# A Modified Gorilla Troops Optimizer for Global Optimization Problem

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- A modified GTO, which is called MGTO, is proposed in this paper. The modified algorithm introduces three improvement strategies. Firstly, the Quadratic Interpolated Beetle-Antennae Search (QIBAS) [31] is embedded into the GTO that can get the diversity of the silverback’s position. In addition, Teaching–Learning-Based Optimization (TLBO) [32] is hybridized with GTO to stabilize the performance between the silverback and other gorillas. Finally, the Quasi-Reflection-Based Learning (QRBL) [36] mechanism is used to enhance the quality of the optimal position.
- (2)
- To verify the effectiveness of the MGTO, 23 classical benchmark functions, 30 CEC2014 benchmark functions and 10 CEC2020 benchmark functions are adopted to conduct a simulation experiment. The performance of the MGTO is evaluated through a variety of comparisons with the basic GTO and eight state-of-the-art optimization algorithms.
- (3)
- Furthermore, the MGTO is applied to solve the welded-beam-design problem, pressure-vessel-design problem, reducer problem, compression/tension-spring problem, three-bar-truss-design problem, crash-worthiness-design problem and string-design problem. The experimental results indicate that MGTO has a strong convergence ability and global search ability.

## 2. Gorilla Troops Optimizer (GTO)

#### 2.1. Exploration

_{1}, r

_{2}, r

_{3}and rand are the random values between 0 and 1. UB and LB indicate the upper and lower bounds of the variables, respectively. X

_{r}and GX

_{r}are the candidate position vectors of gorillas that are selected randomly.

_{4}is a random value that is in between [−1,1].

#### 2.2. Exploitation

#### 2.2.1. Following the Silverback

_{silverback}is the vector of the silverback, which presents the optimal solution. M can be expressed as follows:

_{i}(t) refers to the vector position of each candidate gorilla at iteration, t; N indicates the sum of gorillas; and g is estimated by Equation (9) as follows:

#### 2.2.2. Competition for Adult Females

_{5}is a random value between 0 and 1. Equation (12) is used to calculate the coefficient vector of the violence degree in conflict, where β is the parameter that needs to be given before the optimization operation. E is used to simulate the effect of violence on the solution’s dimensions. If rand ≥ 0.5, E will be equal to a random value in the normal distribution and the problem’s dimensions. However, if rand < 0.5, E will be equal to a random value in the normal distribution; rand is a random value between 0 and 1.

## 3. Modified Algorithm Implementation

#### 3.1. Beetle-Antennae Search Based on Quadratic Interpolation (QIBAS)

#### 3.1.1. Searching Behavior of Beetles

_{r}indicates the right side of searching area, x

_{l}denotes the left side of searching area and d represents the length of the antennae.

#### 3.1.2. Detecting Behavior of Beetles

#### 3.1.3. Quadratic Interpolation Based on Beetle-Antennae Search (QIBAS)

_{b}denotes the global optimal solution.

_{i}, which varies from the existing solution, x

_{t}. The fitness values of the two positions are compared to determine whether x

_{t}is preserved or replaced.

#### 3.2. Teaching–Learning-Based Optimization

#### 3.2.1. Teacher Phase

_{i}represents the mean at iteration, i. T

_{i}is the teacher who strives to bring M

_{i}up to his/her level. Hence, the new mean can be designated as M

_{new}. The updated solution based on the difference between the current mean and new mean is given as follows:

_{F}is the teaching factor to change the mean, and r

_{i}is a random value ranging from 0 to 1. The value of T

_{F}can be represented as follows:

#### 3.2.2. Learner Phase

#### 3.3. Quasi-Reflection-Based Learning

^{qr}, of the solution, x, is obtained as follows:

#### 3.4. The Proposed MGTO

_{i}, and initializes the position of the silverback. Then the QIBAS algorithm is used to calculate the search positions on both sides of the silverback. The NewPosition can be calculated by Equation (28). The quadratic interpolation function is employed to generate NewPosition1. NewPosition1 can be expressed by Equation (29). To choose an optimal position, the fitness values of these two positions are compared, and then, if the fitness value of the “new position” is better than the previous one, it will replace the previous position:

_{Silverback}

^{qr}. By comparing the fitness values of X

_{Silverback}and X

_{Silverback}

^{qr}, the position is selected from two positions as the final optimal position:

Algorithm 1. The pseudo-code of MGTO |

% MGTO setting |

Inputs: the size of population, N; the maximum number of iterations, T; and parameters β, p, W, d and s. |

Outputs: X_{silverback} and its fitness value |

% Initialization |

Initialize the random population Xi (I = 1,2,…,N) |

Calculate the fitness values of X_{i} |

% Main Loop |

while (stopping condition is not met) do |

Equation (2) is used to update C |

Equation (4) is used to update L |

Equation (28) is used to update the “new position” of silverback Newposition |

for (j ≤ variables_no) do |

Equation (29) is used to update the “new position” of silverback Newposition1 |

end for |

Calculate the fitness values of Newposition and Newposition1 |

if Newposition1 is better than Newposition, replace it |

if “new position” is better than the previous position, replace it |

% Exploration phase |

for (each Gorilla (X_{i})) do |

Equation (1) is used to update the position of Gorilla |

end for |

% Establish group |

Calculate the fitness values of Gorilla |

if GX is better than X, replace it |

% Exploitation phase |

for (each Gorilla (X_{i})) do |

if (|C| ≥ 1) then |

if rand>0.5 then |

Update the position of Gorilla by using Equation (30) |

else |

Update the position of Gorilla by using Equation (7) |

end if |

else |

Update the position of Gorilla by using Equation (10) |

end if |

end for |

% Establish group |

Calculate the fitness values of Gorilla |

if GX is better than X, replace it |

Equation (31) is used to update the position of silverback |

Calculate the fitness value of silverback |

if “new solution” is better than the previous solution, replace it |

end while |

Return X_{silverback} and its fitness value |

## 4. The Results and Discussion of Experiment

#### 4.1. The Experiments on Classical Benchmark

#### 4.1.1. The Convergence Analysis

#### 4.1.2. The Results of the Classical Benchmark

#### 4.2. The Experiments on CEC2014 and CEC2020

#### 4.3. The Non-Parametric Statistic Test

## 5. MGTO for Solving Engineering-Optimization Problems

#### 5.1. Welded-Beam Design

#### 5.2. The Pressure-Vessel Problem

#### 5.3. Speed-Reducer Design

_{1}), the teeth module (x

_{2}), the discrete design variables representing the teeth in the pinion (x

_{3}), the length of the first shaft between the bearings (x

_{4}), the length of the second shaft between the bearings (x

_{5}), the diameters of the first shaft (x

_{6}) and diameters of the second shaft (x

_{7}) [55]. In this case, there are four constraints that should be satisfied: covered stress, bending stress of the gear teeth, stresses in shafts and transverse deflection of the shafts, which are shown in Figure 7.

#### 5.4. Compression/Tension-Spring Design

#### 5.5. Three-Bar-Truss Design

_{1}, A

_{2}and A

_{3}. It is illustrated in Figure 9.

#### 5.6. Car-Crashworthiness Design

_{1}–x

_{7}), the materials of inside of B-pillar and reinforcement of B-pillar (x

_{8}, x

_{9}), the thickness of barrier height and the impact position (x

_{10}, x

_{11}). The mathematical formula is represented as follows:

#### 5.7. Tubular-Column Design

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Khajehzadeh, M.; Iraji, A.; Majdi, A.; Keawsawasvong, S.; Nehdi, M.L. Adaptive Salp Swarm Algorithm for Optimization of Geotechnical Structures. Appl. Sci.
**2022**, 12, 6749. [Google Scholar] [CrossRef] - Mirjalili, S.; Gandomi, A.H.; Mirjalili, S.Z.; Saremi, S.; Faris, H.; Mirjalili, S.M. Salp Swarm Algorithm: A Bio-Inspired Optimizer for Engineering Design Problems. Adv. Eng. Softw.
**2017**, 114, 163–191. [Google Scholar] [CrossRef] - Das, S.; Das, P.; Das, P. Chemical and Biological Control of Parasite-Borne Disease Schistosomiasis: An Impulsive Optimal Control Approach. Nonlinear Dyn.
**2021**, 104, 603–628. [Google Scholar] [CrossRef] - Das, P.; Upadhyay, R.K.; Misra, A.K.; Rihan, F.A.; Das, P.; Ghosh, D. Mathematical Model of COVID-19 with Comorbidity and Controlling Using Non-Pharmaceutical Interventions and Vaccination. Nonlinear Dyn.
**2021**, 106, 1213–1227. [Google Scholar] [CrossRef] - Das, P.; Das, S.; Upadhyay, R.K.; Das, P. Optimal Treatment Strategies for Delayed Cancer-Immune System with Multiple Therapeutic Approach. Chaos Solitons Fractal.
**2020**, 136, 109806. [Google Scholar] [CrossRef] - Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey Wolf Optimizer. Adv. Eng. Softw.
**2014**, 69, 46–61. [Google Scholar] [CrossRef] [Green Version] - Liu, Q.; Li, N.; Jia, H.; Qi, Q.; Abualigah, L. Modified Remora Optimization Algorithm for Global Optimization and Multilevel Thresholding Image Segmentation. Mathematics
**2022**, 10, 1014. [Google Scholar] [CrossRef] - Das, P.; Upadhyay, R.K.; Das, P.; Ghosh, D. Exploring Dynamical Complexity in a Time-Delayed Tumor-Immune Model. Chaos
**2020**, 30, 123118. [Google Scholar] [CrossRef] - Das, P.; Das, S.; Das, P.; Rihan, F.A.; Uzuntarla, M.; Ghosh, D. Optimal Control Strategy for Cancer Remission Using Combinatorial Therapy: A Mathematical Model-Based Approach. Chaos Solitons Fractals
**2021**, 145, 110789. [Google Scholar] [CrossRef] - Wang, S.; Jia, H.; Laith, A.; Liu, Q.; Zheng, R. An Improved Hybrid Aquila Optimizer and Harris Hawks Algorithm for Solving Industrial Engineering Optimization Problems. Processes
**2021**, 9, 1551. [Google Scholar] [CrossRef] - Rashedi, E.; Nezamabadi-Pour, H.; Saryazdi, S. GSA: A Gravitational Search Algorithm. Inf. Sci.
**2009**, 179, 2232–2248. [Google Scholar] [CrossRef] - Mirjalili, S.; Mirjalili, S.M.; Hatamlou, A. Multi-Verse Optimizer: A Nature-Inspired Algorithm for Global Optimization. Neural Comput. Appl.
**2016**, 27, 495–513. [Google Scholar] [CrossRef] - Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P. Optimization by Simulated Annealing. Science
**1983**, 220, 671–680. [Google Scholar] [CrossRef] [PubMed] - Faramarzi, A.; Heidarinejad, M.; Stephens, B.; Mirjalili, S. Equilibrium Optimizer: A Novel Optimization Algorithm. Knowl.-Based Syst.
**2020**, 191, 105190. [Google Scholar] [CrossRef] - Holland, J.H. Genetic Algorithms. Sci. Am.
**1992**, 267, 66–73. [Google Scholar] [CrossRef] - Hussain, S.F.; Iqbal, S. Genetic ACCGA: Co-Similarity Based Co-Clustering Using Genetic Algorithm. Appl. Soft Comput.
**2018**, 72, 30–42. [Google Scholar] [CrossRef] - Storn, R.; Price, K. Differential Evolution–A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces. J. Glob. Optim.
**1997**, 11, 341–359. [Google Scholar] [CrossRef] - Yao, X.; Liu, Y.; Lin, G. Evolutionary Programming Made Faster. IEEE Trans. Evol. Comput.
**1999**, 3, 82–102. [Google Scholar] - Koza, J.R. Genetic Programming: On the Programming of Computers by Means of Natural Selection; MIT Press: Cambridge, MA, USA, 1922. [Google Scholar]
- Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the ICNN95—International Conference on Neural Networks, Perth, WA, Australia, 27 November 1995–1 December 1995; pp. 1942–1948. [Google Scholar]
- Kiran, M.S.; Gunduz, M. A Novel Artificial Bee Colony-based Algorithm for Solving the Numerical Optimization Problems. Int. J. Innov. Comput. I
**2012**, 8, 6107–6121. [Google Scholar] - Yang, X.S. Firefly algorithm. In Nature-Inspired Metaheuristic Algorithms; Luniver Press: Bristol, UK, 2010; Volume 2, pp. 1–148. [Google Scholar]
- Yang, X.S.; Gandomi, A.H. Bat Algorithm: A Novel Approach for Global Engineering Optimization. Eng. Comput.
**2012**, 29, 464–483. [Google Scholar] [CrossRef] [Green Version] - Heidari, A.A.; Mirjalili, S.; Faris, H.; Aljarah, I.; Mafarja, M.; Chen, H. Harris Hawks Optimization: Algorithm and Applications. Future Gener. Comput. Systems.
**2019**, 97, 849–872. [Google Scholar] [CrossRef] - Faramarzi, A.; Heidarinejad, M.; Mirjalili, S.; Gandomi, A.H. Marine Predators Algorithm: A Nature-Inspired Metaheuristic. Expert Syst. Appl.
**2020**, 152, 11337. [Google Scholar] [CrossRef] - Lin, M.; Li, Q. A Hybrid Optimization Method of Beetle Antennae Search Algorithm and Particle Swarm Optimization. DEStech Trans. Eng. Technol. Res.
**2018**, 1, 396–401. [Google Scholar] [CrossRef] [Green Version] - Jiang, X.; Li, S. BAS: Beetle Antennae Search Algorithm for Optimization Problems. Int. J. Robot. Control
**2017**. [Google Scholar] [CrossRef] - Zhou, J.; Qian, Q.; Fu, Y.; Feng, Y. Flower pollination algorithm based on beetle antennae search method. In Smart Innovation, Systems and Technologies; Springer: Berlin/Heidelberg, Germany, 2022; pp. 181–189. [Google Scholar]
- Karaboga, D.; Akay, B. A Comparative Study of Artificial Bee Colony Algorithm. Appl. Math. Comput.
**2009**, 214, 108–132. [Google Scholar] [CrossRef] - Cheng, L.; Yu, M.; Yang, J.; Wang, Y. An improved artificial bee colony algorithm based on beetle antennae search. In Proceedings of the 2019 Chinese Control Conference (CCC), Guangzhou, China, 27–30 July 2019; p. 23122316. [Google Scholar]
- Li, Z.; Li, S.; Luo, X. A novel quadratic interpolated beetle antennae search for manipulator calibration. arXiv
**2022**, arXiv:2204.06218. [Google Scholar] - Rao, R.V.; Savsani, V.J.; Vakharia, D. Teaching-Learning-Based Optimization: A Novel Method for Constrained Mechanical Design Optimization Problems. Comput. Aided Des.
**2011**, 43, 303–315. [Google Scholar] [CrossRef] - Tuo, S.; Yong, L.; Deng, F.; Li, Y.; Lin, Y.; Lu, Q. HSTLBO: A hybrid algorithm based on Harmony Search and Teaching-Learning-Based Optimization for Complex High-Dimensional Optimization Problems. PLoS ONE.
**2017**, 12, e0175114. [Google Scholar] [CrossRef] [Green Version] - Keesari, H.S.; Rao, R.V. Optimization of Job Shop Scheduling Problems Using Teaching-Learning-Based Optimization Algorithm. Opsearch
**2014**, 51, 545–561. [Google Scholar] [CrossRef] - Chen, D.; Zou, F.; Li, Z.; Wang, J.; Li, S. An Improved Teaching-Learning-Based Optimization Algorithm for Solving Global Optimization Problem. Inf. Sci.
**2015**, 297, 171–190. [Google Scholar] [CrossRef] - Fan, Q.; Chen, Z.; Xia, Z. A Novel Quasi-Reflected Harris Hawks Optimization Algorithm for Global Optimization Problems. Soft Comput.
**2020**, 24, 14825–14843. [Google Scholar] [CrossRef] - Ahandani, M.A.; Alavi-Rad, H. Opposition-Based Learning in the Shuffled Bidirectional Differential Evolution Algorithm. Soft Comput.
**2016**, 16, 1303–1337. [Google Scholar] [CrossRef] - Simon, D. Biogeography-Based Optimization. IEEE Trans. Evol. Comput.
**2008**, 12, 702–713. [Google Scholar] [CrossRef] - Wang, Y.J.; Ma, C.L. Opposition-Based Learning Differential Ion Motion Algorithm. J. Inf. Hid. Multimed. Signal Process.
**2018**, 9, 987–996. [Google Scholar] - Abedinia, O.; Naslian, M.D.; Bekravi, M. A New Stochastic Search Algorithm Bundled Honeybee Mating for Solving Optimization Problems. Neural Comput. Appl.
**2014**, 25, 1921–1939. [Google Scholar] [CrossRef] - Abdollahzadeh, B.; Soleimanian Gharehchopogh, F.; Mirjalili, S. Artificial Gorilla Troops Optimizer: A New Nature-Inspired Metaheuristic Algorithm for Global Optimization Problems. Int. J Intell. Syst.
**2021**, 36, 5887–5958. [Google Scholar] [CrossRef] - Wolpert, D.H.; Macready, W.G. No Free Lunch Theorems for Optimization. IEEE Trans. Evol. Comput.
**1997**, 1, 67–82. [Google Scholar] [CrossRef] [Green Version] - Abualigah, L.; Diabat, A.; Mirjalili, S.; Abd Elaziz, M.; Gandomi, A.H. The Arithmetic Optimization Algorithm. Comput Meth. Appl. Mat.
**2021**, 376, 113609. [Google Scholar] [CrossRef] - Mirjalili, S.; Lewis, A. The Whale Optimization Algorithm. Adv. Eng. Softw.
**2016**, 95, 51–67. [Google Scholar] [CrossRef] - Long, W.; Jiao, J.; Liang, X.; Cai, S.; Xu, M. A Random Opposition-Based Learning Grey Wolf Optimizer. IEEE Access
**2019**, 7, 113810–113825. [Google Scholar] [CrossRef] - Li, Y.; Zhao, Y.; Liu, J. Dynamic Sine Cosine Algorithm for Large-Scale Global Optimization Problems. Expert Syst. Appl.
**2021**, 177, 114950. [Google Scholar] [CrossRef] - Singh, N.; Kaur, J. Hybridizing Sine-Cosine Algorithm with Harmony Search Strategy for Optimization Design Problems. Soft Comput.
**2021**, 25, 11053–11075. [Google Scholar] [CrossRef] - Sun, K.; Jia, H.; Li, Y.; Jiang, Z. Hybrid Improved Slime Mould Algorithm with Adaptive Β Hill Climbing for Numerical Optimization. J. Intell. Fuzzy Syst.
**2021**, 40, 1667–1679. [Google Scholar] [CrossRef] - Wen, C.; Jia, H.; Wu, D.; Rao, H.; Li, S.; Liu, Q.; Abualigah, L. Modified Remora Optimization Algorithm with Multistrategies for Global Optimization Problem. Mathematics
**2022**, 10, 3604. [Google Scholar] - García, S.; Fernández, A.; Luengo, J.; Herrera, F. Advanced Nonparametric Tests for Multiple Comparisons in the Design of Experiments in Computational Intelligence and Data Mining: Experimental Analysis of Power. Inf. Sci.
**2010**, 180, 2044–2064. [Google Scholar] [CrossRef] - Demsar, J. Statistical Comparisons of Classifiers Over Multiple Data Sets. J. Mach. Learn. Res.
**2006**, 7, 1–30. [Google Scholar] - Jia, H.; Peng, X.; Lang, C. Remora Optimization Algorithm. Expert Syst. Appl.
**2021**, 185, 115665. [Google Scholar] [CrossRef] - Kannan, B.; Kramer, S. An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design. J. Mech. Des.
**1994**, 116, 405–411. [Google Scholar] [CrossRef] - Li, S.; Che, H.; Wang, M.; Heidari, A.A.; Mirjalili, S. Slime Mould Algorithm: A New Method for Stochastic Optimization. Future Gener. Comp. Sy.
**2020**, 111, 300–323. [Google Scholar] [CrossRef] - Jia, H.; Sun, K.; Zhang, W.; Leng, X. An Enhanced Chimp Optimization Algorithm for Continuous Optimization Domains. Complex Intell. Syst.
**2022**, 8, 65–82. [Google Scholar] [CrossRef] - Abualigah, L.; Yousri, D.; Abd Elaziz, M.; Ewees, A.A.; Al-qaness, M.A.A.; Gandomi, A.H. Aquila Optimizer: A Novel Meta-Heuristic Optimization Algorithm. Comput. Ind. Eng.
**2021**, 157, 107250. [Google Scholar] [CrossRef] - Mirjalili, S. Moth–Flame Optimization Algorithm: A Novel Nature-Inspired Heuristic Paradigm. Knowl.–Based Syst.
**2015**, 89, 228–249. [Google Scholar] [CrossRef] - Mirjalili, S. SCA: A Sine Cosine Algorithm for Solving Optimization Problems. Knowl.–Based Syst.
**2016**, 96, 120–133. [Google Scholar] [CrossRef] - Lu, S.; Kim, H.M. A Regularized Inexact Penalty Decomposition Algorithm for Multidisciplinary Design Optimization Problems with Complementarity Constraints. J. Mech. Des.
**2010**, 132, 041005. [Google Scholar] [CrossRef] [Green Version] - Liu, Q.; Li, N.; Jia, H.; Qi, Q.; Abualigah, L.; Liu, Y. A Hybrid Arithmetic Optimization and Golden Sine Algorithm for Solving Industrial Engineering Design Problems. Mathematics
**2022**, 10, 1567. [Google Scholar] [CrossRef] - Ray, T.; Saini, P. Engineering Design Optimization Using a Swarm with an Intelligent Information Sharing Among Individuals. Eng. Optim.
**2001**, 33, 735–748. [Google Scholar] [CrossRef] - Gu, L.; Yang, R.; Tho, C.H.; Makowskit, M.; Faruquet, O.; Li, Y.L. Optimisation and Robustness for Crashworthiness of Side Impact. Int. J. Veh. Des.
**2001**, 26, 348–360. [Google Scholar] [CrossRef]

**Figure 5.**Welded-beam-design problem: three-dimensional model diagram (

**left**) and the structural parament (

**right**).

MGTO | GTO | AOA | SSA | WOA | SHO | RSA | ROLGWO | DSCA | HSCAHS | ||
---|---|---|---|---|---|---|---|---|---|---|---|

F1 | Avg | 0 | 0 | 4.72 × 10^{−6} | 1.49 × 10^{−7} | 3.26 × 10^{−69} | 0 | 0 | 0 | 2.89 × 10^{−111} | 1.33 × 10^{−50} |

Std | 0 | 0 | 1.97 × 10^{−6} | 1.17 × 10^{−7} | 1.78 × 10^{−68} | 0 | 0 | 0 | 1.58 × 10^{−110} | 5.89 × 10^{−50} | |

F2 | Avg | 0 | 3.69 × 10^{−189} | 2.14 × 10^{−3} | 1.93 | 8.20 × 10^{−51} | 0 | 0 | 8.09 × 10^{−204} | 6.39 × 10^{−59} | 1.06 × 10^{−27} |

Std | 0 | 0 | 2.06 × 10^{−3} | 1.40 | 2.24 × 10^{−50} | 0 | 0 | 0 | 3.49 × 10^{−58} | 1.24 × 10^{−27} | |

F3 | Avg | 0 | 0 | 1.07 × 10^{−3} | 1.35 × 10^{3} | 4.45 × 10^{4} | 0 | 0 | 0 | 7.60 × 10^{−62} | 1.92 × 10^{−48} |

Std | 0 | 0 | 7.62× 10^{−4} | 5.88 × 10^{2} | 1.54 × 10^{4} | 0 | 0 | 0 | 4.16 × 10^{−61} | 7.43 × 10^{−48} | |

F4 | Avg | 0 | 8.19 × 10^{−192} | 1.98 × 10^{−2} | 1.31 × 10^{1} | 5.01 × 10^{1} | 0 | 0 | 3.78 × 10^{−183} | 6.09 × 10^{−39} | 1.26 × 10^{−25} |

Std | 0 | 0 | 1.19 × 10^{−2} | 4.83 | 2.94 × 10^{1} | 0 | 0 | 0 | 3.34 × 10^{−38} | 2.55 × 10^{−25} | |

F5 | Avg | 2.54 × 10^{−5} | 4.81 | 2.80 × 10^{1} | 5.26 × 10^{2} | 2.80 × 10^{1} | 2.88 × 10^{1} | 1.55 × 10^{1} | 2.74 × 10^{1} | 2.86 × 10^{1} | 2.88 × 10^{1} |

Std | 3.94 × 10^{−5} | 9.77 | 2.74 × 10^{−1} | 1.15 × 10^{3} | 4.71 × 10^{−1} | 1.12 × 10^{−1} | 1.47 × 10^{1} | 8.20 × 10^{−1} | 3.05 × 10^{−1} | 5.19 × 10^{−2} | |

F6 | Avg | 3.37 × 10^{−14} | 2.06 × 10^{−7} | 3.11 | 1.73 × 10^{−7} | 4.70 × 10^{−1} | 3.55 | 7.24 | 9.06 × 10^{−1} | 5.53 | 6.71 |

Std | 3.76 × 10^{−14} | 2.68 × 10^{−7} | 2.19 × 10^{−1} | 2.69 × 10^{−7} | 2.78 × 10^{−1} | 2.47 | 4.48 × 10^{−1} | 5.21 × 10^{−1} | 2.78 × 10^{−1} | 1.90 × 10^{−1} | |

F7 | Avg | 7.67 × 10^{−5} | 8.68 × 10^{−5} | 9.64 × 10^{−5} | 1.77 × 10^{−1} | 3.16 × 10^{−3} | 1.13 × 10^{−4} | 1.69 × 10^{−4} | 8.21 × 10^{−5} | 1.61 × 10^{−3} | 9.55 × 10^{−5} |

Std | 4.50 × 10^{−5} | 5.90 × 10^{−5} | 9.89 × 10^{−5} | 7.77 × 10^{−2} | 3.97 × 10^{−3} | 1.81 × 10^{−4} | 1.17 × 10^{−4} | 6.62 × 10^{−5} | 1.75 × 10^{−3} | 1.70 × 10^{−4} | |

F8 | Avg | −1.26 × 10^{4} | −1.26 × 10^{4} | −5.44 × 10^{3} | −7.32 × 10^{3} | −1.01 × 10^{4} | −2.45 × 10^{3} | −5.35 × 10^{3} | −5.17 × 10^{3} | −4.48 × 10^{3} | −2.53 × 10^{3} |

Std | 1.03 × 10^{−6} | 6.74 × 10^{−5} | 3.23 × 10^{2} | 6.74 × 10^{2} | 1.77 × 10^{3} | 4.12 × 10^{2} | 4.01 × 10^{2} | 1.50 × 10^{3} | 3.50 × 10^{2} | 2.93 × 10^{2} | |

F9 | Avg | 0 | 0 | 1.35 × 10^{−6} | 6.17 × 10^{1} | 1.89 × 10^{−15} | 0 | 0 | 0 | 0 | 0 |

Std | 0 | 0 | 1.14 × 10^{−6} | 1.96 × 10^{1} | 1.04 × 10^{−14} | 0 | 0 | 0 | 0 | 0 | |

F10 | Avg | 8.88 × 10^{−16} | 8.88 × 10^{−16} | 4.51 × 10^{−4} | 2.49 | 5.03 × 10^{−15} | 8.88 × 10^{−16} | 8.88 × 10^{−16} | 2.07 × 10^{−15} | 8.88 × 10^{−16} | 8.88 × 10^{−16} |

Std | 0 | 0 | 1.81 × 10^{−4} | 7.86 × 10^{−1} | 3.11 × 10^{−15} | 0 | 0 | 1.70 × 10^{−15} | 0 | 0 | |

F11 | Avg | 0 | 0 | 2.41 × 10^{−3} | 1.87 × 10^{−2} | 8.13× 10^{−3} | 0 | 0 | 0 | 0 | 0 |

Std | 0 | 0 | 6.04 × 10^{−3} | 1.25 × 10^{−2} | 4.45 × 10^{−2} | 0 | 0 | 0 | 0 | 0 | |

F12 | Avg | 1.64 × 10^{−8} | 4.27 × 10^{−8} | 7.42 × 10^{−1} | 7.17 | 2.96 × 10^{−2} | 2.09 × 10^{−4} | 1.33 | 5.64 × 10^{−2} | 7.75 × 10^{−1} | 1.06 |

Std | 3.12 × 10^{−8} | 9.20 × 10^{−8} | 2.43 × 10^{−2} | 4.31 | 3.44 × 10^{−2} | 2.39 × 10^{−5} | 4.55 × 10^{−1} | 2.52 × 10^{−2} | 8.18 × 10^{−2} | 1.10 × 10^{−1} | |

F13 | Avg | 1.00 × 10^{−7} | 1.77 × 10^{−3} | 2.96 | 1.19 × 10^{1} | 4.94 × 10^{−1} | 2.94 | 1.19 | 1.09 | 2.84 | 2.84 |

Std | 1.43 × 10^{−7} | 5.61 × 10^{−3} | 2.90 × 10^{−2} | 1.25 × 10^{1} | 2.41 × 10^{−1} | 2.41 × 10^{−2} | 1.41 | 4.99 × 10^{−1} | 4.52 × 10^{−2} | 3.26 × 10^{−2} | |

F14 | Avg | 9.98 × 10^{−1} | 9.98 × 10^{−1} | 1.11 × 10^{1} | 1.33 | 4.04 | 9.47 | 3.57 | 5.30 | 1.65 | 2.91 |

Std | 4.12 × 10^{−17} | 7.14 × 10^{−17} | 3.49 | 9.49 × 10^{−1} | 3.73 | 4.18 | 2.23 | 4.44 | 8.33 × 10^{−1} | 2.70 × 10^{−1} | |

F15 | Avg | 3.07 × 10^{−4} | 3.99 × 10^{−4} | 4.55 × 10^{−3} | 1.59 × 10^{−3} | 7.20 × 10^{−4} | 3.19 × 10^{−4} | 2.72 × 10^{−3} | 3.62 × 10^{−4} | 1.28 × 10^{−3} | 2.70 × 10^{−3} |

Std | 3.29 × 10^{−19} | 2.79 × 10^{−4} | 7.95 × 10^{−3} | 3.56 × 10^{−3} | 3.78 × 10^{−4} | 7.46 × 10^{−6} | 1.55 × 10^{−3} | 7.11 × 10^{−5} | 3.48 × 10^{−4} | 1.69 × 10^{−3} | |

F16 | Avg | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −9.27 × 10^{−1} | −1.03 | −1.03 | −1.03 | −1.02 |

Std | 5.45 × 10^{−16} | 6.58 × 10^{−16} | 2.19 × 10^{−11} | 2.99 × 10^{−14} | 2.51 × 10^{−9} | 2.01 × 10^{−1} | 1.66 × 10^{−3} | 6.88 × 10^{−5} | 1.54 × 10^{−4} | 7.55 × 10^{−3} | |

F17 | Avg | 3.98 × 10^{−1} | 3.98 × 10^{−1} | 3.99 × 10^{−1} | 3.98 × 10^{−1} | 3.98 × 10^{−1} | 6.37 × 10^{−1} | 4.23 × 10^{−1} | 3.98 × 10^{−1} | 4.02 × 10^{−1} | 7.16 × 10^{−1} |

Std | 0 | 0 | 3.58 × 10^{−3} | 9.58 × 10^{−15} | 1.50 × 10^{−5} | 6.71 × 10^{−1} | 2.04 × 10^{−2} | 1.19 × 10^{−6} | 3.22 × 10^{−3} | 3.91 × 10^{−1} | |

F18 | Avg | 3.00 | 3.00 | 2.15 × 10^{1} | 3.00 | 3.00 | 2.83 × 10^{1} | 7.68 | 3.00 | 3.01 | 3.01 |

Std | 1.28 × 10^{−15} | 1.29 × 10^{−15} | 3.02 × 10^{1} | 2.10 × 10^{−13} | 2.62 × 10^{−4} | 5.09 × 10^{1} | 1.68 × 10^{1} | 3.53 × 10^{−5} | 5.91 × 10^{−3} | 1.56 × 10^{−2} | |

F19 | Avg | −3.86 | −3.86 | −3.86 | −3.86 | −3.86 | −3.56 | −3.79 | −3.86 | −3.83 | −3.43 |

Std | 2.60 × 10^{−15} | 2.67 × 10^{−15} | 6.28 × 10^{−6} | 1.31 × 10^{−12} | 4.40 × 10^{−3} | 3.82 × 10^{−1} | 5.65 × 10^{−2} | 1.29 × 10^{−4} | 1.98 × 10^{−2} | 2.62 × 10^{−1} | |

F20 | Avg | −3.30 | −3.27 | −3.27 | −3.25 | −3.24 | −2.57 | −2.66 | −3.26 | −3.01 | −1.64 |

Std | 4.51 × 10^{−2} | 6.03 × 10^{−2} | 5.93 × 10^{−2} | 6.67 × 10^{−2} | 1.25 × 10^{−1} | 3.51 × 10^{−1} | 2.86 × 10^{−1} | 8.43 × 10^{−2} | 9.72 × 10^{−2} | 5.62 × 10^{−1} | |

F21 | Avg | −1.02 × 10^{1} | −1.02 × 10^{1} | −7.38 | −6.81 | −8.01 | −4.08 | −5.06 | −5.10 | −4.19 | −5.78 × 10^{−1} |

Std | 5.83 × 10^{−15} | 6.08 × 10^{−15} | 2.91 | 3.50 | 2.66 | 1.11 | 3.09 × 10^{−7} | 9.97 × 10^{−1} | 1.29 | 1.62 × 10^{−1} | |

F22 | Avg | −1.04 × 10^{1} | −1.04 × 10^{1} | −7.61 | −8.48 | −7.30 | −3.65 | −5.09 | −5.78 | −4.27 | −7.20 × 10^{−1} |

Std | 6.60 × 10^{−16} | 9.33 × 10^{−16} | 3.11 | 3.28 | 3.20 | 1.12 | 7.75 × 10^{−7} | 2.28E | 4.48 × 10^{−1} | 1.79 × 10^{−1} | |

F23 | Avg | −1.05 × 10^{1} | −1.05 × 10^{1} | −7.10 | −8.56 | −7.17 | −4.09 | −5.13 | −6.83 | −4.10 | −8.79 × 10^{−1} |

Std | 1.23 × 10^{−15} | 1.51 × 10^{−15} | 3.39 | 3.37 | 3.06 | 1.21 | 1.97 × 10^{−6} | 2.81 | 5.89 × 10^{−1} | 2.92 × 10^{−1} |

MGTO | GTO | AOA | SSA | WOA | SHO | RSA | ROLGWO | DSCA | HSCAHS | ||
---|---|---|---|---|---|---|---|---|---|---|---|

F1 | Avg | 6.14 × 10^{3} | 1.89 × 10^{4} | 2.45 × 10^{8} | 2.37 × 10^{6} | 1.52 × 10^{7} | 2.07 × 10^{9} | 1.10 × 10^{9} | 8.34 × 10^{6} | 3.34 × 10^{7} | 1.04 × 10^{8} |

Std | 5.43 × 10^{3} | 2.30 × 10^{4} | 2.19 × 10^{8} | 2.25 × 10^{6} | 1.04 × 10^{7} | 2.44 × 10^{8} | 2.67 × 10^{8} | 4.68 × 10^{6} | 1.45 × 10^{7} | 4.35 × 10^{7} | |

F2 | Avg | 2.00 × 10^{2} | 1.96 × 10^{3} | 1.01 × 10^{10} | 3.81 × 10^{3} | 4.09 × 10^{7} | 8.61 × 10^{10} | 7.38 × 10^{10} | 1.02 × 10^{8} | 1.54 × 10^{9} | 7.22 × 10^{9} |

Std | 1.91 × 10^{−1} | 2.38 × 10^{3} | 2.64 × 10^{9} | 3.73 × 10^{3} | 3.33 × 10^{7} | 7.49 × 10^{9} | 4.16 × 10^{9} | 3.24 × 10^{8} | 4.83 × 10^{8} | 9.48 × 10^{8} | |

F3 | Avg | 3.07 × 10^{2} | 3.93 × 10^{2} | 1.90 × 10^{4} | 1.52 × 10^{4} | 6.58 × 10^{4} | 9.36 × 10^{5} | 8.10 × 10^{4} | 6.69 × 10^{3} | 1.82 × 10^{4} | 1.66 × 10^{4} |

Std | 1.65 × 10^{1} | 1.54 × 10^{2} | 4.76 × 10^{3} | 8.05 × 10^{3} | 3.62 × 10^{4} | 1.53 × 10^{6} | 1.01 × 10^{4} | 3.98 × 10^{3} | 5.62 × 10^{3} | 2.41 × 10^{3} | |

F4 | Avg | 4.16 × 10^{2} | 4.24 × 10^{2} | 2.67 × 10^{3} | 4.32 × 10^{2} | 4.55 × 10^{2} | 1.94 × 10^{4} | 1.00 × 10^{4} | 4.37 × 10^{2} | 5.51 × 10^{2} | 1.55 × 10^{3} |

Std | 1.68 × 10^{1} | 1.79 × 10^{1} | 1.43 × 10^{3} | 1.73 × 10^{1} | 3.67 × 10^{1} | 3.33 × 10^{3} | 2.91 × 10^{3} | 2.48 × 10^{1} | 4.59 × 10^{1} | 4.77 × 10^{2} | |

F5 | Avg | 5.20 × 10^{2} | 5.20 × 10^{2} | 5.20 × 10^{2} | 5.20 × 10^{2} | 5.20 × 10^{2} | 5.21 × 10^{2} | 5.21 × 10^{2} | 5.20 × 10^{2} | 5.20 × 10^{2} | 5.21 × 10^{2} |

Std | 5.29 × 10^{2} | 6.87 × 10^{2} | 3.95 × 10^{−3} | 1.05 × 10^{−1} | 1.44 × 10^{−1} | 5.63 × 10^{−2} | 6.15 × 10^{−2} | 1.86 × 10^{−1} | 9.02 × 10^{−2} | 1.11 × 10^{−1} | |

F6 | Avg | 6.04 × 10^{2} | 6.06 × 10^{2} | 6.11 × 10^{2} | 6.05 × 10^{2} | 6.09 × 10^{2} | 6.47 × 10^{2} | 6.40 × 10^{2} | 6.03 × 10^{2} | 6.10 × 10^{2} | 6.10 × 10^{2} |

Std | 1.67 | 1.80 | 9.21 × 10^{−1} | 2.06 | 1.69 | 2.10 | 2.20 | 1.84 | 4.79 × 10^{−1} | 7.12 × 10^{−1} | |

F7 | Avg | 7.00 × 10^{2} | 7.00 × 10^{2} | 9.03 × 10^{2} | 7.00 × 10^{2} | 7.02 × 10^{2} | 1.57 × 10^{3} | 1.35 × 10^{3} | 7.02 × 10^{2} | 7.27 × 10^{2} | 8.47 × 10^{2} |

Std | 7.14 × 10^{−2} | 2.84 × 10^{−1} | 6.65 × 10^{1} | 1.19 × 10^{−1} | 7.09 × 10^{−1} | 9.37 × 10^{1} | 1.10 × 10^{2} | 2.39 | 7.94 | 3.10 × 10^{1} | |

F8 | Avg | 8.07 × 10^{2} | 8.24 × 10^{2} | 8.65 × 10^{2} | 8.28 × 10^{2} | 8.40 × 10^{2} | 1.22 × 10^{3} | 1.16 × 10^{3} | 8.15 × 10^{2} | 8.59 × 10^{2} | 8.96 × 10^{2} |

Std | 5.31 | 1.01 × 10^{1} | 1.45 × 10^{1} | 1.06 × 10^{1} | 1.30 × 10^{1} | 3.38 × 10^{1} | 1.96 × 10^{1} | 6.40 | 7.34 | 8.65 | |

F9 | Avg | 9.29 × 10^{2} | 9.31 × 10^{2} | 9.53 × 10^{2} | 9.34 × 10^{2} | 9.52 × 10^{2} | 1.31 × 10^{3} | 1.24 × 10^{3} | 9.28 × 10^{2} | 9.61 × 10^{2} | 9.70 × 10^{2} |

Std | 1.01 × 10^{1} | 1.03 × 10^{1} | 5.49 | 1.85 × 10^{1} | 2.00 × 10^{1} | 2.21 × 10^{1} | 2.15 × 10^{1} | 1.40 × 10^{1} | 7.87 | 5.19 | |

F10 | Avg | 1.25 × 10^{3} | 1.49 × 10^{3} | 1.75 × 10^{3} | 1.72 × 10^{3} | 1.69 × 10^{3} | 9.94 × 10^{3} | 8.00 × 10^{3} | 1.55 × 10^{3} | 2.39 × 10^{3} | 2.44 × 10^{3} |

Std | 1.50 × 10^{2} | 2.60 × 10^{2} | 1.95 × 10^{2} | 3.27 × 10^{2} | 2.81 × 10^{2} | 6.23 × 10^{2} | 4.68× 10^{2} | 2.20× 10^{2} | 1.54× 10^{2} | 1.48× 10^{2} | |

F11 | Avg | 1.88 × 10^{3} | 1.93 × 10^{3} | 2.25 × 10^{3} | 2.07 × 10^{3} | 2.31 × 10^{3} | 3.48 × 10^{3} | 2.69 × 10^{3} | 1.86 × 10^{3} | 2.81 × 10^{3} | 2.88 × 10^{3} |

Std | 3.06 × 10^{2} | 2.61 × 10^{2} | 2.40 × 10^{2} | 3.48 × 10^{2} | 3.51 × 10^{2} | 2.70 × 10^{2} | 2.12 × 10^{2} | 3.39 × 10^{2} | 1.86 × 10^{2} | 1.38 × 10^{2} | |

F12 | Avg | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} | 1.20 × 10^{3} |

Std | 2.19 × 10^{−1} | 2.12 × 10^{−1} | 5.82 × 10^{−1} | 2.31 × 10^{−1} | 3.83 × 10^{−1} | 9.75 × 10^{−1} | 3.40 × 10^{−1} | 6.99 × 10^{−1} | 3.63 × 10^{−1} | 4.35 × 10^{−1} | |

F13 | Avg | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} | 1.30 × 10^{3} |

Std | 9.91 × 10^{−2} | 1.26 × 10^{−1} | 7.31 × 10^{−1} | 1.75 × 10^{−1} | 1.62 × 10^{−1} | 7.51 × 10^{−1} | 7.51 × 10^{−1} | 6.86 × 10^{−2} | 2.14 × 10^{−1} | 5.47 × 10^{−1} | |

F14 | Avg | 1.40 × 10^{3} | 1.40 × 10^{3} | 1.44 × 10^{3} | 1.40 × 10^{3} | 1.40 × 10^{3} | 1.45 × 10^{3} | 1.42 × 10^{3} | 1.40 × 10^{3} | 1.40 × 10^{3} | 1.42 × 10^{3} |

Std | 7.90 × 10^{−2} | 1.85 × 10^{−1} | 1.20 × 10^{1} | 2.68 × 10^{−1} | 2.00 × 10^{−1} | 7.93 | 8.11 | 2.09 × 10^{−1} | 1.40 | 4.30 | |

F15 | Avg | 1.50 × 10^{3} | 1.50 × 10^{3} | 2.16 × 10^{4} | 1.50 × 10^{3} | 1.50 × 10^{3} | 1.86 × 10^{4} | 5.83 × 10^{3} | 1.50 × 10^{3} | 1.54 × 10^{3} | 2.61 × 10^{3} |

Std | 4.31 × 10^{−1} | 2.30 | 1.14 × 10^{4} | 1.01 | 4.80 | 1.98 × 10^{4} | 4.32 × 10^{3} | 7.88 × 10^{−1} | 3.84 × 10^{1} | 6.20 × 10^{2} | |

F16 | Avg | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} | 1.60 × 10^{3} |

Std | 3.92 × 10^{−1} | 3.28 × 10^{−1} | 2.32 × 10^{−1} | 3.26 × 10^{−1} | 2.93 × 10^{−1} | 2.41 × 10^{−1} | 1.32 × 10^{−1} | 3.24 × 10^{−1} | 1.82 × 10^{−1} | 9.54 × 10^{−2} | |

F17 | Avg | 2.23 × 10^{3} | 2.68 × 10^{3} | 4.73 × 10^{5} | 2.78 × 10^{4} | 4.02 × 10^{5} | 4.92 × 10^{6} | 4.59 × 10^{5} | 3.11 × 10^{4} | 1.70 × 10^{5} | 4.89 × 10^{5} |

Std | 2.40 × 10^{2} | 1.18 × 10^{3} | 9.71 × 10^{4} | 3.72 × 10^{4} | 7.54 × 10^{5} | 4.15 × 10^{6} | 1.27 × 10^{5} | 9.63 × 10^{4} | 1.19 × 10^{5} | 9.53 × 10^{4} | |

F18 | Avg | 1.87 × 10^{3} | 1.92 × 10^{3} | 1.09 × 10^{4} | 1.01 × 10^{4} | 1.41 × 10^{4} | 3.18 × 10^{7} | 3.04 × 10^{5} | 1.17 × 10^{4} | 4.11 × 10^{4} | 6.66 × 10^{4} |

Std | 4.04 × 10^{1} | 8.19 × 10^{1} | 3.89 × 10^{3} | 8.38 × 10^{3} | 1.20 × 10^{4} | 3.29 × 10^{7} | 7.20 × 10^{5} | 3.36 × 10^{3} | 3.35 × 10^{4} | 2.38 × 10^{4} | |

F19 | Avg | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.95 × 10^{3} | 1.90 × 10^{3} | 1.91 × 10^{3} | 1.97 × 10^{3} | 1.93 × 10^{3} | 1.90 × 10^{3} | 1.91 × 10^{3} | 1.92 × 10^{3} |

Std | 9.81 × 10^{−1} | 1.34 | 3.06 × 10^{1} | 1.24 | 1.86 | 4.13 × 10^{1} | 1.37 × 10^{1} | 1.15 | 1.02 | 8.40 | |

F20 | Avg | 2.05 × 10^{3} | 2.08 × 10^{3} | 1.26 × 10^{4} | 7.78 × 10^{3} | 1.08 × 10^{4} | 5.54× 10^{6} | 2.19 × 10^{4} | 7.86 × 10^{3} | 3.39 × 10^{4} | 2.06 × 10^{4} |

Std | 3.90 × 10^{1} | 6.52 × 10^{1} | 3.80 × 10^{3} | 6.77 × 10^{3} | 7.51 × 10^{3} | 9.13 × 10^{6} | 3.30 × 10^{4} | 3.72 × 10^{3} | 2.41 × 10^{4} | 8.97 × 10^{3} | |

F21 | Avg | 2.38 × 10^{3} | 2.48 × 10^{3} | 1.95 × 10^{6} | 7.03 × 10^{3} | 6.03 × 10^{5} | 3.97 × 10^{6} | 9.29 × 10^{5} | 1.11 × 10^{4} | 5.15 × 10^{4} | 2.00 × 10^{5} |

Std | 2.38 × 10^{2} | 3.13× 10^{2} | 2.72 × 10^{6} | 6.91 × 10^{3} | 1.99 × 10^{6} | 5.03 × 10^{6} | 1.66 × 10^{6} | 6.76 × 10^{3} | 3.60 × 10^{4} | 9.92 × 10^{4} | |

F22 | Avg | 2.22 × 10^{3} | 2.24 × 10^{3} | 2.43 × 10^{3} | 2.30 × 10^{3} | 2.32 × 10^{3} | 2.76 × 10^{3} | 2.42 × 10^{3} | 2.30 × 10^{3} | 2.31 × 10^{3} | 2.48 × 10^{3} |

Std | 6.65 | 3.90× 10^{1} | 1.29 × 10^{2} | 7.42× 10^{1} | 8.59× 10^{1} | 1.87 × 10^{2} | 7.55× 10^{1} | 6.25× 10^{1} | 4.01× 10^{1} | 5.16× 10^{1} | |

F23 | Avg | 2.50 × 10^{3} | 2.50 × 10^{3} | 2.50 × 10^{3} | 2.63 × 10^{3} | 2.64 × 10^{3} | 2.50 × 10^{3} | 2.50 × 10^{3} | 2.58 × 10^{3} | 2.52 × 10^{3} | 2.50 × 10^{3} |

Std | 0.00 | 0.00 | 3.81 × 10^{4} | 8.83 | 2.83 × 10^{1} | 0.00 | 0.00 | 6.56 × 10^{1} | 6.02 × 10^{1} | 0.00 | |

F24 | Avg | 2.59 × 10^{3} | 2.57 × 10^{3} | 2.60 × 10^{3} | 2.54 × 10^{3} | 2.58 × 10^{3} | 2.60 × 10^{3} | 2.60 × 10^{3} | 2.57 × 10^{3} | 2.57 × 10^{3} | 2.60 × 10^{3} |

Std | 2.53 × 10^{1} | 3.34 × 10^{1} | 8.14 | 2.35 × 10^{1} | 2.57 × 10^{1} | 0.00 | 6.37 × 10^{−1} | 3.80 × 10^{1} | 9.06 | 6.25 | |

F25 | Avg | 2.69 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.68 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} |

Std | 1.03 × 10^{1} | 1.37 × 10^{1} | 0.00 | 2.60 × 10^{1} | 3.74 | 0.00 | 8.21 × 10^{−2} | 1.19 × 10^{−1} | 4.70 | 1.48 × 10^{−1} | |

F26 | Avg | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.71 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.71 × 10^{3} | 2.71 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} | 2.70 × 10^{3} |

Std | 6.83 × 10^{−2} | 9.84 × 10^{−2} | 2.43 × 10^{1} | 1.24 × 10^{−1} | 1.82 × 10^{1} | 2.43 × 10^{1} | 2.44 × 10^{1} | 1.01 × 10^{−1} | 1.83 × 10^{−1} | 5.51 × 10^{−1} | |

F27 | Avg | 2.83 × 10^{3} | 2.84 × 10^{3} | 3.18 × 10^{3} | 3.03 × 10^{3} | 3.16 × 10^{3} | 2.90 × 10^{3} | 2.90 × 10^{3} | 3.04 × 10^{3} | 3.07 × 10^{3} | 2.90 × 10^{3} |

Std | 9.37 × 10^{1} | 9.08 × 10^{1} | 1.90 × 10^{2} | 1.51 × 10^{2} | 1.13 × 10^{2} | 0.00 | 0.00 | 1.16 × 10^{2} | 1.07 × 10^{2} | 3.08 | |

F28 | Avg | 3.00 × 10^{3} | 3.00 × 10^{3} | 3.37 × 10^{3} | 3.21 × 10^{3} | 3.42 × 10^{3} | 3.00 × 10^{3} | 3.00 × 10^{3} | 3.24 × 10^{3} | 3.24 × 10^{3} | 3.00 × 10^{3} |

Std | 0.00 | 0.00 | 5.04 × 10^{2} | 6.65× 10^{1} | 1.26 × 10^{2} | 0.00 | 0.00 | 6.45 × 10^{1} | 1.10 × 10^{1} | 0.00 | |

F29 | Avg | 3.22 × 10^{3} | 2.01 × 10^{5} | 2.39 × 10^{7} | 1.93 × 10^{5} | 3.06 × 10^{5} | 3.10 × 10^{3} | 3.10 × 10^{3} | 1.72 × 10^{5} | 1.85 × 10^{4} | 2.45 × 10^{6} |

Std | 1.02 × 10^{2} | 7.74 × 10^{5} | 1.95 × 10^{7} | 5.76 × 10^{5} | 9.66 × 10^{5} | 0.00 | 0.00 | 5.40 × 10^{5} | 1.25 × 10^{4} | 2.55 × 10^{6} | |

F30 | Avg | 3.93 × 10^{3} | 3.96 × 10^{3} | 1.52 × 10^{5} | 4.68 × 10^{3} | 6.29 × 10^{3} | 3.20 × 10^{3} | 3.20 × 10^{3} | 4.39 × 10^{3} | 6.54 × 10^{3} | 4.03 × 10^{4} |

Std | 3.99 × 10^{2} | 3.55 × 10^{2} | 3.73 × 10^{5} | 7.67 × 10^{2} | 1.86 × 10^{3} | 0.00 | 0.00 | 6.23 × 10^{2} | 1.48 × 10^{3} | 3.56 × 10^{4} |

MGTO | GTO | AOA | SSA | WOA | SHO | RSA | ROLGWO | DSCA | HSCAHS | ||
---|---|---|---|---|---|---|---|---|---|---|---|

F1 | Avg | 1.51 × 10^{2} | 2.39 × 10^{3} | 1.62 × 10^{10} | 3.39 × 10^{3} | 6.69 × 10^{7} | 1.65 × 10^{10} | 1.18 × 10^{10} | 7.85 × 10^{7} | 4.52 × 10^{9} | 1.08 × 10^{10} |

Std | 1.76 × 10^{2} | 2.62 × 10^{3} | 5.21 × 10^{9} | 3.42 × 10^{3} | 8.73 × 10^{7} | 4.17 × 10^{9} | 3.77 × 10^{9} | 1.61 × 10^{8} | 1.68 × 10^{9} | 2.05 × 10^{9} | |

F2 | Avg | 1.80 × 10^{3} | 1.92 × 10^{3} | 2.32 × 10^{3} | 2.01 × 10^{3} | 2.24 × 10^{3} | 3.55 × 10^{3} | 2.82 × 10^{3} | 1.98 × 10^{3} | 2.59 × 10^{3} | 2.98 × 10^{3} |

Std | 1.82 × 10^{2} | 2.81 × 10^{2} | 2.40 × 10^{2} | 3.22 × 10^{2} | 3.68 × 10^{2} | 2.70 × 10^{2} | 1.98 × 10^{2} | 2.98 × 10^{2} | 2.16 × 10^{2} | 1.90 × 10^{2} | |

F3 | Avg | 7.46 × 10^{2} | 7.53 × 10^{2} | 8.01 × 10^{2} | 7.47 × 10^{2} | 7.86 × 10^{2} | 8.70 × 10^{2} | 8.10 × 10^{2} | 7.44 × 10^{2} | 8.20 × 10^{2} | 8.38 × 10^{2} |

Std | 1.26 × 10^{1} | 1.54 × 10^{1} | 1.24 × 10^{1} | 1.54 × 10^{1} | 2.45 × 10^{1} | 2.47 × 10^{1} | 1.18 × 10^{1} | 1.35 × 10^{1} | 1.20 × 10^{1} | 1.20 × 10^{1} | |

F4 | Avg | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} | 1.90 × 10^{3} |

Std | 0.00 | 0.00 | 0.00 | 1.06 | 4.23 × 10^{−1} | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |

F5 | Avg | 2.15 × 10^{3} | 2.57 × 10^{3} | 4.81 × 10^{5} | 2.80 × 10^{4} | 3.80 × 10^{5} | 3.21 × 10^{6} | 4.43 × 10^{5} | 4.32 × 10^{4} | 3.82 × 10^{5} | 4.91 × 10^{5} |

Std | 2.15 × 10^{2} | 7.72 × 10^{2} | 1.34 × 10^{5} | 4.05 × 10^{4} | 6.12 × 10^{5} | 3.02 × 10^{6} | 1.48 × 10^{5} | 1.42 × 10^{5} | 1.64 × 10^{5} | 8.70 × 10^{4} | |

F6 | Avg | 1.68 × 10^{3} | 1.77 × 10^{3} | 2.22 × 10^{3} | 1.77 × 10^{3} | 1.90 × 10^{3} | 2.65 × 10^{3} | 2.22 × 10^{3} | 1.76 × 10^{3} | 1.90 × 10^{3} | 2.26 × 10^{3} |

Std | 6.65 × 10^{1} | 1.25 × 10^{2} | 1.76 × 10^{2} | 1.22 × 10^{2} | 1.25 × 10^{2} | 2.82 × 10^{2} | 1.68 × 10^{2} | 8.14 × 10^{1} | 1.15 × 10^{2} | 1.46 × 10^{2} | |

F7 | Avg | 2.40 × 10^{3} | 2.50 × 10^{3} | 3.11 × 10^{6} | 9.57 × 10^{3} | 9.69 × 10^{5} | 4.70 × 10^{6} | 1.47 × 10^{6} | 9.38 × 10^{3} | 5.47 × 10^{4} | 1.67 × 10^{5} |

Std | 1.83 × 10^{2} | 2.40 × 10^{2} | 4.14 × 10^{6} | 9.09 × 10^{3} | 1.58 × 10^{6} | 5.60 × 10^{6} | 2.63 × 10^{6} | 5.34 × 10^{3} | 5.64 × 10^{4} | 7.36 × 10^{4} | |

F8 | Avg | 2.30 × 10^{3} | 2.30 × 10^{3} | 3.48 × 10^{3} | 2.38 × 10^{3} | 2.48 × 10^{3} | 3.70 × 10^{3} | 3.37 × 10^{3} | 2.32 × 10^{3} | 2.64 × 10^{3} | 3.03 × 10^{3} |

Std | 1.16 | 1.60 × 10^{1} | 3.78 × 10^{2} | 2.79 × 10^{2} | 4.36 × 10^{2} | 5.55 × 10^{2} | 3.61 × 10^{2} | 2.31 × 10^{1} | 1.14 × 10^{2} | 1.32 × 10^{2} | |

F9 | Avg | 2.66 × 10^{3} | 2.71 × 10^{3} | 2.96 × 10^{3} | 2.74 × 10^{3} | 2.79 × 10^{3} | 2.96 × 10^{3} | 2.91 × 10^{3} | 2.73 × 10^{3} | 2.76 × 10^{3} | 2.86 × 10^{3} |

Std | 9.75 × 10^{1} | 1.06× 10^{2} | 1.23 × 10^{2} | 4.72 × 10^{1} | 4.91 × 10^{1} | 8.53 × 10^{1} | 6.60 × 10^{1} | 7.69 × 10^{1} | 1.18 × 10^{2} | 6.37 × 10^{1} | |

F10 | Avg | 2.93 × 10^{3} | 2.94 × 10^{3} | 3.86 × 10^{3} | 2.93 × 10^{3} | 2.97 × 10^{3} | 3.90 × 10^{3} | 3.46 × 10^{3} | 2.94 × 10^{3} | 3.18 × 10^{3} | 3.53 × 10^{3} |

Std | 2.15 × 10^{1} | 2.79 × 10^{1} | 3.67 × 10^{2} | 2.37 × 10^{1} | 6.41 × 10^{1} | 2.85 × 10^{2} | 2.01 × 10^{2} | 2.46 × 10^{1} | 7.61 × 10^{1} | 5.98 × 10^{1} |

GTO | AOA | SSA | WOA | SHO | RSA | ROLGWO | DSCA | HSCAHS | |
---|---|---|---|---|---|---|---|---|---|

F1 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 1.000000 | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F2 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F3 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 1.000000 | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F4 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F5 | 0.041260 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.002625 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F6 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F7 | 0.006714 | 0.010254 | 6.10 × 10^{−5} | 0.000122 | 0.015076 | 0.002014 | 0.041260 | 6.10 × 10^{−5} | 0.018066 |

F8 | 0.018066 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F9 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.250000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |

F10 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.000977 | 0.500000 | 1.000000 | 0.015625 | 1.000000 | 1.000000 |

F11 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.125000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |

F12 | 0.002014 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F13 | 0.047913 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F14 | 0.500000 | 6.10 × 10^{−5} | 0.015625 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F15 | 0.005615 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F16 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F17 | 1.000000 | 6.10 × 10^{−5} | 0.000977 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F18 | 0.001953 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F19 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F20 | 0.031250 | 6.10 × 10^{−5} | 0.000610 | 0.005371 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F21 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F22 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F23 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

GTO | AOA | SSA | WOA | SHO | RSA | ROLGWO | DSCA | HSCAHS | |
---|---|---|---|---|---|---|---|---|---|

F1 | 0.006714 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F2 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F3 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F4 | 0.013428 | 6.10 × 10^{−5} | 0.015076 | 0.002014 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.002625 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F5 | 0.000854 | 0.002014 | 0.012451 | 0.002625 | 0.000122 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F6 | 0.000610 | 6.10 × 10^{−5} | 0.030151 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.004272 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F7 | 0.004272 | 6.10 × 10^{−5} | 0.047913 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F8 | 0.000183 | 6.10 × 10^{−5} | 0.000183 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.021545 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F9 | 0.041260 | 6.10 × 10^{−5} | 0.041260 | 0.000305 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.012451 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F10 | 0.010254 | 0.000305 | 0.003357 | 0.000427 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.001526 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F11 | 0.000854 | 0.000122 | 0.018066 | 0.005371 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.002014 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F12 | 0.025574 | 0.012451 | 0.021545 | 0.000610 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.030151 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F13 | 0.041260 | 6.10 × 10^{−5} | 0.002014 | 0.000305 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.030151 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F14 | 0.021545 | 6.10 × 10^{−5} | 0.021545 | 0.021545 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.006714 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F15 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.002014 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.047913 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F16 | 0.047913 | 6.10 × 10^{−5} | 0.008362 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.012451 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F17 | 0.047913 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F18 | 0.021545 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F19 | 0.004272 | 6.10 × 10^{−5} | 0.018066 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.001160 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F20 | 0.018066 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F21 | 0.041260 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F22 | 0.030151 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.000427 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F23 | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 0.000122 | 1.000000 | 1.000000 | 0.000977 | 0.003906 | 1.000000 |

F24 | 0.035278 | 0.031250 | 0.000854 | 0.041260 | 0.031250 | 0.031250 | 0.016113 | 0.004272 | 0.015625 |

F25 | 0.046875 | 0.031250 | 0.035339 | 0.021484 | 0.031250 | 0.031250 | 0.031250 | 0.031250 | 0.031250 |

F26 | 0.047913 | 6.10 × 10^{−5} | 0.035339 | 0.005371 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.000122 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F27 | 0.037109 | 6.10 × 10^{−5} | 0.000610 | 0.000122 | 0.031250 | 0.031250 | 0.003357 | 0.015076 | 0.031250 |

F28 | 1.000000 | 0.000977 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 1.000000 |

F29 | 0.012451 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.000488 | 0.000488 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.000305 |

F30 | 0.047913 | 6.10 × 10^{−5} | 0.006714 | 0.000610 | 0.000122 | 0.000122 | 0.021545 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

GTO | AOA | SSA | WOA | SHO | RSA | ROLGWO | DSCA | HSCAHS | |
---|---|---|---|---|---|---|---|---|---|

F1 | 0.000122 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F2 | 0.010254 | 0.000427 | 0.012451 | 0.003357 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.041260 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F3 | 0.021545 | 6.10 × 10^{−5} | 0.025574 | 0.000305 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.021545 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F4 | 1.000000 | 1.000000 | 6.10 × 10^{−5} | 0.031250 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |

F5 | 0.025574 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F6 | 0.047913 | 6.10 × 10^{−5} | 0.041260 | 0.001160 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.000610 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F7 | 0.035339 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F8 | 0.002625 | 6.10 × 10^{−5} | 0.015076 | 0.002625 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.041260 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

F9 | 0.006714 | 0.000122 | 0.003357 | 0.000305 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.041260 | 0.000183 | 6.10 × 10^{−5} |

F10 | 0.021545 | 6.10 × 10^{−5} | 0.041260 | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 6.10 × 10^{−5} | 0.041260 | 6.10 × 10^{−5} | 6.10 × 10^{−5} |

Algorithm | Optimal Values for Variables | Optimal Cost | |||
---|---|---|---|---|---|

h | L | t | B | ||

MGTO | 0.2057 | 3.2531 | 9.0366 | 0.2057 | 1.6952 |

GTO | 0.2059 | 3.2510 | 9.0331 | 0.2059 | 1.6958 |

HS | 0.2442 | 6.2231 | 8.2915 | 0.2400 | 2.3807 |

WOA | 0.205395 | 3.528467 | 9.004233 | 0.207241 | 1.735344 |

GSA | 0.182129 | 3.856979 | 10.000 | 0.202376 | 1.87995 |

MVO | 0.205463 | 3.473193 | 9.044502 | 0.205695 | 1.72645 |

OBSCA | 0.230824 | 3.069152 | 8.988479 | 0.208795 | 1.722315 |

PHSSA | 0.202369 | 3.544214 | 9.04821 | 0.205723 | 1.72802 |

Algorithm | Optimum Variables | Optimum Cost | |||
---|---|---|---|---|---|

Ts | Th | R | L | ||

MGTO | 0.7424 | 0.3702 | 40.3196 | 200 | 5734.9131 |

GTO | 1.2404 | 0.5844 | 65.2252 | 10 | 7141.3611 |

HHO | 0.8175838 | 0.4072927 | 42.09174576 | 176.7196 | 6000.46259 |

SMA | 0.7931 | 0.3932 | 40.6711 | 196.2178 | 5994.1857 |

WOA | 0.8125 | 0.4375 | 42.0982699 | 176.6389 | 6059.7410 |

GWO | 0.8125 | 0.4345 | 42.0892 | 176.7587 | 6051.5639 |

MVO | 0.8125 | 0.4375 | 42.090738 | 176.7386 | 6060.8066 |

GA | 0.8125 | 0.4375 | 42.097398 | 176.6540 | 6059.94634 |

Algorithm | Optimum Variables | Optimum Weight | ||||||
---|---|---|---|---|---|---|---|---|

x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | ||

MGTO | 3.4975 | 0.7 | 17 | 7.3000 | 7.8000 | 3.3500 | 5.2855 | 2995.4373 |

AO | 3.5021 | 0.7 | 17 | 7.3099 | 7.7476 | 3.3641 | 5.2994 | 3007.7328 |

PSO | 3.5001 | 0.7 | 17.0002 | 7.5177 | 7.7832 | 3.3508 | 5.2867 | 3145.922 |

AOA | 3.50384 | 0.7 | 17 | 7.3 | 7.72933 | 3.35649 | 5.2867 | 2997.9157 |

MFO | 3.49745 | 0.7 | 17 | 7.82775 | 7.71245 | 3.35178 | 5.28635 | 2998.9408 |

GA | 3.51025 | 0.7 | 17 | 8.35 | 7.8 | 3.36220 | 5.28772 | 3067.561 |

SCA | 3.50875 | 0.7 | 17 | 7.3 | 7.8 | 3.46102 | 5.28921 | 3030.563 |

MDA | 3.5 | 0.7 | 17 | 7.3 | 7.67039 | 3.54242 | 5.24581 | 3019.5833 |

Algorithm | Optimum Variables | Optimum Weight | ||
---|---|---|---|---|

D | D | N | ||

MGTO | 0.05000 | 0.3744 | 8.5465 | 0.0099 |

AO | 0.0502439 | 0.35262 | 10.5425 | 0.011165 |

HHO | 0.051796393 | 0.359305355 | 11.138859 | 0.012665443 |

SSA | 0.051207 | 0.345215 | 12.004032 | 0.0126763 |

WOA | 0.051207 | 0.345215 | 12.004032 | 0.0126763 |

GWO | 0.05169 | 0.356737 | 11.28885 | 0.012666 |

PSO | 0.051728 | 0.357644 | 11.244543 | 0.0126747 |

HS | 0.051154 | 0.349871 | 12.076432 | 0.0126706 |

Algorithm | Optimum Variables | Optimum Weight | |
---|---|---|---|

x_{1} | x_{2} | ||

MGTO | 0.7884 | 0.4081 | 263.8523464 |

AO | 0.7926 | 0.3966 | 263.8684 |

HHO | 0.788662816 | 0.408283133832900 | 263.8958434 |

SSA | 0.78866541 | 0.408275784 | 263.89584 |

AOA | 0.79369 | 0.39426 | 263.9154 |

MVO | 0.78860276 | 0.408453070000000 | 263.8958499 |

MFO | 0.788244771 | 0.409466905784741 | 263.8959797 |

GOA | 0.788897555578973 | 0.407619570115153 | 263.895881496069 |

Algorithm | MGTO | GTO | AOA | SSA | WOA | ROLGWO | PSO |
---|---|---|---|---|---|---|---|

x1 | 0.5000 | 1.3249 | 0.50000 | 0.6770 | 1.1079 | 0.5008 | 0.5000 |

x2 | 1.2294 | 0.8819 | 1.2827 | 1.1695 | 1.1202 | 1.2439 | 1.2222 |

x3 | 0.5000 | 0.5000 | 0.6364 | 0.5000 | 0.6965 | 0.5000 | 1.5000 |

x4 | 1.2006 | 1.2322 | 1.3636 | 1.1805 | 1.1535 | 1.1921 | 0.7412 |

x5 | 0.5000 | 0.5000 | 0.50000 | 0.9549 | 0.6840 | 0.5037 | 0.5000 |

x6 | 1.0917 | 1.0985 | 1.50000 | 0.9809 | 0.8071 | 1.2917 | 1.5000 |

x7 | 0.5000 | 0.5000 | 0.50000 | 0.5000 | 0.9805 | 0.5012 | 0.5000 |

x8 | 0.3450 | 0.34385 | 0.3450 | 0.3413 | 0.2748 | 0.3449 | 0.34500 |

x9 | 0.3450 | 0.19200 | 0.3084 | 0.2229 | 0.2587 | 0.2536 | 0.34500 |

x10 | 0.6436 | 4.4782 | 0.5795 | 3.5908 | 8.4836 | 3.1707 | −0.20845 |

x11 | 0.3162 | 2.6609 | −9.62291 | −1.22041 | 17.8255 | 3.3177 | 3.2759 |

Optimal weight | 23.1894 | 23.2046 | 25.8678 | 23.3121 | 28.9580 | 23.2527 | 23.1902 |

Algorithm | Optimal Values for Variables | Optimal Cost | |
---|---|---|---|

d | T | ||

MGTO | 5.4511 | 0.2919 | 26.5313 |

HSCAHS | 5.4170 | 0.3128 | 27.4745 |

AOA | 7.5313 | 0.2223 | 31.5088 |

WOA | 5.7562 | 0.2764 | 27.1415 |

GWO | 5.4513 | 0.2919 | 26.5333 |

ROLGWO | 5.4510 | 0.2919 | 26.5326 |

DSCA | 5.5179 | 0.2899 | 26.7494 |

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## Share and Cite

**MDPI and ACS Style**

Wu, T.; Wu, D.; Jia, H.; Zhang, N.; Almotairi, K.H.; Liu, Q.; Abualigah, L.
A Modified Gorilla Troops Optimizer for Global Optimization Problem. *Appl. Sci.* **2022**, *12*, 10144.
https://doi.org/10.3390/app121910144

**AMA Style**

Wu T, Wu D, Jia H, Zhang N, Almotairi KH, Liu Q, Abualigah L.
A Modified Gorilla Troops Optimizer for Global Optimization Problem. *Applied Sciences*. 2022; 12(19):10144.
https://doi.org/10.3390/app121910144

**Chicago/Turabian Style**

Wu, Tingyao, Di Wu, Heming Jia, Nuohan Zhang, Khaled H. Almotairi, Qingxin Liu, and Laith Abualigah.
2022. "A Modified Gorilla Troops Optimizer for Global Optimization Problem" *Applied Sciences* 12, no. 19: 10144.
https://doi.org/10.3390/app121910144