification is carried out on the disclosed data set, and the experimental results show that the algorithm of the application has good performance.

[0120] The above describes the preferred embodiments of the application in detail. It should be understood that those skilled in the art can make many modifications and changes without creative labor according to the concept of the application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment on the basis of the prior art according to the concept of the application shall be within the protection scope determined by the claims.

Claims

1. A two-stage differential optimally driven analog-based work metric method, characterized in that, The method comprises the following steps: receiving a new project; determining historical projects similar to the new project; calculating feature differences between the new project and the historical projects; constructing an objective function based on the feature differences; solving the objective function using a BA algorithm to obtain optimal parameters; weighting the workloads of each historical project involved in the calculation based on the optimal parameters to obtain the workload of the new project; The feature difference refers to the difference in features of the new item and the historical items i.e.: the feature differences comprise positive feature differences and negative feature differences; the construction of the objective function comprises the following steps: constructing a feature weight matrix as: wherein, is the number of similar historical projects to the new project, is the feature weight, represents the number of features for each project; each row in the matrix represents the weight of each feature in each similar historical project; constructing an adjustment factor function as: wherein is a positive adjustment factor, is a negative adjustment factor, ； constructing an average feature difference for each item based on the feature weight matrix and an adjustment factor function : By constructing an objective function to be solved : solving the objective function using a BA algorithm comprises the following steps: BA algorithm initialization each solution is randomly generated each solution is randomly generated each solution is randomly generated from Select from the solutions Perform a neighborhood search on each candidate solution, based on... After evaluating the values, the solutions are sorted in ascending order, from smallest to largest. The best solution; For each solution, one neighborhood solution search is performed For each solution, one neighborhood solution search is performed For each solution, one neighborhood solution search is performed For each solution, one neighborhood solution search is performed For each solution, one neighborhood solution search is performed ; not selected one solution randomly searches within the solution space; The above steps are repeated until the minimum value or maximum number of iterations is met.

2. A two-stage differential optimisation driven analog-based work metric method according to claim 1, wherein, the positive feature differences and the negative feature differences are not consistent with the workloads, and the positive feature differences have a stronger correlation with the workload differences; The correlation between characteristic difference and workload difference is defined as workload elasticity. , Let be called the adjustment factor, then: wherein, is the difference in effort, i.e., the new project effort and the historical project effort the difference between the two. 。 3. A two-stage differential optimisation driven analog-based work metric method according to claim 2, wherein, When a straight line fit is employed, there are: , , is a positive adjustment factor, is a negative adjustment factor; each feature in the item has a corresponding set of (a, b) values .

4. A two-stage differential optimisation driven analog-based work metric method according to claim 1, wherein, the feature weights need to satisfy: 。 5. A two-stage differential optimisation driven analog-based work metric method according to claim 1, wherein, the optimal parameters comprise an optimal number of historical projects, a positive adjustment factor of each feature, a negative adjustment factor of each feature, and a weight coefficient of each feature in each historical project.

6. A two-stage differential optimisation driven analog-based work metric method according to claim 2, wherein, the weighting of the workloads of each historical project involved in the calculation based on the optimal parameters to obtain the workload of the new project comprises the following steps: calculating optimal average feature differences of each project based on the optimal parameters; For each project, the new project effort is estimated based on the optimal average feature difference from the historical project efforts and is expressed as: estimated value for each historical project that participated in the calculation aggregate to get the effort of the new project.

7. A two-stage differential optimisation driven analog-based work metric method according to claim 6, characterised in that, said estimated value for each historical item participating in the calculation The aggregation is specifically performed in accordance with a similarity ranking, comprising the following steps: ranking the similar historical items from small to large according to the optimal average feature difference of each item ​ No. The sorting results of the projects are labeled express, ； The final calculated new project effort is obtained according to the following formula : 。

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