TWGH: A Tripartite Whale–Gray Wolf–Harmony Algorithm to Minimize Combinatorial Test Suite Problem
Abstract
:1. Introduction
- (1)
- A creative strategy to combine the three strategies in a hybrid approach;
- (2)
- An HSA algorithm incorporated into WOA and GWO by utilizing a modified mechanism;
- (3)
- Additionally, an asynchronous approach, employed to improve accuracy.
2. Related Work
3. Covering Array
4. Metaheuristic Algorithms
4.1. Whale Optimization Algorithm
Algorithm 1 Whale Optimization Algorithm |
Input population size N, halt criteria Output the best solution X* Generate initial population Xi (i = 1, 2,...,N) Calculate the fitness for each solution in the population Find the best solution X* with the best fitness while halt criteria not satisfied do Update a for i=1 to N do Update WOA parameters (A, C, l, and p) for j=1 to m do if p < 0.5 then if |A| < 1 then Update the current search agent by else if |A| ≥ 1 then Select a random search agent (Xrnd) Update the current search agent by end if else if p > 0.5 then Update the current search agent by end if end for Evaluate the search agent X* end for Find the best solution X* end while |
4.2. Gray Wolf Optimizer
Algorithm 2 Grey Wolf Optimization Algorithm |
Input population size of wolves’ pop, MaxIter Output optimal grey wolf position Xα Initialize the grey wolf population Xi Randomly initialize a, A and C Determine the fitness of each wolf Xi Xα = the best solution Xβ = the second best solution Xδ = the third best solution while i ≤ MaxIter do for each wolf Xi do update the position end for update a, A and C determine the fitness of each wolf Xi update Xα, Xβ and Xδ i = i + 1 end while return Xα |
4.3. Harmony Search Algorithm
- (1)
- An old pitch from the musician’s recollection is played back;
- (2)
- The adjacent stored pitch is played;
- (3)
- Any pitch that falls within the normal range is played.
- (1)
- A memory value is chosen from among those already stored there;
- (2)
- Some adjacent values to the recorded data are chosen;
- (3)
- An arbitrary number that falls within the standard range is chosen.
Algorithm 3 Harmony Search Algorithm |
Input Generate the initial harmonics randomly Output Optimal solution with its fitness value Initialize the parameters of the HS HMCR, PAR and etc Initialize harmony memory (HM) Evaluate all solutions using the fitness function while Termination criteria do new solution = 0 if rand HMCR then Memory consideration if rand < PAR then Pitch adjustment end if else Random consideration end if Evaluate the fitness function of the new solution Replaces the worst solution in HM by the new solution end while |
5. Proposed Work
Algorithm 4 Pseudo Code of TWGH |
Initialize the population for GWO and WAO Calculate the fitness of each search agent X* is the best search member While (it < MaxIter) For every search agent do Calculate a, A, C, L, and p. if (p < 0.5) then if (A < 1)then update the position of the current search member by else if (A ≥ 1) then Select a random search agent (Xrnd). Update the current search agent by end if else if (p ≥ 0.5) then update the position of the present search member by using Equations (1) and (2). end if end for Find the fitness of all search members If (Objective function of current agent > Objective function of previous position) then Initialize the parameters of the HS HMCR, PAR and etc Initialize harmony memory (HM) Evaluate all solutions using the fitness function while Termination criteria do new solution = 0 if rand HMCR then Memory consideration if rand < PAR then Pitch adjustment end if else Random consideration end if Evaluate the fitness function of the new solution Replaces the worst solution in HM by the new solution end while return to while loop else Update it = it+1 end while return |
6. Results and Discussion
7. Statistical Evaluation
8. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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t | Jenny | TConfig | WHITCH | IPOG | MIPOG | TVG | GTHS | ABCVS | HABC | HABCm | HGHC | Proposed TWGH |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 10 | 9 | 6 | 10 | NA | 10 | 7 | NA | NA | NA | 7 | 6 |
3 | 18 | 20 | 18 | 19 | NA | 17 | 16 | NA | NA | NA | 17 | 16 |
4 | 39 | 45 | 58 | 49 | NA | 41 | 37 | NA | NA | NA | 38 | 36 |
5 | 87 | 95 | NS | 128 | NA | 84 | 81 | NA | NA | NA | 80 | 80 |
6 | 169 | 183 | NS | 352 | NA | 168 | 158 | NA | NA | NA | 175 | 155 |
7 | 311 | NS | NS | NS | NA | 302 | 298 | NA | NA | NA | 300 | 300 |
8 | 521 | NS | NS | NS | NA | 514 | 498 | NA | NA | NA | 505 | 500 |
9 | 788 | NS | NS | NS | NA | 651 | 512 | NA | NA | NA | NA | 510 |
10 | 1024 | NS | NS | NS | NA | NS | 1024 | NA | NA | NA | NA | 1022 |
t | Jenny | TConfig | WHITCH | IPOG | MIPOG | TVG | GTHS | ABCVS | HABC | HABCm | HGHC | Proposed TWGH |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 45 | 48 | 45 | 50 | 45 | 50 | 43 | NA | NA | NA | 43 | 45 |
3 | 225 | 312 | 225 | 313 | 281 | 342 | 276 | NA | NA | NA | 236 | 225 |
4 | 1719 | 1878 | 1750 | 1965 | 1643 | 1971 | 1624 | NA | NA | NA | 1770 | 1625 |
5 | 9437 | NA | NS | 11,009 | 8169 | NA | 8866 | NA | NA | NA | 9933 | 8199 |
6 | NA | NA | NS | 57,290 | 45,168 | NA | 51,001 | NA | NA | NA | 45,339 | 45,244 |
7 | NA | NS | NS | NS | NA | NA | 225,924 | NA | NA | NA | 299,336 | 225,578 |
8 | NA | NS | NS | NS | NA | NA | 990,966 | NA | NA | NA | 994,339 | 990,023 |
9 | NA | NS | NS | NS | NA | NA | 2,971,150 | NA | NA | NA | NA | 2,971,022 |
10 | NA | NS | NS | NS | NA | NS | 9,765,624 | NA | NA | NA | NA | 9,765,145 |
t | Jenny | TConfig | WHITCH | IPOG | MIPOG | TVG | GTHS | ABCVS | HABC | HABCm | HGHC | Proposed TWGH |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 16 | 15 | 15 | 17 | NA | 16 | 14 | 15 | 15 | 14 | 14 | 14 |
3 | 51 | 55 | 55 | 57 | NA | 54 | 50 | 49 | 47 | 46 | 50 | 48 |
4 | 169 | 166 | 216 | 185 | NA | 167 | 157 | 157 | 155 | 149 | 150 | 147 |
5 | 458 | 477 | NS | 561 | NA | 463 | 437 | 442 | 438 | 437 | 440 | 435 |
6 | 1089 | 921 | NS | 1281 | NA | 1049 | 916 | 944 | 836 | 729 | 778 | 725 |
7 | 2187 | NA | NS | NS | NA | NS | 2187 | NA | NA | NA | 2202 | 2184 |
k | Jenny | TConfig | WHITCH | IPOG | MIPOG | TVG | GTHS | ABCVS | HABC | HABCm | HGHC | Proposed TWGH |
---|---|---|---|---|---|---|---|---|---|---|---|---|
5 | 837 | 773 | 625 | 908 | 625 | 849 | 751 | NA | 759 | 750 | 730 | 625 |
6 | 1074 | 1092 | 625 | 1239 | 625 | 1128 | 990 | NA | 1000 | 996 | 956 | 625 |
7 | 1248 | 1320 | 1750 | 1349 | 1125 | 1384 | 1186 | NA | 1189 | 1179 | 1230 | 1132 |
8 | 1424 | 1532 | 1750 | 1792 | 1384 | 1595 | 1358 | NA | 1386 | 1354 | 1395 | 1351 |
9 | 1578 | 1724 | 1750 | 1793 | 1543 | 1795 | 1530 | NA | 1591 | 1526 | 1530 | 1523 |
10 | 1791 | 1878 | 1750 | 1965 | 1643 | 1971 | 1624 | NA | 1798 | 1718 | 1697 | 1624 |
11 | 1839 | 2038 | 1750 | 2091 | 1722 | 2122 | 1860 | NA | NA | NA | 1730 | 1734 |
12 | 1964 | NA | 1750 | 2285 | 1837 | 2268 | 2022 | NA | NA | NA | 1834 | 1755 |
v | Jenny | TConfig | WHITCH | IPOG | MIPOG | TVG | GTHS | ABCVS | HABS | HABSm | HGHC | Proposed TWGH |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 39 | 45 | 58 | 49 | 43 | 40 | 39 | NA | NA | NA | 43 | 38 |
3 | 221 | 235 | 336 | 241 | 217 | 228 | 211 | NA | NA | NA | 218 | 211 |
4 | 703 | 718 | 704 | 707 | 637 | 782 | 691 | NA | NA | NA | 664 | 639 |
5 | 1719 | 1878 | 1750 | 1965 | 1643 | 1917 | 1624 | NA | NA | NA | 1625 | 1622 |
6 | 3519 | NA | NA | 3935 | 3657 | 4159 | 3475 | NA | NA | NA | 3464 | 3464 |
7 | 6462 | NA | NA | 7061 | 5927 | 7854 | 6399 | NA | NA | NA | 6125 | 5929 |
Configurations | Jenny | TConfig | WHITCH | IPOG | MIPOG | TVG | GTHS | HGHC | Proposed TWGH |
---|---|---|---|---|---|---|---|---|---|
MCA (N; 4, 34 45) | 457 | 499 | 704 | 463 | NA | 487 | 436 | 445 | 438 |
MCA (N; 4, 51 38 22) | 303 | 302 | 1683 | 324 | NA | 313 | 286 | 300 | 285 |
MCA (N; 4, 82 72 62 52) | 4580 | 4317 | 4085 | 4776 | NA | 5124 | 4395 | 4090 | 4085 |
MCA (N; 4, 65 54 32) | 3033 | NA | NA | 3273 | NA | 2881 | 2520 | 2656 | 2520 |
MCA (N; 4, 101 91 81 71 61 51 41 31 21) | 6138 | 5495 | 5922 | 5492 | NA | 6698 | 5915 | 5955 | 5485 |
Pairs | Ranks | Test Statistics | Conclusion | ||||
---|---|---|---|---|---|---|---|
TWGH < | TWGH > | TWGH = | Z | Asymp. Sig. (2- tailed) | α Holm | ||
TWGH-GTHS | 15 | 11 | 11 | 2.02260 | 0.0591 | 0.0025 | Retain the null hypothesis |
TWGH-HGHC | 6 | 3 | 0 | 2.0226 | 0.0101 | 0.0125 | Retain the null hypothesis |
TWGH-IPOG | 3 | 0 | 0 | 2.2014 | 0.0361 | 0.0171 | Reject the null hypothesis |
TWGH-Jenny | 7 | 4 | 4 | 2.2014 | 0.0546 | 0.0173 | Reject the null hypothesis |
TWGH-HABCm | 6 | 3 | 3 | 1.5724 | 0.0141 | 0.0014 | Retain the null hypothesis |
TWGH-TVG | 4 | 0 | 1 | 2.2014 | 0.0363 | 0.2301 | Reject the null hypothesis |
TWGH-WHITCH | 7 | 4 | 4 | 2.2014 | 0.0546 | 0.0163 | Reject the null hypothesis |
Pairs | Ranks | Test Statistics | Conclusion | ||||
---|---|---|---|---|---|---|---|
TWGH < | TWGH > | TWGH = | Z | Asymp. Sig. (2- tailed) | α Holm | ||
TWGH-GTHS | 3 | 2 | 2 | 1.0954 | 0.0363 | 0.0641 | Retain the null hypothesis |
TWGH-HGHC | 11 | 7 | 7 | 1.0226 | 0.0591 | 0.0573 | Reject the null hypothesis |
TWGH-IPOG | 5 | 3 | 3 | 2.0226 | 0.0691 | 0.0472 | Reject the null hypothesis |
TWGH-Jenny | 5 | 1 | 1 | 2.0432 | 0.0786 | 0.0435 | Reject the null hypothesis |
TWGH-TVG | 6 | 3 | 0 | 2.678 | 0.0978 | 0.0349 | Reject the null hypothesis |
TWGH-WHITCH | 4 | 2 | 1 | 2.9226 | 0.0991 | 0.0322 | Reject the null hypothesis |
Pairs | Ranks | Test Statistics | Conclusion | ||||
---|---|---|---|---|---|---|---|
TWGH < | TWGH > | TWGH = | Z | Asymp. Sig. (2- tailed) | α Holm | ||
TWGH-GTHS | 13 | 11 | 11 | 2.3664 | 0.0220 | 0.0213 | Reject the null hypothesis |
TWGH-HGHC | 3 | 1 | 1 | 2.3805 | 0.0209 | 0.017 | Reject the null hypothesis |
TWGH-IPOG | 15 | 11 | 11 | 2.5205 | 0.0143 | 0.0127 | Reject the null hypothesis |
TWGH-Jenny | 6 | 0 | 2 | 2.5205 | 0.0183 | 0.0142 | Reject the null hypothesis |
TWGH-MIPOG | 7 | 3 | 3 | 1.5724 | 0.1422 | 0.0085 | Retain the null hypothesis |
TWGH-TVG | 5 | 0 | 2 | 2.5205 | 0.0143 | 0.0107 | Reject the null hypothesis |
TWGH-WHITCH | 3 | 1 | 1 | 1.9917 | 0.0592 | 0.00125 | Retain the null hypothesis |
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Fadhil, H.M.; Abdullah, M.N.; Younis, M.I. TWGH: A Tripartite Whale–Gray Wolf–Harmony Algorithm to Minimize Combinatorial Test Suite Problem. Electronics 2022, 11, 2885. https://doi.org/10.3390/electronics11182885
Fadhil HM, Abdullah MN, Younis MI. TWGH: A Tripartite Whale–Gray Wolf–Harmony Algorithm to Minimize Combinatorial Test Suite Problem. Electronics. 2022; 11(18):2885. https://doi.org/10.3390/electronics11182885
Chicago/Turabian StyleFadhil, Heba Mohammed, Mohammed Najm Abdullah, and Mohammed Issam Younis. 2022. "TWGH: A Tripartite Whale–Gray Wolf–Harmony Algorithm to Minimize Combinatorial Test Suite Problem" Electronics 11, no. 18: 2885. https://doi.org/10.3390/electronics11182885