Hybrid Bio-Optimized Algorithms for Hyperparameter Tuning in Machine Learning Models: A Software Defect Prediction Case Study
Abstract
:1. Introduction
1.1. Motivation
- Based on the aforementioned explanation, hybrid approaches are becoming more and more popular to enhance the convergence performance of individual algorithms.
- The effectiveness and scalability of hybrid BoAs across diverse scientific domains inspired us to propose novel and competitive hybrid methodologies.
- Hyperparameter tuning can be regarded as an optimization problem, as this process involves searching through a range of objective functions to maximize accuracy.
- The use of hybrid BoAs for solving the hyperparameter tuning problem is motivated by their ability to handle efficient exploration–exploitation trade-offs and scalability.
1.2. Contribution
- Design of an Enhanced GOA named gravitational force Lévy flight grasshopper optimization algorithm (GFLFGOA) by introducing LF and GF concepts to balance the exploration and exploitation nature.
- Design of a novel hybrid gravitational force Lévy flight grasshopper optimization algorithm–sparrow search algorithm (GFLFGOA-SSA) that includes GFLFGOA and the sparrow search algorithm (SSA) concept to accelerate convergence rate.
- Design of a hybrid gravitational force grasshopper optimization algorithm–sparrow search algorithm (GFGOA-SSA) by embedding the concepts of gravitational force grasshopper optimization algorithm (GFGOA) and SSA concepts.
- Design of a hybrid Lévy flight grasshopper optimization algorithm–sparrow search algorithm (LFGOA-SSA).
- Extensive experiments conducted on BFs and hyperparameter tuning of XGB and ANN models to prove the above-proposed algorithm’s superiority to the state-of-the-art techniques.
2. Literature Survey
- bio-optimized approach to optimization problems;
- bio-optimized approach to hyperparameter tuning problems.
2.1. Bio-Optimized Approach to Optimization Problems
2.2. Bio-Optimized Approach for Hyperparameter Tuning Problems
3. Concepts
3.1. Grasshopper Optimization Algorithm (GOA)
- grasshopper position;
- Social interaction;
- Gravitational force;
- Wind advection.
- n Number of grasshoppers;
- Distance from grasshopper to grasshopper;
- Unit Vector from grasshopper to grasshopper.
- grasshopper’s position;
- grasshopper’s position.
- f Intensity of attraction;
- l Attractive length.
- g Gravitational constant;
- Unity vector towards the center of the earth.
- u Constant draft;
- Unity vector in the wind direction.
- and Upper bound and lower bound of the dimension of the grasshopper, respectively;
- Target or optimal position in the dimension (best solution found so far);
- c A decreasing coefficient to shrink the comfort repulsion and attraction areas.
- Maximum value;
- Minimum value;
- r Current iteration;
- G Maximum iteration.
3.2. Lévy Flight GOA (LFGOA)
- s Random step length of Lévy’s flight;
- Power-law index [0, 2].
- Step length for random walk;
- 1.5;
- M Normal standard variable with standard deviation that follows a normal distribution;
- P Normal standard variable with standard deviation that follows a normal distribution.
3.3. Gravitational Force GOA (GFGOA)
- g Gravitational constant (0.9);
- .
3.4. Sparrow Search Algorithm (SSA)
- r Current iteration;
- L Matrix of (1 × d);
- d Dimension of the variable;
- Position of the dimension of the sparrow at iteration r;
- G Maximum iterations;
- Q Random number which obeys a normal distribution;
- Random number [0, 1];
- Alarm value [0, 1];
- ST Safety threshold [0.5, 1.0];
- < ST Signals the predator to search on wide mode, as there are no predators;
- ≥ ST Signals sparrows to fly to another place, as there are predators.
- Current global worst location at iteration r;
- ith sparrow’s current best location obtained so far;
- Q Random number which obeys a normal distribution;
- ;
- A One-dimensional vector [−1, 1];
- i ;
- n Number of sparrows.
- Current global optimal location at iteration r;
- Random number [mean = 0, variance = 1];
- K Random number [−1, 1];
- Current sparrow’s fitness value;
- Current global best value;
- Worst fitness value;
- Constant value (c);
- > Sparrows are at the edge of the group;
- = Sparrows are in the middle of the population.
4. Methodology
4.1. Proposed Algorithm
4.1.1. GFLFGOA Hybrid Algorithm
Algorithm 1: GFLFGOA |
4.1.2. LFGOA-SSA Hybrid Algorithm
Algorithm 2: LFGOA-SSA |
4.1.3. GFGOA-SSA Hybrid Algorithm
Algorithm 3: GFGOA-SSA |
4.1.4. GFLFGOA-SSA Hybrid Algorithm
Algorithm 4: GFLFGOA-SSA |
4.2. Optimization on Benchmark Functions (BFs)
4.3. Software Defect Prediction (SDP) Framework
4.3.1. Data Source
4.3.2. Data Pre-Processing
- Label Encoding: Label encoding is a part of data transformation. It is defined as mapping the non-numeric value into the numeric value. In this research work, the dataset consists of yes (Y) and no (N) labels. Yes (Y) and no (N) are mapped to 0 and 1 in this step, respectively.
- Data Cleaning: In this process, the data are cleaned by removing any outliers, and the inconsistent values are transformed with the mean of the attributes. The outliers are removed and replaced by the inter-quartile range (IQR) method.
- Feature Selection: As the dataset consists of more features, to avoid bias towards only one kind of feature, feature selection is performed using the Pearson correlation coefficient, which is tabulated in Table 3.
- Data Scaling: Normally known as normalization, we performed a min-max scaler for normalization.
4.3.3. Hybrid Bio-Optimized Defect Prediction (HBoDP) Model
5. Results and Discussion
5.1. Parameter Settings
5.1.1. NASA Defect Dataset Description
5.1.2. Hyperparameters of the ML Models
5.2. Results
5.2.1. BF Results
5.2.2. SDP Framework Results
5.3. Analysis
5.3.1. BF Analysis
- Mean Analysis: For a better understanding of the mean analysis of BFs, we presented the discussion based on the types of BFs.
- Fixed-dimension Multimodal BFs (–): GFLFGOA-SSA ranks first, achieving the lowest mean value for , as tabulated in Table 7. But in the case of and , the ranking of the proposed algorithm is the same as the base algorithms. Even though the ranking is the same, the convergence rate is relatively equal to the base algorithms, as visualized in Figure 6d,e.
- Multi-dimension Multimodal BFs (–): Except , GFLFGOA-SSA and LFGOA-SSA rank first for and , respectively. Even though SSA ranks first for , the convergence rate is relatively close to GFLFGOA-SSA, as plotted in Figure 6h.
- SD Analysis: To avoid ambiguity, we elaborated the discussion based on the types of BFs.
- Fixed-dimension Multimodal BFs (–): For , GFLFGOA-SSA achieve the lowest SD value, as tabulated in Table 8. In the case of , all of the other proposed algorithms have equal convergence rates, despite the fact that SSA ranks first, as plotted in Figure 6d, while in the case of , the convergence rate of GFGOA is nearly identical to that of the proposed algorithm, despite the SD being zero.
- Multi-dimension Multimodal BFs (–): From Table 8, it can be clearly stated that any one of our proposed algorithms ranks first for –. GFLFGOA-SSA, GFLFGOA, and LFGOA-SSA achieve the lowest SD value for , and , respectively.
5.3.2. SDP Framework Analysis
- Algorithm Accuracy Analysis: From Table 9 and Table 11, it can be clearly stated that for all datasets, there is an enhancement in accuracy when the XGB and ANN models are tuned with BoAs. As tabulated in Table 13, in the case of JM1, MW1, PC1, PC3, PC4, and PC5, our proposed algorithms have better optimization effects as compared to the four base algorithms, while in the cases of CM1, KC3, KC4, MC1, and PC2, the superiority of the proposed algorithm is relatively close to the base approaches. In hyperparameter tuning of the ANN model, GFGOA-SSA, GFLFGOA-SSA, and GFGOA-SSA show better accuracy for JM1, PC3, and PC5, respectively. For the remaining datasets, the superiority of our algorithms is relatively close or equal to the base approaches, as shown in Table 11 and Table 14.
- Algorithm Runtime Analysis: From Table 10, we can justify that the computational runtime is lowest for all datasets except CM1 and MW1 by embedding either the LF or GF or both concepts into the SSA. For CM1 and MW1, the difference in runtime is not too great compared to LFGOA. For CM1, JM1, KC1, KC4, MC1, MW1, PC1, PC3, and PC5, the base algorithm’s computational runtime is low as compared to the proposed algorithm, as listed in Table 12, whereas for other datasets, our proposed algorithm’s runtime shows superiority.
5.3.3. Computational Complexity Analysis
- Time Complexity: In general, the time complexity can be defined as follows:Time Complexity = O(Initialization) + [O(Fitness evaluation of each search agent) + O(Position updation of agents) + O(Sorting)] ∗ Maximum iteration.Mathematically, this can be coded as follows:
- Space Complexity: The maximum number of spaces occupied by the proposed algorithm at any time is decided by the random initialization of the population. So, the space complexity can be calculated as follows:
6. Concluding Remarks and Future Scope
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Symbols | Explanation |
---|---|
r | Current iteration |
G | Maximum iteration |
ST | Safety Threshold [0.5, 1.0] |
SD | Scrounger Sparrow |
PD | Producer Sparrow |
Return the best position and the corresponding fitness value. With respect to our flowchart, as drawn in Figure 1, Figure 2, Figure 3 and Figure 4, returns the current best individual after the initialization step, whereas, after the condition becomes false, returns the global best position and the corresponding fitness value. |
Name | Mathematical Equation | Type | (n, G, dim) | Range | |
---|---|---|---|---|---|
Quartic | Unimodal | 100, 200, 30 | [−1.28,1.28] | 0 | |
Rosenbrock | Unimodal | 100, 200, 30 | [−30, 30] | 0 | |
Schwefel 2.21 | Unimodal | 100, 200, 30 | [−100, 100] | 0 | |
Six Hump Camel | Fixed-dimension Multimodal | 100, 200, 2 | [−5, 5] | −1.0316 | |
Branin | Fixed-dimension Multimodal | 100, 200, 2 | [−5, 0, 10, 15] | 0.397887 | |
Booth | Fixed-dimension Multimodal | 100, 200, 2 | [−10, 10] | 0 | |
Zakharov | Mullti-dimension Multimodal | 100, 200, 30 | [−5, 10] | 0 | |
Rastrigin | Multi-dimension Multimodal | 100, 200, 30 | [−5.12, 5.12] | 0 | |
Schaffer 6 | Multi-dimension Multimodal | 100, 200, 30 | [−100, 100] | 0 |
Dataset | Description | Target Feature | Original Features | Selected Features | Instances |
---|---|---|---|---|---|
CM1 | Spacecraft instrument’s software | Defective | 38 | 26 | 327 |
JM1 | Real-time predictive ground system | label | 22 | 16 | 10,878 |
KC1 | spacecraft’s ground data system (storage management) | Defective | 22 | 15 | 2107 |
KC3 | Flight software system | Defective | 40 | 25 | 194 |
KC4 | Software system related to spacecraft operations | Defective | 41 | 35 | 125 |
MC1 | Spacecraft’s data processing system | Defective | 40 | 30 | 9466 |
MC2 | spacecraft’s power distribution software system | Defective | 40 | 27 | 124 |
MW1 | Ground data system for a weather satellite | Defective | 38 | 28 | 250 |
PC1 | Air traffic control software system | Defective | 38 | 26 | 679 |
PC2 | Spacecraft’s altitude control software system | Defective | 37 | 25 | 722 |
PC3 | University’s administration software system | Defective | 38 | 25 | 1053 |
PC4 | Spacecraft’s orbit determination software system | Defective | 38 | 27 | 1270 |
PC5 | Satellite’s ground software system | Defective | 39 | 26 | 1694 |
Hyperparameters | Lower Bound | Upper Bound |
---|---|---|
Learning rate | 0.001 | 0.1 |
Neurons in layer1 | 8 | 10 |
Neurons in layer 2 | 6 | 10 |
Batch size | 4 | 32 |
Epochs | 10 | 50 |
Hyperparameters | Lower Bound | Upper Bound |
---|---|---|
Learning rate | 0.001 | 0.1 |
Max depth | 3 | 18 |
Subsample | 0 | 1 |
N estimator | 50 | 200 |
Specification | Size |
---|---|
RAM | 32 GB |
Hard Disk | 512 GB |
Processor | Intel core I7 |
OS Name | Ubuntu |
OS Type | 64-bit |
BF | Index | GFLFGOA | GFLFGOA-SSA | LFGOA-SSA | GFGOA-SSA | LFGOA | GFGOA | GOA | SSA |
---|---|---|---|---|---|---|---|---|---|
Mean | |||||||||
Rank | 7 | 3 | 4 | 2 | 5 | 8 | 6 | 1 | |
Mean | |||||||||
Rank | 6 | 2 | 4 | 1 | 7 | 5 | 8 | 3 | |
Mean | |||||||||
Rank | 6 | 3 | 4 | 2 | 8 | 5 | 7 | 1 | |
Mean | |||||||||
Rank | 5 | 2 | 1 | 4 | 2 | 6 | 3 | 1 | |
Mean | |||||||||
Rank | 4 | 2 | 2 | 2 | 1 | 5 | 3 | 1 | |
Mean | |||||||||
Rank | 8 | 1 | 2 | 3 | 4 | 6 | 5 | 7 | |
Mean | |||||||||
Rank | 7 | 1 | 4 | 3 | 6 | 8 | 5 | 2 | |
Mean | |||||||||
Rank | 8 | 4 | 2 | 3 | 5 | 7 | 6 | 1 | |
Mean | |||||||||
Rank | 6 | 4 | 1 | 3 | 7 | 5 | 8 | 2 |
BF | Index | GFLFGOA | GFLFGOA-SSA | LFGOA-SSA | GFGOA-SSA | LFGOA | GFGOA | GOA | SSA |
---|---|---|---|---|---|---|---|---|---|
SD | |||||||||
Rank | 1 | 5 | 6 | 4 | 8 | 2 | 7 | 3 | |
SD | |||||||||
Rank | 6 | 2 | 4 | 1 | 7 | 5 | 8 | 3 | |
SD | |||||||||
Rank | 7 | 2 | 4 | 3 | 5 | 8 | 6 | 1 | |
SD | |||||||||
Rank | 8 | 5 | 2 | 7 | 6 | 4 | 3 | 1 | |
SD | |||||||||
Rank | 8 | 5 | 6 | 3 | 4 | 1 | 7 | 2 | |
SD | |||||||||
Rank | 7 | 1 | 2 | 3 | 5 | 8 | 4 | 6 | |
SD | |||||||||
Rank | 4 | 1 | 8 | 3 | 7 | 5 | 6 | 2 | |
SD | |||||||||
Rank | 1 | 6 | 4 | 5 | 8 | 2 | 7 | 3 | |
SD | |||||||||
Rank | 7 | 4 | 1 | 3 | 6 | 5 | 8 | 2 |
Dataset | Without Optimization | GFLFGOA | GFLFGOA-SSA | LFGOA-SSA | GFGOA-SSA | LFGOA | GFGOA | GOA | SSA |
---|---|---|---|---|---|---|---|---|---|
CM1 | 0.89024 | 0.93902 | 0.93902 | 0.92683 | 0.93902 | 0.92683 | 0.92683 | 0.92683 | 0.93902 |
JM1 | 0.81066 | 0.81471 | 0.81507 | 0.81434 | 0.81691 | 0.81434 | 0.81213 | 0.81397 | 0.81654 |
KC1 | 0.86338 | 0.87666 | 0.87666 | 0.87097 | 0.87666 | 0.86717 | 0.87856 | 0.86907 | 0.87856 |
KC3 | 0.81633 | 0.85714 | 0.85714 | 0.85714 | 0.85714 | 0.83674 | 0.85714 | 0.83674 | 0.85714 |
KC4 | 0.6875 | 0.75 | 0.78125 | 0.78125 | 0.78125 | 0.71875 | 0.78125 | 0.75 | 0.75 |
MC1 | 0.99451 | 0.99620 | 0.99662 | 0.99620 | 0.99620 | 0.99535 | 0.99662 | 0.99620 | 0.99620 |
MC2 | 0.70968 | 0.83871 | 0.83871 | 0.83871 | 0.83871 | 0.80645 | 0.83871 | 0.838710 | 0.90323 |
MW1 | 0.88 | 0.90476 | 0.90476 | 0.90476 | 0.92064 | 0.90476 | 0.90476 | 0.90476 | 0.90476 |
PC1 | 0.91176 | 0.92941 | 0.92941 | 0.92941 | 0.93529 | 0.91765 | 0.92353 | 0.92941 | 0.92941 |
PC2 | 0.98895 | 0.99448 | 0.99448 | 0.99448 | 0.99448 | 0.99448 | 0.99448 | 0.99448 | 0.99448 |
PC3 | 0.86364 | 0.88258 | 0.88258 | 0.875 | 0.88258 | 0.87879 | 0.87879 | 0.875 | 0.875 |
PC4 | 0.90252 | 0.94025 | 0.93306 | 0.93082 | 0.93082 | 0.93711 | 0.93711 | 0.92453 | 0.93082 |
PC5 | 0.77830 | 0.82075 | 0.80896 | 0.81132 | 0.81604 | 0.81368 | 0.81604 | 0.81132 | 0.81604 |
Dataset | GFLFGOA | GFLFGOA-SSA | LFGOA-SSA | GFGOA-SSA | LFGOA | GFGOA | GOA | SSA |
---|---|---|---|---|---|---|---|---|
CM1 | 8.63894 | 2.62227 | 5.97816 | 8.16711 | 6.80014 | 4.67062 | 17.40778 | 4.14228 |
JM1 | 49.11337 | 11.16519 | 23.01613 | 6.44055 | 20.11788 | 18.97812 | 100.45693 | 32.35944 |
KC1 | 10.98801 | 13.28012 | 4.71760 | 2.79241 | 9.85696 | 7.21173 | 30.87882 | 6.74143 |
KC3 | 5.16992 | 4.89649 | 4.92847 | 3.61582 | 7.55046 | 2.61733 | 11.18174 | 7.2783 |
KC4 | 3.37044 | 2.72615 | 1.03054 | 8.00315 | 3.01872 | 7.93459 | 7.89999 | 10.81161 |
MC1 | 20.06377 | 16.28936 | 17.45409 | 3.18721 | 20.94327 | 10.61918 | 36.69793 | 7.54776 |
MC2 | 6.51045 | 7.53665 | 6.08344 | 3.0346 | 4.42068 | 3.79698 | 19.6863 | 5.38492 |
MW1 | 11.61992 | 8.84075 | 8.75449 | 8.91545 | 6.90571 | 7.68827 | 17.27596 | 14.46098 |
PC1 | 16.15804 | 5.14336 | 2.1437 | 7.26307 | 5.33309 | 11.99368 | 7.72782 | 13.36885 |
PC2 | 8.65440 | 7.13130 | 4.98462 | 8.60696 | 9.58645 | 5.79961 | 6.66192 | 12.31117 |
PC3 | 15.00149 | 16.57482 | 8.22984 | 3.48169 | 11.09310 | 4.54789 | 25.59780 | 11.45645 |
PC4 | 11.35519 | 12.56271 | 9.46519 | 11.60129 | 18.41754 | 14.41984 | 31.31732 | 43.08894 |
PC5 | 14.16040 | 3.07928 | 8.78662 | 7.02953 | 22.22073 | 8.27753 | 20.31468 | 21.10666 |
Dataset | Without Optimization | GFLFGOA | GFLFGOA-SSA | LFGOA-SSA | GFGOA-SSA | LFGOA | GFGOA | GOA | SSA |
---|---|---|---|---|---|---|---|---|---|
CM1 | 0.87805 | 0.93902 | 0.95122 | 0.93902 | 0.93902 | 0.91463 | 0.93902 | 0.91463 | 0.95122 |
JM1 | 0.79669 | 0.81471 | 0.81544 | 0.81397 | 0.81581 | 0.81544 | 0.81544 | 0.81360 | 0.81544 |
KC1 | 0.84820 | 0.87476 | 0.86907 | 0.87287 | 0.87287 | 0.87287 | 0.87097 | 0.87856 | 0.88046 |
KC3 | 0.77551 | 0.85714 | 0.85714 | 0.87755 | 0.85714 | 0.83674 | 0.85714 | 0.87755 | 0.85714 |
KC4 | 0.5625 | 0.71875 | 0.71875 | 0.8125 | 0.78125 | 0.71875 | 0.84375 | 0.71875 | 0.75 |
MC1 | 0.99408 | 0.99578 | 0.99535 | 0.99578 | 0.99535 | 0.99471 | 0.99578 | 0.99535 | 0.99578 |
MC2 | 0.74194 | 0.83871 | 0.83871 | 0.87097 | 0.87097 | 0.83871 | 0.90323 | 0.87097 | 0.87097 |
MW1 | 0.88889 | 0.93651 | 0.93651 | 0.93651 | 0.93651 | 0.93651 | 0.93651 | 0.93651 | 0.93651 |
PC1 | 0.89412 | 0.94118 | 0.94706 | 0.94706 | 0.93529 | 0.92941 | 0.94118 | 0.94706 | 0.93529 |
PC2 | 0.98895 | 1 | 1 | 1 | 1 | 0.99448 | 1 | 0.99448 | 0.99448 |
PC3 | 0.82576 | 0.86742 | 0.88258 | 0.87879 | 0.87121 | 0.875 | 0.87879 | 0.85606 | 0.875 |
PC4 | 0.90252 | 0.93082 | 0.92767 | 0.92453 | 0.93082 | 0.93396 | 0.93082 | 0.93711 | 0.94339 |
PC5 | 0.74057 | 0.81132 | 0.80425 | 0.80660 | 0.81368 | 0.80660 | 0.80660 | 0.80660 | 0.80896 |
Dataset | GFLFGOA | GFLFGOA-SSA | LFGOA-SSA | GFGOA-SSA | LFGOA | GFGOA | GOA | SSA |
---|---|---|---|---|---|---|---|---|
CM1 | 14.15148 | 19.03989 | 10.93558 | 14.25837 | 19.88457 | 20.53972 | 49.70118 | 59.26953 |
JM1 | 329.74139 | 461.88978 | 280.21241 | 258.71992 | 372.32476 | 428.38037 | 100.74072 | 677.38826 |
KC1 | 67.28775 | 40.93038 | 34.27968 | 43.71838 | 33.20376 | 27.49754 | 127.15726 | 370.54866 |
KC3 | 16.96921 | 10.03377 | 16.24724 | 22.79089 | 10.27701 | 12.48286 | 22.32237 | 25.73986 |
KC4 | 13.65393 | 17.94655 | 11.18101 | 10.96659 | 28.47858 | 8.85138 | 16.14852 | 30.20686 |
MC1 | 403.20674 | 185.79484 | 196.88806 | 375.0098 | 138.50669 | 213.44733 | 413.83031 | 505.23935 |
MC2 | 20.73147 | 9.0823 | 9.80959 | 16.01918 | 12.00442 | 12.04628 | 13.47418 | 26.23941 |
MW1 | 25.6989 | 10.81326 | 11.2502 | 16.40268 | 13.56527 | 9.44403 | 17.95148 | 27.54926 |
PC1 | 26.2941 | 24.40644 | 19.09213 | 19.34053 | 24.48024 | 33.99985 | 17.26851 | 58.35074 |
PC2 | 10.24549 | 54.52347 | 33.17081 | 26.83333 | 36.66479 | 101.2086 | 22.20873 | 41.70491 |
PC3 | 19.32979 | 33.10067 | 32.45259 | 40.49498 | 14.1666 | 31.19656 | 23.19152 | 71.15856 |
PC4 | 28.11799 | 30.82265 | 35.64099 | 32.15147 | 68.57497 | 45.70245 | 31.37875 | 100.55374 |
PC5 | 287.27928 | 72.0665 | 62.88953 | 70.00658 | 27.62535 | 30.31593 | 46.86406 | 91.27525 |
Dataset | Accuracy (Highest) | Runtime (Lowest) |
---|---|---|
CM1 | GFLFGOA-SSA, GFLFGOA, GFGOA-SSA, SSA | GFLFGOA-SSA |
JM1 | GFGOA-SSA | GFGOA-SSA |
KC1 | GFGOA, SSA | GFGOA-SSA |
KC3 | GFGOA, GFLFGOA-SSA, SSA, GFGOA-SSA, GFLFGOA | GFGOA |
KC4 | GFGOA-SSA, GFGOA, LFGOA-SSA, GFLFGOA-SSA | LFGOA-SSA |
MC1 | GFLFGOA-SSA, GFGOA | GFGOA-SSA |
MC2 | SSA | GFGOA-SSA |
MW1 | GFGOA-SSA | LFGOA |
PC1 | GFGOA-SSA | LFGOA-SSA |
PC2 | GFLFGOA, GFLFGOA-SSA, LFGOA-SSA, GFGOA-SSA, LFGOA, GFGOA, GOA, SSA | LFGOA-SSA |
PC3 | GFGOA-SSA, GFLFGOA, GFLFGOA-SSA | GFGOA-SSA |
PC4 | GFLFGOA | LFGOA-SSA |
PC5 | GFLFGOA | GFLFGOA-SSA |
Dataset | Accuracy (Highest) | Runtime (Lowest) |
---|---|---|
CM1 | GFLFGOA-SSA, SSA | GOA |
JM1 | GFGOA-SSA | GOA |
KC1 | SSA | GFGOA |
KC3 | LFGOA-SSA, GOA | GFLFGOA-SSA |
KC4 | GFGOA | GFGOA |
MC1 | GFLFGOA, LFGOA-SSA, GFGOA, SSA | LFGOA |
MC2 | GFGOA | GFLFGOA-SSA |
MW1 | GFLFGOA, GFLFGOA-SSA, LFGOA-SSA, GFGOA-SSA, LFGOA, GFGOA, GOA, SSA | GFGOA |
PC1 | GFLFGOA-SSA, LFGOA-SSA, GOA | GOA |
PC2 | GFGOA-SSA, GFGOA, GFLFGOA, GFLFGOA-SSA, LFGOA-SSA | GFLFGOA |
PC3 | GFLFGOA-SSA | LFGOA |
PC4 | SSA | GFLFGOA |
PC5 | GFGOA-SSA | LFGOA |
Datasets | CM1 | JM1 | KC1 | KC3 | KC4 | MC1 | MC2 | MW1 | PC1 | PC2 | PC3 | PC4 | PC5 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[67] | 0.8687 | 0.7912 | - | - | - | - | 0.6842 | 0.8933 | 0.9216 | - | 0.8797 | 0.8714 | - |
[57] | 0.83 | 0.78 | - | - | - | - | 0.68 | - | 0.91 | - | 0.84 | 0.84 | - |
[56] | 0.878 | 0.803 | 0.850 | - | - | - | - | - | 0.922 | - | - | - | - |
[68] | - | 0.89 | 0.84 | - | - | 0.95 | - | - | 0.85 | 0.86 | 0.83 | 0.89 | 0.91 |
[48] | - | 0.81 | 0.79 | - | - | - | - | - | - | - | 0.89 | - | - |
[59] | 0.7755 | 0.7396 | - | - | - | - | 0.6486 | 0.8266 | - | - | 0.8259 | 0.8608 | - |
[69] | 0.8179 | - | - | - | - | - | - | - | 0.8979 | - | - | - | - |
[70] | - | - | - | - | - | - | - | - | - | - | 0.8192 | - | - |
[71] | - | - | - | - | - | - | 0.6832 | 0.6005 | - | - | 0.737 | 0.869 | - |
[72] | - | - | - | - | - | - | - | - | - | - | - | 0.8661 | - |
[53] (GA-SVM) | 0.9035 | - | 0.8514 | 0.7989 | 0.9035 | 0.9950 | 0.6710 | 0.9183 | 0.9367 | 0.9959 | 0.9014 | 0.8821 | - |
[53] (PSO-SVM) | 0.9037 | - | 0.8514 | 0.9040 | 0.6885 | 0.9950 | 0.6706 | 0.9179 | 0.9367 | 0.9959 | 0.9021 | 0.8793 | - |
[53] (GAPSO-SVM) | 0.9049 | - | 0.8438 | 0.8995 | 0.6782 | 0.9951 | 0.6783 | 0.9157 | 0.9386 | 0.9959 | 0.9040 | 0.8779 | - |
Proposed (GFLFGOA-XGB) | 0.9390 | 0.8147 | 0.8767 | 0.8571 | 0.75 | 0.9962 | 0.8387 | 0.9048 | 0.9294 | 0.9945 | 0.8826 | 0.9403 | 0.8208 |
Proposed (GFLFGOA-SSA-XGB) | 0.9390 | 0.8151 | 0.8767 | 0.8571 | 0.7813 | 0.9966 | 0.8387 | 0.9048 | 0.9294 | 0.9945 | 0.8826 | 0.9331 | 0.8090 |
Proposed (LFGOA-SSA-XGB) | 0.9268 | 0.8143 | 0.8710 | 0.8571 | 0.7813 | 0.9962 | 0.8387 | 0.9048 | 0.9294 | 0.9945 | 0.875 | 0.9308 | 0.8113 |
Proposed (GFGOA-SSA-XGB) | 0.9390 | 0.8169 | 0.8767 | 0.8571 | 0.7813 | 0.9962 | 0.8387 | 0.9206 | 0.9353 | 0.9945 | 0.8826 | 0.9308 | 0.8160 |
Proposed (GFLFGOA-ANN) | 0.9390 | 0.8147 | 0.8748 | 0.8571 | 0.7188 | 0.9958 | 0.8387 | 0.9365 | 0.9412 | 1.0 | 0.8674 | 0.9308 | 0.8113 |
Proposed (GFLFGOA-SSA-ANN) | 0.9512 | 0.8154 | 0.8691 | 0.8571 | 0.7188 | 0.9954 | 0.8387 | 0.9365 | 0.9471 | 1.0 | 0.8826 | 0.9277 | 0.8043 |
Proposed (LFGOA-SSA-ANN) | 0.9390 | 0.8140 | 0.8729 | 0.8776 | 0.8125 | 0.9958 | 0.8710 | 0.9365 | 0.9471 | 1.0 | 0.8788 | 0.9245 | 0.8066 |
Proposed (GFGOA-SSA-ANN) | 0.9390 | 0.8158 | 0.8729 | 0.8571 | 0.7813 | 0.9954 | 0.8710 | 0.9365 | 0.9353 | 1.0 | 0.8712 | 0.9308 | 0.8137 |
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Das, M.; Mohan, B.R.; Guddeti, R.M.R.; Prasad, N. Hybrid Bio-Optimized Algorithms for Hyperparameter Tuning in Machine Learning Models: A Software Defect Prediction Case Study. Mathematics 2024, 12, 2521. https://doi.org/10.3390/math12162521
Das M, Mohan BR, Guddeti RMR, Prasad N. Hybrid Bio-Optimized Algorithms for Hyperparameter Tuning in Machine Learning Models: A Software Defect Prediction Case Study. Mathematics. 2024; 12(16):2521. https://doi.org/10.3390/math12162521
Chicago/Turabian StyleDas, Madhusmita, Biju R. Mohan, Ram Mohana Reddy Guddeti, and Nandini Prasad. 2024. "Hybrid Bio-Optimized Algorithms for Hyperparameter Tuning in Machine Learning Models: A Software Defect Prediction Case Study" Mathematics 12, no. 16: 2521. https://doi.org/10.3390/math12162521