Particle Swarm Optimization for Predicting the Development Effort of Software Projects
Abstract
:1. Introduction
2. Related Work
- (a)
- An increase in the computational cost inherent to CBR models by incorporating the use of optimization techniques.
- (b)
- Allowing selecting the best SDEP model from a set of predefined models, but without an automatically adjustment of the parameters of the selected model.
- (c)
- Define a priori the SDEP model to be used, and only adjusting its parameters.
- (1)
- The selection of the SDEP model, and
- (2)
- The automatic adjustment of the SDEP model parameters.
3. Particle Swarm Optimization (PSO) and PSO-SRE
3.1. PSO
3.2. PSO-SRE
4. Data Sets of Software Projects
5. Results
- Test 1: Up to 500 iterations, and up to 250 individuals in the swarm;
- Test 2: Up to 1500 iterations, and up to 750 individuals in the swarm;
- Test 3: Up to 1000 iterations, and up to 500 individuals in the swarm.
- not have memory of its own nor a search direction,
- repeat the random search of “the best particle” for a number of times that is equal to the number of fitness evaluations in the proposed PSO-SRE,
- compare its best solution with the best solution yielded by PSO-SRE.
6. Conclusions
- (a)
- New software projects coded in 3GL and developed in either Mainframe or Multiplatform and coded in 4GL and developed in Multiplatform.
- (b)
- Software enhancement projects coded in 3GL and developed in Multiplatform, MidRange or personal computer, as well as in those projects coded in 4GL and developed in Multiplatform.
- (c)
- Since the performance of the PSO-SRE resulted statistically equal than SRE, a software manager could also apply PSO-SRE as alternative to an SRE to software enhancement projects coded in 3GL and developed in Mainframe.
7. Discussion
- None of them generate their models by using a recent repository of software projects.
- Regarding the four studies where the ISBSG is used (1) their releases correspond to those published in the years 2007 and 2009, (2) all of them only select one data set from the ISBSG whose sizes are between 134 and 505, and (3) none of them take into account the version of the FSM to select the data set; whereas in our study, (1) the ISBSG release 2018 was used, (2) eight data sets containing between 53 and 440 projects were selected, and (3) all of them took into account the guidelines suggested by the ISBSG, including the type of FSM, that is, our data sets did not mix IFPUG V4 type with V4 and post V4 one.
- The majority of them base their conclusions on a biased prediction accuracy measure, and on a nondeterministic validation method.
- The half of them bases their conclusions on statistically significance.
- (1)
- The use of PSO incorporating an additional component by allowing automatic completion, in a single step, of the selection of the SDEP model, and automatic adjustment of the parameters of the SDEP model.
- (2)
- New and enhancement software projects obtained from the ISBSG release 2018.
- (3)
- Software projects selected taking into account the TD, DP, PLT, and FSM as suggested by the ISBSG.
- (4)
- Preprocessing of data sets through outliers’ analysis, and correlation and determination coefficients.
- (5)
- A nonbiased prediction accuracy measure (i.e., AR) to compare the performance between PSO-SRE and SRE models.
- (6)
- The use of a deterministic validation method for training and testing the models (i.e., LOOCV)
- (7)
- Selection of a suitable statistical test based on number of data sets to be compared, data dependence, and data distribution for comparing the prediction accuracy between PSO-SRE and SRE by data set.
- (8)
- Hypotheses tested from statistically significance.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
2GL | Programming languages of second generation |
3GL | Programming languages of third generation |
4GL | Programming languages of fourth generation |
ABC | Artificial bee colony |
AFP | Adjusted function points |
ApG | Application generator |
AR | Absolute residual |
CBR | Case-based reasoning |
COCOMO | Constructive cost model |
DP | Development platform |
FSM | Functional sizing method |
GA | Genetic algorithm |
IFPUG | International Function Point Users Group |
ISBSG | International Software Benchmarking Standards Group |
LOOCV | Leave one-out cross validation |
MAR | Mean absolute residuals |
MdAR | Median of absolute residuals |
MF | Mainframe |
ML | Machine learning |
MR | Midrange |
Multi | Multiplatform |
PC | Personal computer |
PLT | Programming language type |
PSO | Particle swarm optimization |
PSO-SRE | SRE optimized by means of PSO |
SDEP | Software development effort prediction |
SRE | Statistical regression equation |
TD | Type of development |
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Study | Data Set(s) 1 | Prediction Accuracy | Validation Method | Statistical Significance? |
---|---|---|---|---|
[25] | Six software organizations (21) | AR MRE r2 | NS | Wilcoxon |
[33] | Albrecht (24) Kemerer (15) Nasa (18) ISBSG Release 10 (505) Desharnais (77) Desharnais L1 (44) 3 Desharnais L2 (23) Desharnais L3 (10) Cocomo (63) Cocomo E (28) Cocomo O (24) Cocomo S (11) China (499) Maxwell (62) Telecom (18) | BRE IBRE | LOOCV | ANOVA |
[34] | Canadian organization (21) IBM (24) ISBSG Release 11 (134) | MRE | k-fold cross validation (k = 3) | No |
[35] | ISBSG Release 2011 (380) Cocomo (63) Maxwell (62) | MRE | k-fold cross validation (k = 10) | Wilcoxon |
[29] | Cocomo NASA 2 (93) Cocomo (60) | MRE | NS | No |
[40] | Albrecht (24) China (499) COCOMO (252) 2 Desharnais (77) ISBSG Release 8, 2003 (148) Kemerer (15) Miyazaki (48) | AR MRE LSD BRE IBRE | LOOCV | Scott-Knott |
[38] | Nasa (18) | MRE | Hold-out | No |
[36] | Desharnais (77) Maxwell (62) | MRE | k-fold cross validation (k = 3) | No |
[37] | Desharnais (77) Miyazaki (48) | MRE | k-fold cross validation (k = 3) | t-Student |
[32] | Cocomo (63) | MRE | Hold-out | No |
No. | Model | Equation | Reference |
---|---|---|---|
1 | Linear equation | [56] | |
2 | Exponential equation | [56] | |
3 | Exponential decrease or increase between limits | [57] | |
4 | Double exponential decay to zero | [57] | |
5 | Power | [57] | |
6 | Asymptotic equation | [58] | |
7 | Asymptotic regression model | [56] | |
8 | Logarithmic | [57] | |
9 | “Plateau” curve—Michaelis-Menten equation | [57] | |
10 | Yield-loss/density curves | [54] | |
11 | Logistic Function | [57] | |
12 | Logistic curves with additional parameters | [57] | |
13 | Logistic curve with offset on the y-Axis | [57] | |
14 | Gaussian curve | [57] | |
15 | Log vs. Reciprocal | [57] | |
16 | Trigonometric functions | [57] | |
17 | Trigonometric functions (2) | [57] | |
18 | Trigonometric functions (3) | [57] | |
19 | Quadratic polynomial regression | [57] | |
20 | Cubic polynomial regression | [57] |
Attribute | Selected Value(s) | Projects |
---|---|---|
Adjusted Function Point not null | --- | 6394 |
Data quality rating | A, B | 6061 |
Unadjusted Function Point Rating | A, B | 5316 |
Functional sizing methods | IFPUG 4+ | 4602 |
Development platform not null | --- | 3040 |
Language type not null | --- | 2711 |
Resource level | 1 | 2054 |
TD | DP | PLT | NSP |
---|---|---|---|
New | MF | 2GL | 3 |
MF | 3GL | 133 | |
MF | 4GL | 28 | |
MF | ApG | 4 | |
MR | 3GL | 36 | |
MR | 4GL | 22 | |
Multi | 3GL | 105 | |
Multi | 4GL | 102 | |
PC | 3GL | 55 | |
PC | 4GL | 118 | |
Proprietary | 5GL | 12 | |
Enhancement | MF | 2GL | 4 |
MF | 3GL | 457 | |
MF | 4GL | 48 | |
MF | ApG | 53 | |
MR | 3GL | 67 | |
MR | 4GL | 53 | |
Multi | 3GL | 442 | |
Multi | 4GL | 195 | |
PC | 3GL | 55 | |
PC | 4GL | 42 |
TD | DP | PLT | NSP | Variable | Normality Test | |||
---|---|---|---|---|---|---|---|---|
χ2 | S-W | Skewness | Kurtosis | |||||
New | MF | 3GL | 133 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
MR | 3GL | 36 | AFP | 0.0354 | 0.0075 | 0.1836 | 0.8342 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
Multi | 3GL | 105 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
Multi | 4GL | 102 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
PC | 3GL | 55 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
PC | 4GL | 118 | AFP | 0.0000 | 0.0000 | 0.0002 | 0.0158 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
Enhancement | MF | 3GL | 457 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
MF | 4GL | 48 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0186 | 0.0000 | 0.0104 | 0.0300 | ||||
MF | ApG | 53 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0002 | 0.0000 | ||||
MR | 3GL | 67 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
MR | 4GL | 53 | AFP | 0.0000 | 0.0000 | 0.0117 | 0.1535 | |
Effort | 0.0000 | 0.0000 | 0.0001 | 0.0000 | ||||
Multi | 3GL | 442 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
Multi | 4GL | 195 | AFP | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
PC | 3GL | 55 | AFP | 0.0000 | 0.0000 | 0.0003 | 0.0003 | |
Effort | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||
PC | 4GL | 42 | AFP | 0.0000 | 0.0000 | 0.0006 | 0.0001 | |
Effort | 0.0203 | 0.0000 | 0.0047 | 0.0006 |
TD | DP | LT | NSP | NO | FDSS | % | r | r2 |
---|---|---|---|---|---|---|---|---|
New | MF | 3GL | 133 | 3 | 130 | 2.25 | 0.7345 | 0.5396 |
MR | 3GL | 36 | 6 | 30 | 16.6 | 0.7390 | 0.5461 | |
Multi | 3GL | 105 | 6 | 99 | 5.71 | 0.7227 | 0.5223 | |
Multi | 4GL | 102 | 6 | 96 | 5.88 | 0.8513 | 0.7247 | |
PC | 3GL | 55 | 7 | 48 | 12.72 | 0.7978 | 0.6365 | |
PC | 4GL | 118 | 6 | 112 | 5.08 | 0.6515 | 0.4245 | |
Enhancement | MF | 3GL | 457 | 17 | 440 | 3.86 | 0.7916 | 0.6266 |
MF | 4GL | 48 | 4 | 44 | 9.09 | 0.4751 | 0.2257 | |
MF | ApG | 53 | 4 | 49 | 8.16 | 0.6571 | 0.4318 | |
MR | 3GL | 67 | 3 | 64 | 4.68 | 0.8052 | 0.6483 | |
MR | 4GL | 53 | 6 | 47 | 11.32 | 0.7127 | 0.5080 | |
Multi | 3GL | 442 | 14 | 428 | 3.16 | 0.8016 | 0.6427 | |
Multi | 4GL | 195 | 5 | 190 | 2.56 | 0.7640 | 0.5838 | |
PC | 3GL | 55 | 2 | 53 | 3.77 | 0.8019 | 0.6431 | |
PC | 4GL | 42 | 6 | 36 | 14.28 | 0.6418 | 0.4119 |
TD | DP | LT | SRE |
---|---|---|---|
New | MF | 3GL | |
Multi | 3GL | ||
Multi | 4GL | ||
Enhancement | MF | 3GL | |
MR | 3GL | ||
Multi | 3GL | ||
Multi | 4GL | ||
PC | 3GL |
TD | DP | LT | NSP | ID SRE | Model Name | Test 1 | Test 2 | Test 3 | |||
---|---|---|---|---|---|---|---|---|---|---|---|
SS | Iterations | SS | Iterations | SS | Iterations | ||||||
New | MF | 3GL | 130 | 1 | DEDZ | 50 | 250 | 150 | 750 | 100 | 500 |
Multi | 3GL | 99 | 2 | LE | 50 | 250 | 150 | 750 | 100 | 500 | |
Multi | 4GL | 96 | 3 | LE | 50 | 250 | 150 | 750 | 100 | 500 | |
Enhancement | MF | 3GL | 440 | 4 | LE | 250 | 500 | 750 | 1500 | 500 | 1000 |
MR | 3GL | 64 | 5 | LE | 50 | 250 | 150 | 750 | 100 | 500 | |
Multi | 3GL | 428 | 6 | Pcu | 50 | 250 | 150 | 750 | 100 | 500 | |
Multi | 4GL | 190 | 7 | Pcu | 50 | 250 | 150 | 750 | 100 | 500 | |
PC | 3GL | 53 | 8 | AE | 50 | 500 | 150 | 1500 | 100 | 1000 |
TD | ID SRE | LT | NSP | SRE | RS | PSO-SRE | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Test 1 | Test 2 | Test 3 | |||||||||||
MAR | MdAR | MAR | MdAR | MAR | MdAR | MAR | MdAR | MAR | MdAR | ||||
New | 1 | 3GL | 130 | 0.66 | 0.60 | 1.73 | 1.83 | 0.54 | 0.41 | 0.61 | 0.51 | 0.61 | 0.51 |
2 | 3GL | 99 | 0.62 | 0.56 | 1.46 | 1.35 | 0.56 | 0.43 | 0.61 | 0.55 | 0.61 | 0.55 | |
3 | 4GL | 96 | 0.53 | 0.49 | 0.74 | 0.57 | 0.43 | 0.32 | 0.52 | 0.47 | 0.52 | 0.47 | |
Enhancement | 4 | 3GL | 440 | 0.61 | 0.52 | 1.99 | 2.01 | 0.61 | 0.50 | 0.61 | 0.50 | 0.61 | 0.52 |
5 | 3GL | 64 | 0.60 | 0.50 | 1.33 | 1.21 | 0.53 | 0.35 | 0.59 | 0.49 | 0.59 | 0.49 | |
6 | 3GL | 428 | 0.56 | 0.50 | 1.62 | 1.60 | 0.40 | 0.28 | 0.55 | 0.48 | 0.54 | 0.46 | |
7 | 4GL | 190 | 0.52 | 0.44 | 1.37 | 1.46 | 0.46 | 0.41 | 0.51 | 0.45 | 0.51 | 0.45 | |
8 | 3GL | 53 | 0.72 | 0.70 | 1.18 | 1.06 | 0.48 | 0.36 | 0.72 | 0.70 | 0.65 | 0.55 |
TD | DP | LT | NSP | Pair | χ2 | S-W | Skewness | Kurtosis | p-Value |
---|---|---|---|---|---|---|---|---|---|
New | MF | 3GL | 130 | SRE | 0.0000 | 0.0000 | 0.3410 | 0.0000 | 0.0000 |
RS | 0.0000 | 0.0000 | 0.0073 | 0.9537 | 0.0000 | ||||
Multi | 3GL | 99 | SRE | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0040 | |
RS | 0.1462 | 0.0160 | 0.2573 | 0.6616 | 0.0000 | ||||
Multi | 4GL | 96 | SRE | 0.0000 | 0.0000 | 0.2251 | 0.0000 | 0.0000 | |
RS | 0.2261 | 0.0387 | 0.8034 | 0.0428 | 0.0000 | ||||
Enhancement | MF | 3GL | 440 | SRE | 0.0000 | 0.0000 | 0.6019 | 0.0000 | 0.3878 |
RS | 0.0000 | 0.0000 | 0.0000 | 0.0014 | 0.0000 | ||||
MR | 3GL | 64 | SRE | 0.0016 | 0.5511 | 0.7769 | 0.9573 | 0.0267 | |
RS | 0.7847 | 0.8470 | 0.6219 | 0.9685 | 0.0000 | ||||
Multi | 3GL | 428 | SRE | 0.0000 | 0.0000 | 0.1028 | 0.0000 | 0.0000 | |
RS | 0.0000 | 0.0000 | 0.0000 | 0.5221 | 0.0000 | ||||
Multi | 4GL | 190 | SRE | 0.0000 | 0.0000 | 0.8475 | 0.0000 | 0.0000 | |
RS | 0.0002 | 0.0000 | 0.0322 | 0.1907 | 0.0000 | ||||
PC | 3GL | 53 | SRE | 0.0347 | 0.0002 | 0.0961 | 0.0155 | 0.0000 | |
RS | 0.8419 | 0.2107 | 0.5087 | 0.3184 | 0.0000 |
TD | DP | LT | NSP | Model Name | Execution Time (Minutes) | |||
---|---|---|---|---|---|---|---|---|
Test 1 | Test 2 | Test 3 | Prediction | |||||
New | MF | 3GL | 130 | Double Exponential Decay to Zero | 14.5 | 23.6 | 36.1 | 0.28 |
Multi | 3GL | 99 | Linear equation | 10.8 | 19.1 | 30.0 | 0.30 | |
Multi | 4GL | 96 | Linear equation | 10.7 | 18.9 | 28.9 | 0.30 | |
Enhancement | MF | 3GL | 440 | Linear equation | 61.6 | 122.2 | 183.6 | 0.42 |
MR | 3GL | 64 | Linear equation | 7.1 | 14.4 | 17.9 | 0.28 | |
Multi | 3GL | 428 | “Plateau” curve | 49.8 | 103.8 | 165.1 | 0.39 | |
Multi | 4GL | 190 | “Plateau” curve | 18.9 | 27.9 | 49.8 | 0.26 | |
PC | 3GL | 53 | Asymptotic equation | 5.3 | 9.2 | 15.1 | 0.28 |
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Alanis-Tamez, M.D.; López-Martín, C.; Villuendas-Rey, Y. Particle Swarm Optimization for Predicting the Development Effort of Software Projects. Mathematics 2020, 8, 1819. https://doi.org/10.3390/math8101819
Alanis-Tamez MD, López-Martín C, Villuendas-Rey Y. Particle Swarm Optimization for Predicting the Development Effort of Software Projects. Mathematics. 2020; 8(10):1819. https://doi.org/10.3390/math8101819
Chicago/Turabian StyleAlanis-Tamez, Mariana Dayanara, Cuauhtémoc López-Martín, and Yenny Villuendas-Rey. 2020. "Particle Swarm Optimization for Predicting the Development Effort of Software Projects" Mathematics 8, no. 10: 1819. https://doi.org/10.3390/math8101819
APA StyleAlanis-Tamez, M. D., López-Martín, C., & Villuendas-Rey, Y. (2020). Particle Swarm Optimization for Predicting the Development Effort of Software Projects. Mathematics, 8(10), 1819. https://doi.org/10.3390/math8101819