# A Dynamic Adjusting Novel Global Harmony Search for Continuous Optimization Problems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. HS, IHS, SGHS, and NGHS

#### 2.1. Harmony Search Algorithm

**Step 1.**Initialization: the algorithm and problem parameters

**Step 2.**Initialization: the decision variable values and the harmony memory

**Step 3.**Movement: improvise a new harmony

Algorithm 1 The Movement Steps of HS (Pseudocode 1) | |

1: | For $\mathrm{j}=1\text{}\mathrm{to}\text{}\mathrm{D}$ do |

2: | If ${\mathrm{r}}_{1}\le \mathrm{H}\mathrm{M}\mathrm{C}\mathrm{R}$ then |

3: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}$ % memory consideration |

4: | If ${\mathrm{r}}_{2}\le \mathrm{P}\mathrm{A}\mathrm{R}$ then |

5: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}-\mathrm{B}\mathrm{W}+{\mathrm{r}}_{3}\times 2\times \mathrm{B}\mathrm{W}$ % pitch adjustment |

6: | If ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}>{\mathrm{x}}_{\mathrm{j}\mathrm{U}}$ then |

7: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{i}\mathrm{U}}$ |

8: | Else if ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}<{\mathrm{x}}_{\mathrm{j}\mathrm{L}}$ then |

9: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{i}\mathrm{L}}$ |

10: | End |

11: | End |

12: | Else |

13: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{j}\mathrm{L}}+{\mathrm{r}}_{4}\times \left({\mathrm{x}}_{\mathrm{j}\mathrm{U}}-{\mathrm{x}}_{\mathrm{j}\mathrm{L}}\right)$ % random selection |

14: | End |

15: | End |

^{th}component of ${x}^{k+1}$. $i$ is an uniformly generated random number in [1, m], and ${x}_{ij}^{k}$ is the j

^{th}component of the i

^{th}candidate solution vector in the HM. ${r}_{1}$, ${r}_{2}$, ${r}_{3}$ and ${r}_{4}$ are the uniformly generated random numbers in the region of [0, 1], and BW is a given distance bandwidth.

**Step 4.**Replacement: update harmony memory

**Step 5.**Iteration: check the stopping criterion

#### 2.2. Improved Harmony Search Algorithm

#### 2.3. Self-Adaptive Global Best Harmony Search Algorithm

**Step 1.**Initialization: the problem and algorithm parameters

**Step 2.**Initialization: the decision variable values and the harmony memory

**Step 3.**Movement: generate the algorithm parameters

**Step 4.**Movement: improvise a new harmony

Algorithm 2 The Movement Steps of SGHS (Pseudocode 2) [24] | |

1: | For $\mathrm{j}=1\text{}\mathrm{to}\text{}\mathrm{D}$ do |

2: | If ${\mathrm{r}}_{1}\le {\mathrm{HMCR}}^{\mathrm{k}}$ then |

3: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}-\mathrm{B}{\mathrm{W}}^{\mathrm{k}}+{\mathrm{r}}_{2}\times 2\times \mathrm{B}{\mathrm{W}}^{\mathrm{k}}$ |

4: | If ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}>{\mathrm{x}}_{\mathrm{j}\mathrm{U}}$ then |

5: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{i}\mathrm{U}}$ |

6: | Else if ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}<{\mathrm{x}}_{\mathrm{j}\mathrm{L}}$ then |

7: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{i}\mathrm{L}}$ |

8: | End |

9: | If ${\mathrm{r}}_{3}\le {\mathrm{PAR}}^{\mathrm{k}}$ then |

10: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},\mathrm{j}}^{\mathrm{k}}$ |

11: | End |

12: | Else |

13: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{j}\mathrm{L}}+{\mathrm{r}}_{4}\times \left({\mathrm{x}}_{\mathrm{j}\mathrm{U}}-{\mathrm{x}}_{\mathrm{j}\mathrm{L}}\right)$ % random selection |

14: | End |

15: | End |

^{th}component of ${x}^{k+1}$. $i$ is an uniformly generated random number in [1, m], and ${x}_{ij}^{k}$ is the j

^{th}component of the i

^{th}candidate solution vector in the HM. ${x}_{best,j}^{k}$ is the j

^{th}component of the best candidate solution vector in the HM. ${r}_{1}$, ${r}_{2}$, ${r}_{3}$ and ${r}_{4}$ are uniformly generated random numbers in [0, 1]. ${r}_{1}$ is used for position updating, ${r}_{2}$ determines the distance of the BW, ${r}_{3}$ is used for pitch adjustment, and ${r}_{4}$ is used for random selection.

**Step 5.**Replacement: update harmony memory

**Step 6.**Replacement: update $HMC{R}_{m}$ and $PA{R}_{m}$

**Step 7.**Iteration: check the stopping criterion

#### 2.4. Novel Global Harmony Search Algorithm

^{th}decision variable. This adaptive step can dynamically balance the performance of global exploration and local exploitation in the NGHS algorithm. As Zou et al. [26] points out, “In the early stage of optimization, all solution vectors are sporadic in the solution space, so most adaptive steps are large, and most trust regions are wide, which is beneficial to the global search of NGHS. However, in the late stage of optimization, all non-best solution vectors are inclined to move to the global best solution vector, so most solution vectors are close to each other. In this case, most adaptive steps are small and most trust regions are narrow, which is beneficial to the local search of NGHS.”

**Step 1.**Initialization: the algorithm and problem parameters

- (1)
- Set parameters m, NI, and the current iteration k = 1.
- (2)
- The genetic mutation probability (${p}_{m}$) is included in NGHS, while the harmony memory considering rate (HMCR), pitch adjusting rate (PAR) and the bandwidth (BW) are excluded from NGHS.

**Step 2.**Initialization: the decision variable values and the harmony memory

**Step 3.**Movement: improvise a new harmony

Algorithm 3 The Movement Steps of NGHS (Pseudocode 3) [25,26,27]. | |

1: | For $\mathrm{j}=1\text{}\mathrm{to}\text{}\mathrm{D}$ do |

2: | ${\mathrm{x}}_{\mathrm{R}}=2\times {\mathrm{x}}_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},\mathrm{j}}^{\mathrm{k}}-{\mathrm{x}}_{\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{t},\mathrm{j}}^{\mathrm{k}}$ |

3: | If ${\mathrm{x}}_{\mathrm{R}}>{\mathrm{x}}_{\mathrm{j}\mathrm{U}}$ then |

4: | ${\mathrm{x}}_{\mathrm{R}}={\mathrm{x}}_{\mathrm{j}\mathrm{U}}$ |

5: | Else if ${\mathrm{x}}_{\mathrm{R}}<{\mathrm{x}}_{\mathrm{j}\mathrm{L}}$ then |

6: | ${\mathrm{x}}_{\mathrm{R}}={\mathrm{x}}_{\mathrm{j}\mathrm{L}}$ |

7: | End |

8: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{t},\mathrm{j}}^{\mathrm{k}}+{\mathrm{r}}_{1}\times ({\mathrm{x}}_{\mathrm{R}}-{\mathrm{x}}_{\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{t},\mathrm{j}}^{\mathrm{k}})$ % position updating |

9: | If ${\mathrm{r}}_{2}\le {\mathrm{p}}_{\mathrm{m}}$ then |

10: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{j}\mathrm{L}}+{\mathrm{r}}_{3}\times \left({\mathrm{x}}_{\mathrm{j}\mathrm{U}}-{\mathrm{x}}_{\mathrm{j}\mathrm{L}}\right)$ % genetic mutation |

11: | End |

12: | End |

**Step 4.**Replacement: update harmony memory

**Step 5.**Iteration: check the stopping criterion

## 3. Dynamic Adjusting Novel Global Harmony Search (DANGHS) Algorithm

- (1)
- Straight linear increasing strategy (Straight_1):The genetic mutation probability is increased by Equation (6), which is a linear function.$${p}_{m}^{k}={p}_{m\_min}+\frac{\left({p}_{m\_max}-{p}_{m\_min}\right)}{NI}\times k.$$
- (2)
- Straight linear decreasing strategy (Straight_2):The genetic mutation probability is decreased by Equation (7), which is a linear function.$${p}_{m}^{k}={p}_{m\_max}+\frac{\left({p}_{m\_min}-{p}_{m\_max}\right)}{NI}\times k$$
- (3)
- Threshold linear prior increasing strategy (Threshold_1):The genetic mutation probability is increased by Equation (8), which is a linear function with a threshold. The genetic mutation probability is raised before the threshold, but the genetic mutation probability is a fixed maximum value after the threshold.$${p}_{m}^{k}=\{\begin{array}{cc}{p}_{m\_min}+\frac{{P}_{m\_max}-{P}_{m\_min}}{NI}\times 2k& if\text{}kNI/2\\ {p}_{m\_max}& if\text{}k\ge NI/2\end{array}$$
- (4)
- Threshold linear prior decreasing strategy (Threshold_2):The genetic mutation probability is decreased by Equation (9), which is a linear function with a threshold. The genetic mutation probability is reduced before the threshold, but the genetic mutation probability is a fixed minimum value after the threshold.$${p}_{m}^{k}=\{\begin{array}{cc}{p}_{m\_max}+\frac{{P}_{m\_min}-{P}_{m\_max}}{NI}\times 2k& if\text{}kNI/2\\ {p}_{m\_min}& if\text{}k\ge NI/2\end{array}$$
- (5)
- Threshold linear posterior increasing strategy (Threshold_3):The genetic mutation probability is increased by Equation (10), which is a linear function with a threshold. The genetic mutation probability is a fixed minimum value before the threshold, but the genetic mutation probability is raised after the threshold.$${p}_{m}^{k}=\{\begin{array}{cc}{p}_{m\_min}& if\text{}kNI/2\\ {p}_{m\_min}+\frac{{P}_{m\_max}-{P}_{m\_min}}{NI}\times 2k& if\text{}k\ge NI/2\end{array}$$
- (6)
- Threshold linear posterior decreasing strategy (Threshold_4):The genetic mutation probability is decreased by Equation (11), which is a linear function with a threshold. The genetic mutation probability is a fixed maximum value before the threshold, but the genetic mutation probability is reduced after the threshold.$${p}_{m}^{k}=\{\begin{array}{cc}{p}_{m\_max}& if\text{}kNI/2\\ {p}_{m\_max}+\frac{{P}_{m\_min}-{P}_{m\_max}}{NI}\times 2k& if\text{}k\ge NI/2\end{array}$$
- (7)
- Natural exponential increasing strategy (Exponential_1):The genetic mutation probability is increased by Equation (12), which is a non-linear function.$${p}_{m}^{k}={p}_{m\_min}\times {e}^{\left(\mathrm{ln}\left(\frac{{p}_{m\_max}}{{p}_{m\_min}}\right)\times k/NI\right)}$$
- (8)
- Natural exponential decreasing strategy (Exponential_2):The genetic mutation probability is decreased by Equation (13), which is a non-linear function.$${p}_{m}^{k}={p}_{m\_max}\times {e}^{(\mathrm{ln}(\frac{{p}_{m\_min}}{{p}_{m\_max}})\times k/NI)}$$
- (9)
- Exponential increasing strategy:The genetic mutation probability is increased by Equation (14), which is a non-linear function. We can control the increasing rate by the modification rate ($mr$).$${p}_{m}^{k}={p}_{m\_min}+\left({p}_{m\_max}-{p}_{m\_min}\right)\times m{r}^{\left(NI-k\right)/NI}$$
- (10)
- Exponential decreasing strategy:The genetic mutation probability is decreased by Equation (15), which is a non-linear function. We can control the decreasing rate by the modification rate ($mr$).$${p}_{m}^{k}={p}_{m\_min}+\left({p}_{m\_max}-{p}_{m\_min}\right)\times m{r}^{k/NI}$$
- (11)
- Concave cosine strategy:The genetic mutation probability is changed by Equation (16), which is a periodic function. The shape of this function is a concave, and we can control the cycle time of this function by the coefficient of cycle (cc).$${p}_{m}^{k}=\frac{{p}_{m\_max}+{p}_{m\_min}}{2}+\frac{{p}_{m\_max}-{p}_{m\_min}}{2}\times \mathrm{cos}\frac{k\times cc\times 2\pi}{NI}$$
- (12)
- Convex cosine strategy:The genetic mutation probability is changed by Equation (17), which is a periodic function. The shape of this function is a convex, and we can control the cycle time of this function by the coefficient of cycle (cc).$${p}_{m}^{k}=\frac{{p}_{m\_max}+{p}_{m\_min}}{2}-\frac{{p}_{m\_max}-{p}_{m\_min}}{2}\times \mathrm{cos}\frac{k\times cc\times 2\pi}{NI}$$

**Step 1.**Initialization: the problem and algorithm parameters

**Step 2.**Initialization: the decision variable values and the harmony memory

**Step 3.**Movement: generate the algorithm parameters

**Step 4.**Movement: improvise a new harmony

Algorithm 4 The Movement Steps of DANGHS (Pseudocode 4) | |

1: | For $\mathrm{j}=1\text{}\mathrm{to}\text{}\mathrm{D}$ do |

2: | If ${\mathrm{r}}_{1}>{\mathrm{p}}_{\mathrm{m}}^{\mathrm{k}}$ then |

3: | ${\mathrm{x}}_{\mathrm{R}}=2\times {\mathrm{x}}_{\mathrm{best},\mathrm{j}}^{\mathrm{k}}-{\mathrm{x}}_{\mathrm{worst},\mathrm{j}}^{\mathrm{k}}$ |

4: | If ${\mathrm{x}}_{\mathrm{R}}>{\mathrm{x}}_{\mathrm{jU}}$ then |

5: | ${\mathrm{x}}_{\mathrm{R}}={\mathrm{x}}_{\mathrm{jU}}$ |

6: | Else if ${\mathrm{x}}_{\mathrm{R}}<{\mathrm{x}}_{\mathrm{jL}}$ then |

7: | ${\mathrm{x}}_{\mathrm{R}}={\mathrm{x}}_{\mathrm{jL}}$ |

8: | End |

9: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{worst},\mathrm{j}}^{\mathrm{k}}+{\mathrm{r}}_{2}\times ({\mathrm{x}}_{\mathrm{R}}-{\mathrm{x}}_{\mathrm{worst},\mathrm{j}}^{\mathrm{k}})$ % position updating |

10: | Else |

11: | ${\mathrm{x}}_{\mathrm{j}}^{\mathrm{k}+1}={\mathrm{x}}_{\mathrm{jL}}+{\mathrm{r}}_{3}\times \left({\mathrm{x}}_{\mathrm{jU}}-{\mathrm{x}}_{\mathrm{jL}}\right)$ % genetic mutation |

12: | End |

13: | End |

**Step 5.**Replacement: update harmony memory

**Step 6.**Iteration: check the stopping criterion

## 4. Experiments and Analysis

^{−31}; 1.2209 × 10

^{−14}), 3 (1.9511 × 10

^{−18}7.9778 × 10

^{−9}) and 6 (9.6308 × 10

^{−14}; 9.3030 × 10

^{−9}); the threshold linear prior decreasing strategy (Threshold_2) can find the best objective function value for problem 9 (3.8183 × 10

^{−4}; 1.2728 × 10

^{−3}). More specifically, the convex cosine strategy with k = 3 (Cosine_4), which is the periodic strategy, can find the best objective function value for problem 13 (3.9875 × 10

^{2}; 5.3644 × 10

^{2}).

^{1}). However, the threshold linear posterior increasing strategy (Threshold_3) can find the best objective function value for problem 7 with D = 100 (6.1559 × 10

^{1}). Besides, the decreasing strategy can find the best objective function value for problems 4, 5, 10, 11, 12, and 14. According to the experimental results, the threshold linear posterior decreasing strategy (Threshold_4) can find the best objective function value for problems 4 (6.0249 × 10

^{1}), 5 (3.1209 × 10

^{−2}) and 11 (−3.7419 × 10

^{2}) with D = 30. However, the natural exponential decreasing strategy (Exponential_2) can find the best objective function value for problems 4 (8.6301 × 10

^{3}), 5 (6.4754 × 10

^{−3}), and 11 (1.1471 × 10

^{4}) with D = 100. The natural exponential decreasing strategy (Exponential _2) can find the best objective function value for problem 10 with D = 30 (−4.5000 × 10

^{2}). However, the threshold linear prior decreasing strategy (Threshold_2) can find the best objective function value for problem 10 with D = 100 (−4.5000 × 10

^{2}). The straight linear decreasing strategy (Straight_2) can find the best objective function value for problem 12 with D = 30 (−1.7821 × 10

^{2}). However, the exponential decreasing strategy with $mr$ = 0.001 (Exponential_6) can find the best objective function value for problem 12 with D = 100 (−1.6037 × 10

^{2}). The straight linear decreasing strategy (Straight_2) can find the best objective function value for problem 14 with D = 30 (−3.3000 × 10

^{2}). However, the exponential decreasing strategy with $mr$ = 0.01 (Exponential_4) can find the best objective function value for problem 14 with D = 100 (−3.2997 × 10

^{2}).

^{−2}).

^{−39}). The Exponential_6 strategy had the best maximum objective function value (3.7601 × 10

^{−30}) and had the minimum standard deviation value (7.0604 × 10

^{−31}) for problems 1 with D = 30.

## 5. Conclusions

- The decreasing dynamic adjustment strategies should be applied to some problems in which the DANGHS algorithm needs a larger, ${p}_{m}$, in the early iterations, in order to have a larger probability of finding a better trial solution around the current one.
- The increasing dynamic adjustment strategies should be applied to other problems. For these problems, if the current solution is trapped in a local optimum, the DANGHS algorithm requires a larger probability, ${p}_{m}$, in later iterations in order to avoid the local optima.
- The periodic dynamic adjustment strategy can find the best objective function value for problem 13. These particular results show that there are not only two kinds of adjustment strategies, decreasing and increasing strategies, which are suitable for all problems. This viewpoint is different from the common views: the adjustment strategy is as small as possible or as large as possible with a generation number. For a specific problem, the periodic dynamic adjustment strategy could have better performance in comparison with other decreasing or increasing strategies. Therefore, these results inspire us to further investigate this kind of periodic dynamic adjustment strategy in future experiments.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Chiu, C.Y.; Fan, S.K.S.; Shih, P.C.; Weng, Y.H. Applying HBMO-based SOM in predicting the Taiwan steel price fluctuation. Int. J. Electron. Bus. Manag.
**2014**, 12, 1–14. [Google Scholar] - Chen, K.H.; Chen, L.F.; Su, C.T. A new particle swarm feature selection method for classification. J. Intell. Inf. Syst.
**2014**, 42, 507–530. [Google Scholar] [CrossRef] - Petrović, M.; Vuković, N.; Mitić, M.; Miljković, Z. Integration of process planning and scheduling using chaotic particle swarm optimization algorithm. Expert Syst. Appl.
**2016**, 64, 569–588. [Google Scholar] [CrossRef] - Khaled, N.; Hemayed, E.E.; Fayek, M.B. A GA-based approach for epipolar geometry estimation. Int. J. Pattern Recognit. Artif. Intell.
**2013**, 27, 1355014. [Google Scholar] [CrossRef] - Metawaa, N.; Hassana, M.K.; Elhoseny, M. Genetic algorithm based model for optimizing bank lending decisions. Expert Syst. Appl.
**2017**, 80, 75–82. [Google Scholar] [CrossRef] - Song, S. Design of distributed database systems: an iterative genetic algorithm. J. Intell. Inf. Syst.
**2015**, 45, 29–59. [Google Scholar] [CrossRef] - Gambardella, L.M.; Montemanni, R.; Weyland, D. Coupling ant colony systems with strong local searches. Eur. J. Oper. Res.
**2012**, 220, 831–843. [Google Scholar] [CrossRef] - D’Andreagiovanni, F.; Mett, F.; Nardin, A.; Pulaj, J. Integrating LP-guided variable fixing with MIP heuristics in the robust design of hybrid wired-wireless FTTx access networks. Appl. Soft. Comput.
**2017**, 61, 1074–1087. [Google Scholar] [CrossRef] - D’Andreagiovanni, F.; Nardin, A. Towards the fast and robust optimal design of wireless body area networks. Appl. Soft. Comput.
**2015**, 37, 971–982. [Google Scholar] [CrossRef] [Green Version] - Kennedy, J.; Eberhart, R. Particle Swarm Optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995. [Google Scholar]
- Eberhart, R.; Kennedy, J. A new optimizer using particle swarm theory. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4–6 October 1995; pp. 39–43. [Google Scholar]
- Ozcan, E.; Mohan, C.K. Analysis of a simple particle swarm optimization system. Intell. Eng. Syst. Artif. Neural Netw.
**1998**, 8, 253–258. [Google Scholar] - Holland, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence; University of Michigan Press: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Holland, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence; MIT Press: Cambridge, MA, USA, 1992. [Google Scholar]
- Gordini, N. A genetic algorithm approach for SMEs bankruptcy prediction: Empirical evidence from Italy. Expert Syst. Appl.
**2014**, 41, 6433–6445. [Google Scholar] [CrossRef] - Geem, Z.W.; Kim, J.H.; Loganathan, G.V. A new heuristic optimization algorithm: harmony search. Simulation
**2001**, 76, 60–68. [Google Scholar] [CrossRef] - Haddad, O.B.; Afshar, A.; Marino, M.A. Honey-bees mating optimization (HBMO) algorithm: A new heuristic approach for water resources optimization. Water Resour. Manag.
**2006**, 20, 661–680. [Google Scholar] [CrossRef] - Ouyang, A.; Peng, X.; Liu, Y.; Fan, L.; Li, K. An efficient hybrid algorithm based on HS and SFLA. Int. J. Pattern Recognit. Artif. Intell.
**2016**, 30, 1659012. [Google Scholar] [CrossRef] - Tavakoli, S.; Valian, E.; Mohanna, S. Feedforward neural network training using intelligent global harmony search. Evol. Syst.
**2012**, 3, 125–131. [Google Scholar] [CrossRef] - Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P. Optimization by simulated annealing. Science
**1983**, 220, 671–680. [Google Scholar] [CrossRef] [PubMed] - Assad, A.; Deep, K. A Hybrid Harmony search and Simulated Annealing algorithm for continuous optimization. Inf. Sci.
**2018**, 450, 246–266. [Google Scholar] [CrossRef] - Assad, A.; Deep, K. A two-phase harmony search algorithm for continuous optimization. Comput. Intell.
**2017**, 33, 1038–1075. [Google Scholar] [CrossRef] - Mahdavi, M.; Fesanghary, M.; Damangir, E. An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput.
**2007**, 188, 1567–1579. [Google Scholar] [CrossRef] - Pan, Q.K.; Suganthan, P.N.; Tasgetiren, M.F.; Liang, J.J. A self-adaptive global best harmony search algorithm for continuous optimization problems. Appl. Math. Comput.
**2010**, 216, 830–848. [Google Scholar] [CrossRef] - Zou, D.; Gao, L.; Li, S.; Wu, J.; Wang, X. A novel global harmony search algorithm for task assignment problem. J. Syst. Softw.
**2010**, 83, 1678–1688. [Google Scholar] [CrossRef] - Zou, D.; Gao, L.; Wu, J.; Li, S.; Li, Y. A novel global harmony search algorithm for reliability problems. Comput. Ind. Eng.
**2010**, 58, 307–316. [Google Scholar] [CrossRef] - Zou, D.; Gao, L.; Wu, J.; Li, S. Novel global harmony search algorithm for unconstrained problems. Neurocomputing
**2010**, 73, 3308–3318. [Google Scholar] [CrossRef] - Valian, E.; Tavakoli, S.; Mohanna, S. An intelligent global harmony search approach to continuous optimization problems. Appl. Math. Comput.
**2014**, 232, 670–684. [Google Scholar] [CrossRef] - Kattan, A.; Abdullah, R. Training of feed-forward neural networks for pattern-classification applications using music inspired algorithm. Inter. J. Comput. Sci. Inf. Secur.
**2011**, 9, 44–57. [Google Scholar] - Lee, K.S.; Geem, Z.W. A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput. Method Appl. Mech. Eng.
**2005**, 194, 3902–3933. [Google Scholar] [CrossRef] - Omran, M.G.H.; Mahdavi, M. Global-best harmony search. Appl. Math. Comput.
**2008**, 198, 643–656. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Variation of pitch adjusting rate (PAR) versus iteration number; (

**b**) Variation of bandwidth (BW) versus iteration number.

**Figure 7.**Typical convergence graph of five different algorithms for problems 1 to 8 (D = 30). (

**a**) Problem 1; (

**b**) Problem 2; (

**c**) Problem 3; (

**d**) Problem 4; (

**e**) Problem 5; (

**f**) Problem 6; (

**g**) Problem 7; (

**h**) Problem 8.

**Figure 8.**Typical convergence graph of five different algorithms for problems 9 to 14 (D = 30). (

**a**) Problem 9; (

**b**) Problem 10; (

**c**) Problem 11; (

**d**) Problem 12; (

**e**) Problem 13; (

**f**) Problem 14.

**Figure 9.**Typical convergence graph of five different algorithms for problems 1 to 8 (D = 100). (

**a**) Problem 1; (

**b**) Problem 2; (

**c**) Problem 3; (

**d**) Problem 4; (

**e**) Problem 5; (

**f**) Problem 6; (

**g**) Problem 7; (

**h**) Problem 8.

**Figure 10.**Typical convergence graph of five different algorithms for problems 9 to 14 (D = 100). (

**a**) Problem 9; (

**b**) Problem 10; (

**c**) Problem 11; (

**d**) Problem 12; (

**e**) Problem 13; (

**f**) Problem 14.

Name | Function | Search Space | Optimum |
---|---|---|---|

${\mathit{f}}_{\mathbf{1}}$ Sphere function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}{x}_{i}^{2}$ | [−100, 100]^{n} | 0 |

${\mathit{f}}_{\mathbf{2}}$ Step function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left(\u23a3{x}_{i}+0.5\u23a6\right)}^{2}$ | [−100, 100]^{n} | 0 |

${\mathit{f}}_{\mathbf{3}}$ Schwefel’s problem 2.22 | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left|{x}_{i}\right|+{\displaystyle {\displaystyle \prod}_{i=1}^{N}}\left|{x}_{i}\right|$ | [−10, 10]^{n} | 0 |

${\mathit{f}}_{\mathbf{4}}$ Rotated hyper-ellipsoid function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}{({\displaystyle {\displaystyle \sum}_{j=1}^{i}}{x}_{j})}^{2}$ | [−100, 100]^{n} | 0 |

${\mathit{f}}_{\mathbf{5}}$ Griewank function | $\mathrm{min}f\left({x}_{i}\right)=\frac{1}{4000}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{x}_{i}^{2}-{\displaystyle {\displaystyle \prod}_{i=1}^{N}}\mathrm{cos}\left(\frac{{x}_{i}}{\sqrt{i}}\right)+1$ | [−600, 600]^{n} | 0 |

${\mathit{f}}_{\mathbf{6}}$ Ackley’s function | $\mathrm{min}f\left({x}_{i}\right)=20+\mathrm{e}-20\mathrm{exp}\left(-0.2\sqrt{{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{x}_{i}^{2}/n}\right)-\mathrm{exp}\left({\displaystyle {\displaystyle \sum}_{i=1}^{N}}\mathrm{cos}\left(2\pi {x}_{i}\right)/n\right)$ | [−32, 32]^{n} | 0 |

${\mathit{f}}_{\mathbf{7}}$ Rosenbrock function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N-1}}\left(100{\left({x}_{i+1}-{x}_{i}^{2}\right)}^{2}+{\left(1-{x}_{i}\right)}^{2}\right)$ | [−30, 30]^{n} | 0 |

${\mathit{f}}_{\mathbf{8}}$ Rastrigin function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left({x}_{i}^{2}-10\mathrm{cos}\left(2\pi {x}_{i}\right)+10\right)$ | [−5.12, 5.12]^{n} | 0 |

${\mathit{f}}_{\mathbf{9}}$ Schwefel’s problem 2.26 | $\mathrm{min}f\left({x}_{i}\right)=418.9829N-{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left({x}_{i}\mathrm{sin}\left(\sqrt{\left|{x}_{i}\right|}\right)\right)$ | [−500, 500]^{n} | 0 |

${\mathit{f}}_{\mathbf{10}}$ Shifted Sphere function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}{z}_{i}^{2}-450$ | [−100, 100]^{n} | −450 |

${\mathit{f}}_{\mathbf{11}}$ Shifted Rotated hyper-ellipsoid function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}{({\displaystyle {\displaystyle \sum}_{j=1}^{i}}{z}_{i})}^{2}-450$ | [−100, 100]^{n} | −450 |

${\mathit{f}}_{\mathbf{12}}$ Shifted Rotated Griewank function | $\mathrm{min}f\left({x}_{i}\right)=\frac{1}{4000}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{z}_{i}^{2}-{\displaystyle {\displaystyle \prod}_{i=1}^{N}}\mathrm{cos}\left(\frac{{z}_{i}}{\sqrt{i}}\right)+1-180$ | [−600, 600]^{n} | −180 |

${\mathit{f}}_{\mathbf{13}}$ Shifted Rosenbrock function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N-1}}\left(100{\left({z}_{i+1}-{z}_{i}^{2}\right)}^{2}+{\left(1-{z}_{i}\right)}^{2}\right)+390$ | [−30, 30]^{n} | 390 |

${\mathit{f}}_{\mathbf{14}}$ Shifted Rastrigin function | $\mathrm{min}f\left({x}_{i}\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left({z}_{i}^{2}-10\mathrm{cos}\left(2\pi {z}_{i}\right)+10\right)-330$ | [−5.12, 5.12]^{n} | −330 |

Algorithm | m ^{1} | HMCR ^{2} | PAR ^{3} | BW ^{4} | LP ^{5} | ${\mathit{p}}_{\mathit{m}}$^{6} |
---|---|---|---|---|---|---|

HS | 5 | 0.9 | 0.3 | 0.01 | – | – |

IHS | 5 | 0.9 | $PA{R}_{min}=0.01$ $PA{R}_{max}=0.99$ | $B{W}_{max}=\left({x}_{jU}-{x}_{jL}\right)/20$ $B{W}_{min}=0.0001$ | – | – |

SGHS | 5 | $HMC{R}_{m}=0.98$ | $PA{R}_{m}=0.9$ | $B{W}_{max}=\left({x}_{jU}-{x}_{jL}\right)/10$ $B{W}_{min}=0.0005$ | 100 | – |

NGHS | 5 | – | – | – | – | 0.005 |

DANGHS | 5 | – | – | – | – | ${P}_{min}=0.001$ ${P}_{max}=0.010$. |

^{1}m: the harmony memory size;

^{2}HMCR: the harmony memory considering rate;

^{3}PAR: the pitch adjusting rate;

^{4}BW: the bandwidth;

^{5}LP: the learning period;

^{6}${p}_{m}$: the genetic mutation probability.

No. | Dimension (D) = 30 | Dimension (D) = 100 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Adjustment strategy | Min | Max | Mean | SD | Adjustment strategy | Min | Max | Mean | SD | |

${\mathit{f}}_{\mathbf{1}}$ | Straight_1 | 1.0461 × 10^{−17} | 4.3759 × 10^{−15} | 6.7177 × 10^{−16} | 1.1026 × 10^{−15} | Straight_1 | 7.4075 × 10^{−6} | 3.1563 × 10^{−4} | 3.3196 × 10^{−5} | 5.3403 × 10^{−5} |

Straight_2 | 3.1999 × 10^{−23} | 2.5783 × 10^{−18} | 3.6341 × 10^{−19} | 6.7121 × 10^{−19} | Straight_2 | 1.0715 × 10^{−7} | 7.1045 × 10^{−6} | 8.4864 × 10^{−7} | 1.2362 × 10^{−6} | |

Threshold_1 | 1.5431 × 10^{−13} | 7.3069 × 10^{−11} | 6.6315 × 10^{−12} | 1.3094 × 10^{−11} | Threshold_1 | 1.0024 × 10^{−3} | 9.1452 × 10^{−3} | 2.7025 × 10^{−3} | 1.6455 × 10^{−3} | |

Threshold_2 | 7.1381 × 10^{−39} | 2.0446 × 10^{−26} | 6.8264 × 10^{−28} | 3.6700 × 10^{−27} | Threshold_2 | 3.9739 × 10^{−16} | 8.5814 × 10^{−14} | 1.7158 × 10^{−14} | 2.2275 × 10^{−14} | |

Threshold_3 | 1.5233 × 10^{−32} | 1.4639 × 10^{−22} | 4.9489 × 10^{−24} | 2.6266 × 10^{−23} | Threshold_3 | 5.5110 × 10^{−15} | 4.3556 × 10^{−12} | 3.2639 × 10^{−13} | 7.8921 × 10^{−13} | |

Threshold_4 | 3.3374 × 10^{−18} | 4.3038 × 10^{−12} | 1.4919 × 10^{−13} | 7.7155 × 10^{−13} | Threshold_4 | 3.2962 × 10^{−5} | 1.8976 × 10^{−4} | 8.5947 × 10^{−5} | 4.0524 × 10^{−5} | |

Exponential_1 | 1.5745 × 10^{−24} | 1.0309 × 10^{−18} | 4.3948 × 10^{−20} | 1.8663 × 10^{−19} | Exponential_1 | 2.6917 × 10^{−9} | 4.3964 × 10^{−8} | 1.3508 × 10^{−8} | 9.5937 × 10^{−9} | |

Exponential_2 | 1.9177 × 10^{−30} | 9.0711 × 10^{−23} | 4.0772 × 10^{−24} | 1.6377 × 10^{−23} | Exponential_2 | 3.3307 × 10^{−11} | 2.2886E × 10^{−9} | 4.9657 × 10^{−10} | 5.7327 × 10^{−10} | |

Exponential_3 | 1.4165 × 10^{−30} | 2.0068 × 10^{−23} | 9.8918 × 10^{−25} | 3.6255 × 10^{−24} | Exponential_3 | 4.3579 × 10^{−12} | 9.8204 × 10^{−11} | 3.2054 × 10^{−11} | 2.5181 × 10^{−11} | |

Exponential_4 | 6.4644 × 10^{−35} | 4.5295 × 10^{−25} | 1.7018 × 10^{−26} | 8.1269 × 10^{−26} | Exponential_4 | 9.8540 × 10^{−14} | 7.9844 × 10^{−12} | 1.7156 × 10^{−12} | 1.8932 × 10^{−12} | |

Exponential_5 | 2.5044 × 10^{−34} | 1.9318 × 10^{−25} | 6.4846 × 10^{−27} | 3.4669 × 10^{−26} | Exponential_5 | 1.0612 × 10^{−14} | 6.4803 × 10^{−12} | 3.7018 × 10^{−13} | 1.1689 × 10^{−12} | |

Exponential_6 | 2.3735 × 10^{−38} | 3.7601 × 10^{−30} | 1.8344 × 10^{−31} | 7.0604 × 10^{−31} | Exponential_6 | 1.6615 × 10^{−16} | 8.0332 × 10^{−14} | 1.2209 × 10^{−14} | 1.9706 × 10^{−14} | |

Cosine_1 | 1.0929 × 10^{−25} | 2.6839 × 10^{−19} | 1.2194 × 10^{−20} | 4.8268 × 10^{−20} | Cosine_1 | 1.3660 × 10^{−9} | 8.8086 × 10^{−8} | 1.7253 × 10^{−8} | 2.0154 × 10^{−8} | |

Cosine_2 | 4.4254 × 10^{−21} | 3.5110 × 10^{−16} | 2.1719 × 10^{−17} | 7.1432 × 10^{−17} | Cosine_2 | 5.6587 × 10^{−8} | 2.9214 × 10^{−6} | 5.8827 × 10^{−7} | 7.8914 × 10^{−7} | |

Cosine_3 | 1.2834 × 10^{−22} | 1.3530 × 10^{−17} | 7.1008 × 10^{−19} | 2.4622 × 10^{−18} | Cosine_3 | 1.9881 × 10^{−9} | 2.8788 × 10^{−7} | 5.6503 × 10^{−8} | 6.6569 × 10^{−8} | |

Cosine_4 | 2.2000 × 10^{−22} | 6.3880 × 10^{−16} | 3.4309 × 10^{−17} | 1.1748 × 10^{−16} | Cosine_4 | 1.7535 × 10^{−8} | 2.7122 × 10^{−6} | 2.0647 × 10^{−7} | 4.7558 × 10^{−7} | |

${\mathit{f}}_{\mathbf{2}}$ | Straight_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Straight_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

Straight_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Straight_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Threshold_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Threshold_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Threshold_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Threshold_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Threshold_3 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Threshold_3 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Threshold_4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Threshold_4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Exponential_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Exponential_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Exponential_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Exponential_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Exponential_3 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Exponential_3 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Exponential_4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Exponential_4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Exponential_5 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Exponential_5 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Exponential_6 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Exponential_6 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Cosine_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Cosine_1 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Cosine_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Cosine_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Cosine_3 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Cosine_3 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

Cosine_4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Cosine_4 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

${\mathit{f}}_{\mathbf{3}}$ | Straight_1 | 7.6101 × 10^{−11} | 2.1913 × 10^{−8} | 1.4051 × 10^{−9} | 3.9001 × 10^{−9} | Straight_1 | 8.8188 × 10^{−4} | 2.8473 × 10^{−3} | 1.4467 × 10^{−3} | 4.5882 × 10^{−4} |

Straight_2 | 6.3744 × 10^{−14} | 8.2891 × 10^{−10} | 5.6932 × 10^{−11} | 1.5070 × 10^{−10} | Straight_2 | 1.0465 × 10^{−4} | 3.6867 × 10^{−4} | 2.0451 × 10^{−4} | 7.2735 × 10^{−5} | |

Threshold_1 | 4.6938 × 10^{−8} | 1.3461 × 10^{−6} | 2.1964 × 10^{−7} | 2.5585 × 10^{−7} | Threshold_1 | 1.4060 × 10^{−2} | 3.5936 × 10^{−2} | 1.9850 × 10^{−2} | 4.3707 × 10^{−3} | |

Threshold_2 | 5.6623 × 10^{−23} | 8.2711 × 10^{−17} | 2.9440 × 10^{−18} | 1.4815 × 10^{−17} | Threshold_2 | 2.5513 × 10^{−9} | 4.2922 × 10^{−8} | 1.0152 × 10^{−8} | 8.0648 × 10^{−9} | |

Threshold_3 | 4.7815 × 10^{−20} | 5.0811 × 10^{−11} | 1.7085 × 10^{−12} | 9.1183 × 10^{−12} | Threshold_3 | 7.0365 × 10^{−9} | 1.3972 × 10^{−7} | 4.1610 × 10^{−8} | 3.3889 × 10^{−8} | |

Threshold_4 | 1.7455 × 10^{−10} | 1.3321 × 10^{−7} | 1.7945 × 10^{−8} | 3.2820 × 10^{−8} | Threshold_4 | 1.3864 × 10^{−3} | 6.5341 × 10^{−3} | 3.0170 × 10^{−3} | 1.0805 × 10^{−3} | |

Exponential_1 | 9.8893 × 10^{−15} | 8.8305 × 10^{−11} | 6.3308 × 10^{−12} | 1.8435 × 10^{−11} | Exponential_1 | 8.0177 × 10^{−6} | 7.4683 × 10^{−5} | 2.0822 × 10^{−5} | 1.1771 × 10^{−5} | |

Exponential_2 | 1.7782 × 10^{−17} | 6.9813 × 10^{−12} | 3.7142 × 10^{−13} | 1.4030 × 10^{−12} | Exponential_2 | 7.3854 × 10^{−7} | 6.7228 × 10^{−6} | 3.3092 × 10^{−6} | 1.5847 × 10^{−6} | |

Exponential_3 | 7.5286 × 10^{−18} | 4.4195 × 10^{−13} | 2.0483 × 10^{−14} | 7.9637 × 10^{−14} | Exponential_3 | 2.6791 × 10^{−7} | 1.9304 × 10^{−6} | 6.8633 × 10^{−7} | 3.3018 × 10^{−7} | |

Exponential_4 | 2.5827 × 10^{−20} | 1.1413 × 10^{−14} | 4.3303 × 10^{−16} | 2.0473 × 10^{−15} | Exponential_4 | 3.1645 × 10^{−8} | 1.2139 × 10^{−6} | 2.0931 × 10^{−7} | 2.3506 × 10^{−7} | |

Exponential_5 | 1.5957 × 10^{−20} | 3.0055 × 10^{−15} | 1.1154 × 10^{−16} | 5.3828 × 10^{−16} | Exponential_5 | 9.3641 × 10^{−9} | 1.3374 × 10^{−7} | 3.2879 × 10^{−8} | 2.5806 × 10^{−8} | |

Exponential_6 | 5.1270 × 10^{−23} | 2.5548 × 10^{−17} | 1.9511 × 10^{−18} | 5.5869 × 10^{−18} | Exponential_6 | 1.7326 × 10^{−9} | 2.2346 × 10^{−8} | 7.9778 × 10^{−9} | 5.9706 × 10^{−9} | |

Cosine_1 | 8.2615 × 10^{−15} | 4.1648 × 10^{−10} | 1.9989 × 10^{−11} | 7.5562 × 10^{−11} | Cosine_1 | 7.5681 × 10^{−6} | 9.0058 × 10^{−5} | 2.7007 × 10^{−5} | 1.7485 × 10^{−5} | |

Cosine_2 | 2.2087 × 10^{−12} | 1.3549 × 10^{−9} | 1.5788 × 10^{−10} | 2.9202 × 10^{−10} | Cosine_2 | 5.0087 × 10^{−5} | 2.4876 × 10^{−4} | 1.1495 × 10^{−4} | 4.8700 × 10^{−5} | |

Cosine_3 | 8.7106 × 10^{−14} | 4.3784 × 10^{−11} | 6.6558 × 10^{−12} | 1.0409 × 10^{−11} | Cosine_3 | 1.1137 × 10^{−5} | 1.2211 × 10^{−4} | 4.6150 × 10^{−5} | 2.7857 × 10^{−5} | |

Cosine_4 | 1.7511 × 10^{−13} | 4.2184 × 10^{−10} | 3.9035 × 10^{−11} | 8.5768 × 10^{−11} | Cosine_4 | 1.6561 × 10^{−5} | 4.1825 × 10^{−4} | 8.5160 × 10^{−5} | 7.5082 × 10^{−5} | |

${\mathit{f}}_{\mathbf{4}}$ | Straight_1 | 3.8707 × 10^{1} | 2.0746 × 10^{2} | 9.2469 × 10^{1} | 4.2467 × 10^{1} | Straight_1 | 7.4364 × 10^{3} | 1.5798 × 10^{4} | 1.2838 × 10^{4} | 2.0788 × 10^{3} |

Straight_2 | 2.9107 × 10^{1} | 2.9786 × 10^{2} | 7.7546 × 10^{1} | 5.2474 × 10^{1} | Straight_2 | 6.1981 × 10^{3} | 1.2256 × 10^{4} | 9.9557 × 10^{3} | 1.5833 × 10^{3} | |

Threshold_1 | 2.5223 × 10^{1} | 2.4305 × 10^{2} | 6.8420 × 10^{1} | 4.2239 × 10^{1} | Threshold_1 | 1.2769 × 10^{4} | 2.1277 × 10^{4} | 1.6990 × 10^{4} | 2.1766 × 10^{3} | |

Threshold_2 | 8.2738 × 10^{1} | 4.8897 × 10^{2} | 2.4674 × 10^{2} | 1.0081 × 10^{2} | Threshold_2 | 7.0477 × 10^{3} | 1.6115 × 10^{4} | 1.0330 × 10^{4} | 1.9585 × 10^{3} | |

Threshold_3 | 1.6962 × 10^{2} | 7.4402 × 10^{2} | 3.4890 × 10^{2} | 1.5861 × 10^{2} | Threshold_3 | 7.9459 × 10^{3} | 2.0032 × 10^{4} | 1.3965 × 10^{4} | 2.6464 × 10^{3} | |

Threshold_4 | 1.5038 × 10^{1} | 1.5980 × 10^{2} | 6.0249 × 10^{1} | 3.5686 × 10^{1} | Threshold_4 | 8.9389 × 10^{3} | 1.9386 × 10^{4} | 1.3070 × 10^{4} | 2.9327 × 10^{3} | |

Exponential_1 | 5.2571 × 10^{1} | 3.3140 × 10^{2} | 1.7427 × 10^{2} | 7.7406 × 10^{1} | Exponential_1 | 7.8519 × 10^{3} | 1.5283 × 10^{4} | 1.1462 × 10^{4} | 2.1096 × 10^{3} | |

Exponential_2 | 3.7816 × 10^{1} | 2.9649 × 10^{2} | 1.4459 × 10^{2} | 6.2181 × 10^{1} | Exponential_2 | 4.6763 × 10^{3} | 1.3135 × 10^{4} | 8.6301 × 10^{3} | 1.9698 × 10^{3} | |

Exponential_3 | 9.1368 × 10^{1} | 7.9952 × 10^{2} | 3.4719 × 10^{2} | 1.6819 × 10^{2} | Exponential_3 | 8.0589 × 10^{3} | 1.7800 × 10^{4} | 1.1645 × 10^{4} | 2.4428 × 10^{3} | |

Exponential_4 | 5.2605 × 10^{1} | 6.6496 × 10^{2} | 2.5585 × 10^{2} | 1.3827 × 10^{2} | Exponential_4 | 6.8390 × 10^{3} | 1.4895 × 10^{4} | 9.8522 × 10^{3} | 1.6440 × 10^{3} | |

Exponential_5 | 1.9773 × 10^{2} | 1.0629 × 10^{3} | 5.5626 × 10^{2} | 2.1853 × 10^{2} | Exponential_5 | 7.2667 × 10^{3} | 1.7819 × 10^{4} | 1.2364 × 10^{4} | 2.4484 × 10^{3} | |

Exponential_6 | 1.1519 × 10^{2} | 1.1733 × 10^{3} | 5.4639 × 10^{2} | 2.6598 × 10^{2} | Exponential_6 | 7.0572 × 10^{3} | 1.4985 × 10^{4} | 1.0313 × 10^{4} | 1.8035 × 10^{3} | |

Cosine_1 | 2.2677 × 10^{1} | 1.6215 × 10^{2} | 8.4233 × 10^{1} | 3.8116 × 10^{1} | Cosine_1 | 8.5285 × 10^{3} | 1.6216 × 10^{4} | 1.1657 × 10^{4} | 2.0568 × 10^{3} | |

Cosine_2 | 3.5648 × 10^{1} | 2.5791 × 10^{2} | 1.0386 × 10^{2} | 4.7531 × 10^{1} | Cosine_2 | 7.3675 × 10^{3} | 1.6256 × 10^{4} | 1.1952 × 10^{4} | 2.1374 × 10^{3} | |

Cosine_3 | 3.9845 × 10^{1} | 2.5401 × 10^{2} | 1.0903 × 10^{2} | 5.1737 × 10^{1} | Cosine_3 | 8.7901 × 10^{3} | 1.5058 × 10^{4} | 1.2176 × 10^{4} | 1.5990 × 10^{3} | |

Cosine_4 | 4.0827 × 10^{1} | 1.9696 × 10^{2} | 9.1923 × 10^{1} | 4.1878 × 10^{1} | Cosine_4 | 8.2399 × 10^{3} | 1.4967 × 10^{4} | 1.1576 × 10^{4} | 1.6474 × 10^{3} | |

${\mathit{f}}_{\mathbf{5}}$ | Straight_1 | 1.2321 × 10^{−2} | 2.7805 × 10^{−1} | 1.0051 × 10^{−1} | 6.7510 × 10^{−2} | Straight_1 | 4.1360 × 10^{−6} | 3.5617 × 10^{−1} | 1.0453 × 10^{−1} | 9.3265 × 10^{−2} |

Straight_2 | 0.0000 | 2.0030 × 10^{−1} | 4.1983 × 10^{−2} | 4.2581 × 10^{−2} | Straight_2 | 5.1016 × 10^{−8} | 6.3390 × 10^{−2} | 1.1625 × 10^{−2} | 1.5055 × 10^{−2} | |

Threshold_1 | 1.7855 × 10^{−8} | 2.6377 × 10^{−1} | 9.8336 × 10^{−2} | 6.8880 × 10^{−2} | Threshold_1 | 8.8364 × 10^{−4} | 2.8092 × 10^{−1} | 7.3770 × 10^{−2} | 6.8845 × 10^{−2} | |

Threshold_2 | 0.0000 | 1.8867 × 10^{−1} | 4.0923 × 10^{−2} | 4.6115 × 10^{−2} | Threshold_2 | 1.4433 × 10^{−15} | 9.4723 × 10^{−2} | 1.7078 × 10^{−2} | 2.3582 × 10^{−2} | |

Threshold_3 | 3.6320 × 10^{−6} | 2.2197 × 10^{−1} | 1.1814 × 10^{−1} | 6.0107 × 10^{−2} | Threshold_3 | 1.3545 × 10^{−14} | 3.6928 × 10^{−1} | 1.0457 × 10^{−1} | 9.8452 × 10^{−2} | |

Threshold_4 | 6.6613 × 10^{−16} | 8.0817 × 10^{−2} | 3.1209 × 10^{−2} | 2.3482 × 10^{−2} | Threshold_4 | 1.7774 × 10^{−5} | 3.6827 × 10^{−2} | 9.0876 × 10^{−3} | 9.4618 × 10^{−3} | |

Exponential_1 | 0.0000 | 2.4379 × 10^{−1} | 7.9307 × 10^{−2} | 5.8015 × 10^{−2} | Exponential_1 | 2.4888 × 10^{−9} | 4.4986 × 10^{−1} | 1.2518 × 10^{−1} | 9.4176 × 10^{−2} | |

Exponential_2 | 0.0000 | 1.7609 × 10^{−1} | 4.5556 × 10^{−2} | 4.1760 × 10^{−2} | Exponential_2 | 3.5352 × 10^{−11} | 4.8906 × 10^{−2} | 6.4754 × 10^{−3} | 9.8313 × 10^{−3} | |

Exponential_3 | 4.2099 × 10^{−10} | 3.2955 × 10^{−1} | 1.1643 × 10^{−1} | 8.0421 × 10^{−2} | Exponential_3 | 3.6280 × 10^{−12} | 3.2945 × 10^{−1} | 1.0033 × 10^{−1} | 9.5541 × 10^{−2} | |

Exponential_4 | 0.0000 | 2.0253 × 10^{−1} | 4.8723 × 10^{−2} | 4.6463 × 10^{−2} | Exponential_4 | 8.5154 × 10^{−14} | 1.6488 × 10^{−1} | 1.2543 × 10^{−2} | 3.0277 × 10^{−2} | |

Exponential_5 | 8.8818 × 10^{−16} | 2.5708 × 10^{−1} | 8.4472 × 10^{−2} | 6.4674 × 10^{−2} | Exponential_5 | 1.2990 × 10^{−14} | 4.9613 × 10^{−1} | 1.2331 × 10^{−1} | 1.0636 × 10^{−1} | |

Exponential_6 | 0.0000 | 1.6595 × 10^{−1} | 4.9137 × 10^{−2} | 3.9865 × 10^{−2} | Exponential_6 | 2.2204 × 10^{−16} | 8.3124 × 10^{−2} | 1.2513 × 10^{−2} | 1.8702 × 10^{−2} | |

Cosine_1 | 0.0000 | 1.4149 × 10^{−1} | 4.2637 × 10^{−2} | 4.3674 × 10^{−2} | Cosine_1 | 8.3748 × 10^{−10} | 5.4050 × 10^{−2} | 1.0821 × 10^{−2} | 1.5102 × 10^{−2} | |

Cosine_2 | 1.6653 × 10^{−15} | 3.3647 × 10^{−1} | 1.1985 × 10^{−1} | 8.0014 × 10^{−2} | Cosine_2 | 6.3283 × 10^{−8} | 4.0323 × 10^{−1} | 9.7344 × 10^{−2} | 9.0742 × 10^{−2} | |

Cosine_3 | 0.0000 | 1.3191 × 10^{−1} | 5.2162 × 10^{−2} | 3.7768 × 10^{−2} | Cosine_3 | 2.6663 × 10^{−9} | 1.7983 × 10^{−1} | 3.1360 × 10^{−2} | 4.5413 × 10^{−2} | |

Cosine_4 | 1.1102 × 10^{−16} | 2.7598 × 10^{−1} | 9.9773 × 10^{−2} | 6.7164 × 10^{−2} | Cosine_4 | 1.6227 × 10^{−8} | 2.4487 × 10^{−1} | 5.5685 × 10^{−2} | 6.5963 × 10^{−2} | |

${\mathit{f}}_{\mathbf{6}}$ | Straight_1 | 4.4632 × 10^{−9} | 2.1372 × 10^{−7} | 3.9100 × 10^{−8} | 4.0940 × 10^{−8} | Straight_1 | 9.1269 × 10^{−4} | 3.1804 × 10^{−3} | 1.6518 × 10^{−3} | 5.3523 × 10^{−4} |

Straight_2 | 3.7761 × 10^{−12} | 8.6966 × 10^{−10} | 1.0236 × 10^{−10} | 2.0891 × 10^{−10} | Straight_2 | 4.2112 × 10^{−5} | 3.8837 × 10^{−4} | 1.1886 × 10^{−4} | 7.9706 × 10^{−5} | |

Threshold_1 | 9.1029 × 10^{−7} | 8.0166 × 10^{−6} | 2.4129 × 10^{−6} | 1.5101 × 10^{−6} | Threshold_1 | 1.2113 × 10^{−2} | 2.5585 × 10^{−2} | 1.9902 × 10^{−2} | 3.4669 × 10^{−3} | |

Threshold_2 | 7.4163 × 10^{−14} | 6.3549 × 10^{−13} | 1.6938 × 10^{−13} | 1.0610 × 10^{−13} | Threshold_2 | 1.7921 × 10^{−9} | 6.5055 × 10^{−8} | 1.2631 × 10^{−8} | 1.2902 × 10^{−8} | |

Threshold_3 | 1.0014 × 10^{−12} | 5.2655 × 10^{−10} | 6.8025 × 10^{−11} | 1.2657 × 10^{−10} | Threshold_3 | 2.5582 × 10^{−8} | 1.5023 × 10^{−6} | 2.2886 × 10^{−7} | 2.7137 × 10^{−7} | |

Threshold_4 | 1.4622 × 10^{−9} | 2.7494 × 10^{−7} | 3.1953 × 10^{−8} | 4.9739 × 10^{−8} | Threshold_4 | 5.3312 × 10^{−4} | 3.8584 × 10^{−3} | 1.5894 × 10^{−3} | 7.9124 × 10^{−4} | |

Exponential_1 | 1.8744 × 10^{−11} | 4.9544 × 10^{−9} | 4.4463 × 10^{−10} | 8.7649 × 10^{−10} | Exponential_1 | 1.7624 × 10^{−5} | 9.1723 × 10^{−5} | 4.3472 × 10^{−5} | 1.7983 × 10^{−5} | |

Exponential_2 | 1.1324 × 10^{−13} | 4.9805 × 10^{−12} | 9.3889 × 10^{−13} | 1.1256 × 10^{−12} | Exponential_2 | 6.4716 × 10^{−7} | 6.8428 × 10^{−6} | 2.1846 × 10^{−6} | 1.3670 × 10^{−6} | |

Exponential_3 | 4.9338 × 10^{−13} | 5.5745 × 10^{−11} | 6.6129 × 10^{−12} | 1.1049 × 10^{−11} | Exponential_3 | 6.0042 × 10^{−7} | 6.0591 × 10^{−6} | 2.4126 × 10^{−6} | 1.5002 × 10^{−6} | |

Exponential_4 | 7.4163 × 10^{−14} | 1.1862 × 10^{−12} | 1.7826 × 10^{−13} | 1.9564 × 10^{−13} | Exponential_4 | 3.8729 × 10^{−8} | 3.1068 × 10^{−7} | 1.2811 × 10^{−7} | 6.7689 × 10^{−8} | |

Exponential_5 | 1.5588 × 10^{−13} | 4.0887 × 10^{−12} | 8.2758 × 10^{−13} | 8.0931 × 10^{−13} | Exponential_5 | 3.9803 × 10^{−8} | 5.7158 × 10^{−7} | 1.4832 × 10^{−7} | 1.2402 × 10^{−7} | |

Exponential_6 | 4.9294 × 10^{−14} | 2.2338 × 10^{−13} | 9.6308 × 10^{−14} | 3.4392 × 10^{−14} | Exponential_6 | 1.0897 × 10^{−9} | 2.9882 × 10^{−8} | 9.3030 × 10^{−9} | 7.9441 × 10^{−9} | |

Cosine_1 | 1.1506 × 10^{−12} | 9.2267 × 10^{−11} | 2.2030 × 10^{−11} | 2.6803 × 10^{−11} | Cosine_1 | 2.3571 × 10^{−6} | 1.0218 × 10^{−4} | 1.8274 × 10^{−5} | 1.7509 × 10^{−5} | |

Cosine_2 | 1.7620 × 10^{−10} | 5.8307 × 10^{−8} | 6.5754 × 10^{−9} | 1.2324 × 10^{−8} | Cosine_2 | 6.1209 × 10^{−5} | 5.0676 × 10^{−4} | 1.8226 × 10^{−4} | 1.1078 × 10^{−4} | |

Cosine_3 | 5.0302 × 10^{−12} | 7.4329 × 10^{−10} | 1.1653 × 10^{−10} | 1.6314 × 10^{−10} | Cosine_3 | 8.4419 × 10^{−6} | 8.5649 × 10^{−5} | 2.7943 × 10^{−5} | 1.8587 × 10^{−5} | |

Cosine_4 | 7.7018 × 10^{−12} | 5.7757 × 10^{−9} | 5.7647 × 10^{−10} | 1.2234 × 10^{−9} | Cosine_4 | 2.9068 × 10^{−5} | 1.9156 × 10^{−4} | 6.7917 × 10^{−5} | 4.2305 × 10^{−5} | |

${\mathit{f}}_{\mathbf{7}}$ | Straight_1 | 9.3515 × 10^{−3} | 2.2089 × 10^{1} | 1.0089 × 10^{1} | 8.7452 | Straight_1 | 1.1325 | 5.6386 × 10^{2} | 1.0620 × 10^{2} | 1.2570 × 10^{2} |

Straight_2 | 8.6741 × 10^{−3} | 5.1406 × 10^{2} | 4.4419 × 10^{1} | 9.3454 × 10^{1} | Straight_2 | 1.0018 × 10^{2} | 6.9565 × 10^{2} | 2.6307 × 10^{2} | 1.3802 × 10^{2} | |

Threshold_1 | 7.9026 × 10^{−2} | 4.7147 × 10^{2} | 2.5678 × 10^{1} | 8.3161 × 10^{1} | Threshold_1 | 3.4344 × 10^{1} | 2.3308 × 10^{3} | 3.2695 × 10^{2} | 5.9498 × 10^{2} | |

Threshold_2 | 1.4559 × 10^{−3} | 6.1627 × 10^{2} | 8.4192 × 10^{1} | 1.6666 × 10^{2} | Threshold_2 | 1.1503 × 10^{2} | 5.1947 × 10^{2} | 2.3270 × 10^{2} | 9.2809 × 10^{1} | |

Threshold_3 | 4.4533 × 10^{−2} | 3.9917 × 10^{2} | 3.9657 × 10^{1} | 9.6881 × 10^{1} | Threshold_3 | 5.6804 × 10^{−2} | 1.1562 × 10^{3} | 6.1559 × 10^{1} | 2.0554 × 10^{2} | |

Threshold_4 | 1.5343 × 10^{−3} | 1.6611 × 10^{2} | 3.2721 × 10^{1} | 4.3985 × 10^{1} | Threshold_4 | 1.8240 × 10^{2} | 7.1746 × 10^{2} | 2.8865 × 10^{2} | 1.1583 × 10^{2} | |

Exponential_1 | 8.0795 × 10^{−4} | 2.2094 × 10^{1} | 1.2282 × 10^{1} | 8.8145 | Exponential_1 | 2.3784 × 10^{−1} | 1.2901 × 10^{3} | 1.0700 × 10^{2} | 2.5169 × 10^{2} | |

Exponential_2 | 1.2988 × 10^{−2} | 2.2802 × 10^{2} | 4.6231 × 10^{1} | 5.4244 × 10^{1} | Exponential_2 | 1.1174 × 10^{2} | 6.4584 × 10^{2} | 2.2362 × 10^{2} | 9.2963 × 10^{1} | |

Exponential_3 | 5.6146 × 10^{−3} | 9.7058 × 10^{2} | 5.8068 × 10^{1} | 1.8542 × 10^{2} | Exponential_3 | 4.0212 × 10^{−2} | 1.0768 × 10^{3} | 1.0022 × 10^{2} | 2.1852 × 10^{2} | |

Exponential_4 | 5.5288 × 10^{−3} | 9.3064 × 10^{1} | 2.6240 × 10^{1} | 3.2270 × 10^{1} | Exponential_4 | 7.6558 × 10^{1} | 2.8626 × 10^{2} | 2.0961 × 10^{2} | 5.1587 × 10^{1} | |

Exponential_5 | 2.7747 × 10^{−3} | 1.6422 × 10^{3} | 1.3893 × 10^{2} | 3.7163 × 10^{2} | Exponential_5 | 1.2275 × 10^{−3} | 1.5623 × 10^{3} | 9.0305 × 10^{1} | 2.8689 × 10^{2} | |

Exponential_6 | 1.2831 × 10^{−5} | 4.9205 × 10^{2} | 4.0422 × 10^{1} | 9.0413 × 10^{1} | Exponential_6 | 5.8594 × 10^{1} | 6.3056 × 10^{2} | 2.1990 × 10^{2} | 9.4453 × 10^{1} | |

Cosine_1 | 1.8015 × 10^{−3} | 1.3748 × 10^{2} | 2.9047 × 10^{1} | 3.8603 × 10^{1} | Cosine_1 | 1.0997 × 10^{2} | 1.2606 × 10^{3} | 2.6362 × 10^{2} | 2.0716 × 10^{2} | |

Cosine_2 | 4.4398 × 10^{−3} | 5.3878 × 10^{2} | 3.6644 × 10^{1} | 1.0520 × 10^{2} | Cosine_2 | 8.8583 × 10^{−1} | 1.6674 × 10^{3} | 1.5580 × 10^{2} | 3.2284 × 10^{2} | |

Cosine_3 | 1.1943 × 10^{−1} | 3.6476 × 10^{2} | 3.5174 × 10^{1} | 6.8477 × 10^{1} | Cosine_3 | 1.4076 × 10^{2} | 1.7107 × 10^{3} | 3.5751 × 10^{2} | 3.8108 × 10^{2} | |

Cosine_4 | 8.0777 × 10^{−3} | 8.0590 × 10^{1} | 1.4814 × 10^{1} | 1.8135 × 10^{1} | Cosine_4 | 1.0177 | 1.7477 × 10^{3} | 1.9765 × 10^{2} | 3.2461 × 10^{2} | |

${\mathit{f}}_{\mathbf{8}}$ | Straight_1 | 3.1974 × 10^{−14} | 3.3089 × 10^{−7} | 1.1716 × 10^{−8} | 5.9285 × 10^{−8} | Straight_1 | 2.0388 × 10^{−3} | 3.3216 | 6.6242 × 10^{−1} | 8.8988 × 10^{−1} |

Straight_2 | 0.0000 | 3.5527 × 10^{−15} | 5.9212 × 10^{−16} | 1.1543 × 10^{−15} | Straight_2 | 1.9115 × 10^{−7} | 2.9849 | 3.9804 × 10^{−1} | 7.9594 × 10^{−1} | |

Threshold_1 | 3.6512 × 10^{−10} | 2.1702 × 10^{−7} | 4.1154 × 10^{−8} | 6.3766 × 10^{−8} | Threshold_1 | 2.2994 | 8.4160 | 5.4959 | 1.4385 | |

Threshold_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | Threshold_2 | 1.4211 × 10^{−14} | 1.9899 | 1.9909 × 10^{−1} | 4.7366 × 10^{−1} | |

Threshold_3 | 0.0000 | 9.9496 × 10^{−1} | 6.6407 × 10^{−2} | 2.4817 × 10^{−1} | Threshold_3 | 3.2097 × 10^{−10} | 1.9918 | 4.5307 × 10^{−1} | 6.0607 × 10^{−1} | |

Threshold_4 | 0.0000 | 8.8285 × 10^{−13} | 1.0646 × 10^{−13} | 2.0045 × 10^{−13} | Threshold_4 | 9.9507 × 10^{−1} | 7.9637 | 3.2612 | 1.7811 | |

Exponential_1 | 5.3291 × 10^{−15} | 7.1937 × 10^{−8} | 9.0557 × 10^{−9} | 2.0970 × 10^{−8} | Exponential_1 | 6.3110 × 10^{−6} | 9.9714 × 10^{−1} | 1.4900 × 10^{−1} | 3.3483 × 10^{−1} | |

Exponential_2 | 0.0000 | 1.7764 × 10^{−15} | 1.7764 × 10^{−16} | 5.3291 × 10^{−16} | Exponential_2 | 1.1186 × 10^{−10} | 9.9496 × 10^{−1} | 9.9549 × 10^{−2} | 2.9847 × 10^{−1} | |

Exponential_3 | 0.0000 | 6.4209 × 10^{−6} | 3.3419 × 10^{−7} | 1.2242 × 10^{−6} | Exponential_3 | 3.5170 × 10^{−8} | 5.9362 × 10^{−1} | 2.7729 × 10^{−2} | 1.0943 × 10^{−1} | |

Exponential_4 | 0.0000 | 1.9899 | 9.9496 × 10^{−2} | 3.9382 × 10^{−1} | Exponential_4 | 1.3145 × 10^{−13} | 9.9496 × 10^{−1} | 9.9497 × 10^{−2} | 2.9849 × 10^{−1} | |

Exponential_5 | 0.0000 | 9.9496 × 10^{−1} | 9.9534 × 10^{−2} | 2.9848 × 10^{−1} | Exponential_5 | 1.9582 × 10^{−10} | 1.0029 | 1.3296 × 10^{−1} | 3.3892 × 10^{−1} | |

Exponential_6 | 0.0000 | 2.6645 × 10^{−14} | 1.0066 × 10^{−15} | 4.7815 × 10^{−15} | Exponential_6 | 1.0658 × 10^{−14} | 1.9899 | 6.6332 × 10^{−2} | 3.5720 × 10^{−1} | |

Cosine_1 | 0.0000 | 4.7731 × 10^{−10} | 1.5911 × 10^{−11} | 8.5680 × 10^{−11} | Cosine_1 | 4.0101 × 10^{−7} | 2.9978 | 6.8374 × 10^{−1} | 8.4558 × 10^{−1} | |

Cosine_2 | 0.0000 | 8.7041 × 10^{−14} | 1.0836 × 10^{−14} | 1.6641 × 10^{−14} | Cosine_2 | 7.9506 × 10^{−7} | 1.9900 | 9.2880 × 10^{−1} | 7.2337 × 10^{−1} | |

Cosine_3 | 0.0000 | 4.4409 × 10^{−13} | 2.6053 × 10^{−14} | 8.0975 × 10^{−14} | Cosine_3 | 9.6632 × 10^{−6} | 2.0318 | 6.9709 × 10^{−1} | 6.1734 × 10^{−1} | |

Cosine_4 | 0.0000 | 7.4181 × 10^{−9} | 3.8545 × 10^{−10} | 1.4870 × 10^{−9} | Cosine_4 | 3.2724 × 10^{−5} | 2.9858 | 7.9728 × 10^{−1} | 8.2825 × 10^{−1} | |

${\mathit{f}}_{\mathbf{9}}$ | Straight_1 | 3.8183 × 10^{−4} | 3.8184 × 10^{−4} | 3.8184 × 10^{−4} | 2.3807 × 10^{−9} | Straight_1 | 8.5055 × 10^{−3} | 2.7732 × 10^{1} | 1.5810 | 5.5711 |

Straight_2 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 1.5953 × 10^{−13} | Straight_2 | 1.2731 × 10^{−3} | 1.3293 × 10^{−3} | 1.2773 × 10^{−3} | 1.0150 × 10^{−5} | |

Threshold_1 | 3.8183 × 10^{−4} | 3.8229 × 10^{−4} | 3.8190 × 10^{−4} | 9.3441 × 10^{−8} | Threshold_1 | 6.0293 × 10^{−1} | 1.3343 × 10^{2} | 1.6668 × 10^{1} | 3.6662 × 10^{1} | |

Threshold_2 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 1.3763 × 10^{−13} | Threshold_2 | 1.2728 × 10^{−3} | 1.2728 × 10^{−3} | 1.2728 × 10^{−3} | 1.4537 × 10^{−9} | |

Threshold_3 | 3.8183 × 10^{−4} | 4.0474 × 10^{−4} | 3.8314 × 10^{−4} | 4.2676 × 10^{−6} | Threshold_3 | 1.2728 × 10^{−3} | 1.1844 × 10^{2} | 4.6076 | 2.1276 × 10^{1} | |

Threshold_4 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 2.0629 × 10^{−12} | Threshold_4 | 1.3933 × 10^{−3} | 1.1844 × 10^{2} | 7.9095 | 2.9541 × 10^{1} | |

Exponential_1 | 3.8183 × 10^{−4} | 1.5644 × 10^{−4} | 4.2241 × 10^{−4} | 2.1212 × 10^{−4} | Exponential_1 | 1.2781 × 10^{−3} | 1.7045 × 10^{−2} | 2.7552 × 10^{−3} | 3.2908 × 10^{−3} | |

Exponential_2 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 1.4555 × 10^{−13} | Exponential_2 | 1.2728 × 10^{−3} | 1.2728 × 10^{−3} | 1.2728 × 10^{−3} | 4.9514 × 10^{−9} | |

Exponential_3 | 3.8183 × 10^{−4} | 3.9497 × 10^{−4} | 3.8261 × 10^{−4} | 2.8259 × 10^{−6} | Exponential_3 | 1.2728 × 10^{−3} | 4.6522 × 10^{−3} | 1.4855 × 10^{−3} | 6.7891 × 10^{−4} | |

Exponential_4 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 1.6171 × 10^{−13} | Exponential_4 | 1.2728 × 10^{−3} | 1.3827 × 10^{−3} | 1.2764 × 10^{−3} | 1.9734 × 10^{−5} | |

Exponential_5 | 3.8183 × 10^{−4} | 4.2990 × 10^{−4} | 3.8366 × 10^{−4} | 8.6277 × 10^{−6} | Exponential_5 | 1.2728 × 10^{−3} | 1.1844 × 10^{2} | 6.9547 | 2.6270 × 10^{1} | |

Exponential_6 | 3.8183 × 10^{−4} | 1.1844 × 10^{2} | 3.9483 | 2.1260 × 10^{1} | Exponential_6 | 1.2728 × 10^{−3} | 1.2730 × 10^{−3} | 1.2728 × 10^{−3} | 4.1256 × 10^{−8} | |

Cosine_1 | 3.8183 × 10^{−4} | 3.8231 × 10^{−4} | 3.8184 × 10^{−4} | 8.6835 × 10^{−8} | Cosine_1 | 1.2728 × 10^{−3} | 1.1844 × 10^{2} | 4.1934 | 2.1251 × 10^{1} | |

Cosine_2 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 5.5438 × 10^{−13} | Cosine_2 | 1.2765 × 10^{−3} | 1.4798 × 10^{−3} | 1.3277 × 10^{−3} | 5.8337 × 10^{−5} | |

Cosine_3 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 8.8412 × 10^{−13} | Cosine_3 | 1.2731 × 10^{−3} | 1.5879 × 10^{−3} | 1.3274 × 10^{−3} | 8.8845 × 10^{−5} | |

Cosine_4 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.6890 × 10^{−13} | Cosine_4 | 1.2732 × 10^{−3} | 4.8779 × 10^{−2} | 3.7520 × 10^{−3} | 8.8272 × 10^{−3} | |

${\mathit{f}}_{\mathbf{10}}$ | Straight_1 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.0008 × 10^{−13} | Straight_1 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.1952 × 10^{−5} |

Straight_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 7.3385 × 10^{−14} | Straight_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.4478 × 10^{−6} | |

Threshold_1 | −4.5000 × 10^{2} | −4.4999 × 10^{2} | −4.4999 × 10^{2} | 8.3459 × 10^{−12} | Threshold_1 | −4.5000 × 10^{2} | −4.4999 × 10^{2} | −4.4999 × 10^{2} | 1.7050 × 10^{−3} | |

Threshold_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 6.3128 × 10^{−14} | Threshold_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 2.4117 × 10^{−13} | |

Threshold_3 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 9.7356 × 10^{−14} | Threshold_3 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 4.6932 × 10^{−13} | |

Threshold_4 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.9443 × 10^{−13} | Threshold_4 | −4.5000 × 10^{2} | −4.4999 × 10^{2} | −4.4999 × 10^{2} | 9.0431 × 10^{−5} | |

Exponential_1 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 7.4115 × 10^{−14} | Exponential_1 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.1789 × 10^{−8} | |

Exponential_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 5.4916 × 10^{−14} | Exponential_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 4.2493 × 10^{−10} | |

Exponential_3 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 7.4838 × 10^{−14} | Exponential_3 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 2.2269 × 10^{−10} | |

Exponential_4 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 6.8841 × 10^{−14} | Exponential_4 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.5991 × 10^{−12} | |

Exponential_5 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 7.3385 × 10^{−14} | Exponential_5 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 5.9672 × 10^{−13} | |

Exponential_6 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 7.1149 × 10^{−14} | Exponential_6 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 2.8686 × 10^{−13} | |

Cosine_1 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 9.0475 × 10^{−14} | Cosine_1 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.9650 × 10^{−8} | |

Cosine_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 9.0475 × 10^{−14} | Cosine_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.1307 × 10^{−6} | |

Cosine_3 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 8.3025 × 10^{−14} | Cosine_3 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 2.3531 × 10^{−7} | |

Cosine_4 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 8.5580 × 10^{−14} | Cosine_4 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 1.5911 × 10^{−7} | |

${\mathit{f}}_{\mathbf{11}}$ | Straight_1 | −4.2165 × 10^{2} | −1.3296 × 10^{2} | −3.0000 × 10^{2} | 7.4536 × 10^{1} | Straight_1 | 1.1767 × 10^{4} | 2.3516 × 10^{4} | 1.6891 × 10^{4} | 3.1744 × 10^{3} |

Straight_2 | −4.3444 × 10^{2} | −1.0722 × 10^{2} | −3.2701 × 10^{2} | 8.4417 × 10^{1} | Straight_2 | 8.4226 × 10^{3} | 1.8619 × 10^{4} | 1.2552 × 10^{4} | 2.2028 × 10^{3} | |

Threshold_1 | −4.0106 × 10^{2} | −1.4896 × 10^{2} | −3.3088 × 10^{2} | 5.8709 × 10^{1} | Threshold_1 | 1.5199 × 10^{4} | 2.8379 × 10^{4} | 2.1552 × 10^{4} | 3.2507 × 10^{3} | |

Threshold_2 | −3.4901 × 10^{2} | 2.5368 × 10^{2} | −6.2125 × 10^{1} | 1.5696 × 10^{2} | Threshold_2 | 8.7977 × 10^{3} | 1.7870 × 10^{4} | 1.3695 × 10^{4} | 2.2976 × 10^{3} | |

Threshold_3 | −3.3390 × 10^{2} | 9.3989 × 10^{2} | 1.2263 × 10^{2} | 3.1892 × 10^{2} | Threshold_3 | 1.2026 × 10^{4} | 3.1616 × 10^{4} | 2.1121 × 10^{4} | 4.5467 × 10^{3} | |

Threshold_4 | −4.4289 × 10^{2} | −2.5392 × 10^{2} | −3.7419 × 10^{2} | 4.4269 × 10^{1} | Threshold_4 | 9.0435 × 10^{3} | 2.5277 × 10^{4} | 1.6287 × 10^{4} | 3.1871 × 10^{3} | |

Exponential_1 | −3.1846 × 10^{2} | 2.1908 × 10^{2} | −9.9376 × 10^{1} | 1.4315 × 10^{2} | Exponential_1 | 1.0395 × 10^{4} | 2.1639 × 10^{4} | 1.5861 × 10^{4} | 3.1550 × 10^{3} | |

Exponential_2 | −3.8982 × 10^{2} | 3.1632 × 10^{2} | −1.6371 × 10^{2} | 1.6523 × 10^{2} | Exponential_2 | 6.9718 × 10^{3} | 1.7181 × 10^{4} | 1.1471 × 10^{4} | 2.4981 × 10^{3} | |

Exponential_3 | −3.0139 × 10^{2} | 2.1120 × 10^{3} | 1.5585 × 10^{2} | 4.5585 × 10^{2} | Exponential_3 | 1.2034 × 10^{4} | 2.4924 × 10^{4} | 1.7356 × 10^{4} | 2.6542 × 10^{3} | |

Exponential_4 | −3.3706 × 10^{2} | 2.7787 × 10^{2} | −5.1714 × 10^{1} | 1.6504 × 10^{2} | Exponential_4 | 8.1868 × 10^{3} | 1.8387 × 10^{4} | 1.2757 × 10^{4} | 2.9393 × 10^{3} | |

Exponential_5 | −2.5225 × 10^{2} | 1.5514 × 10^{3} | 5.6252 × 10^{2} | 4.1866 × 10^{2} | Exponential_5 | 1.2930 × 10^{4} | 2.3952 × 10^{4} | 1.8058 × 10^{4} | 2.9540 × 10^{3} | |

Exponential_6 | −2.8287 × 10^{2} | 9.9251 × 10^{2} | 2.6238 × 10^{2} | 3.3327 × 10^{2} | Exponential_6 | 9.7956 × 10^{3} | 2.0311 × 10^{4} | 1.3953 × 10^{4} | 2.4149 × 10^{3} | |

Cosine_1 | −4.1764 × 10^{2} | −1.8561 × 10^{1} | −2.6591 × 10^{2} | 9.4610 × 10^{1} | Cosine_1 | 9.0379 × 10^{3} | 2.5832 × 10^{4} | 1.5303 × 10^{4} | 3.5867 × 10^{3} | |

Cosine_2 | −4.2366 × 10^{2} | −4.9167 × 10^{1} | −2.7333 × 10^{2} | 9.0290 × 10^{1} | Cosine_2 | 1.2007 × 10^{4} | 2.5142 × 10^{4} | 1.7464 × 10^{4} | 3.3184 × 10^{3} | |

Cosine_3 | −4.2193 × 10^{2} | 8.5517 × 10^{1} | −2.2015 × 10^{2} | 1.2019 × 10^{2} | Cosine_3 | 1.0444 × 10^{4} | 2.0965 × 10^{4} | 1.4526 × 10^{4} | 2.5147 × 10^{3} | |

Cosine_4 | −4.0935 × 10^{2} | 4.8281 × 10^{1} | −2.5462 × 10^{2} | 1.2357 × 10^{2} | Cosine_4 | 1.0484 × 10^{4} | 2.3679 × 10^{4} | 1.6049 × 10^{4} | 3.3138 × 10^{3} | |

${\mathit{f}}_{\mathbf{12}}$ | Straight_1 | −1.7895 × 10^{2} | −1.7527 × 10^{2} | −1.7807 × 10^{2} | 9.8257 × 10^{−1} | Straight_1 | −1.5655 × 10^{2} | −9.8500 × 10^{1} | −1.3288 × 10^{2} | 1.5417 × 10^{1} |

Straight_2 | −1.7894 × 10^{2} | −1.7562 × 10^{2} | −1.7821 × 10^{2} | 7.6813 × 10^{−1} | Straight_2 | −1.6750 × 10^{2} | −1.2621 × 10^{2} | −1.4904 × 10^{2} | 1.1365 × 10^{1} | |

Threshold_1 | −1.7886 × 10^{2} | −1.7403 × 10^{2} | −1.7782 × 10^{2} | 1.0687 | Threshold_1 | −1.3312 × 10^{2} | −5.8638 × 10^{1} | −9.9192 × 10^{1} | 2.1166 × 10^{1} | |

Threshold_2 | −1.7891 × 10^{2} | −1.7361 × 10^{2} | −1.7769 × 10^{2} | 1.0980 | Threshold_2 | −1.6995 × 10^{2} | −1.2583 × 10^{2} | −1.5366 × 10^{2} | 1.0233 × 10^{1} | |

Threshold_3 | −1.7883 × 10^{2} | −1.7150 × 10^{2} | −1.7711 × 10^{2} | 1.4020 | Threshold_3 | −1.6505 × 10^{2} | −1.2822 × 10^{2} | −1.4608 × 10^{2} | 1.0842 × 10^{1} | |

Threshold_4 | −1.7888 × 10^{2} | −1.7563 × 10^{2} | −1.7812 × 10^{2} | 7.7099 × 10^{−1} | Threshold_4 | −1.6802 × 10^{2} | −1.0750 × 10^{2} | −1.3614 × 10^{2} | 1.5041 × 10^{1} | |

Exponential_1 | −1.7881 × 10^{2} | −1.7636 × 10^{2} | −1.7781 × 10^{2} | 7.2018 × 10^{−1} | Exponential_1 | −1.6142 × 10^{2} | −1.1356 × 10^{2} | −1.4376 × 10^{2} | 1.2858 × 10^{1} | |

Exponential_2 | −1.7883 × 10^{2} | −1.7565 × 10^{2} | −1.7788 × 10^{2} | 9.6280 × 10^{−1} | Exponential_2 | −1.6950 × 10^{2} | −1.4032 × 10^{2} | −1.5798 × 10^{2} | 6.6526 | |

Exponential_3 | −1.7909 × 10^{2} | −1.7556 × 10^{2} | −1.7747 × 10^{2} | 9.0208 × 10^{−1} | Exponential_3 | −1.6515 × 10^{2} | −1.2713 × 10^{2} | −1.5275 × 10^{2} | 9.8056 | |

Exponential_4 | −1.7890 × 10^{2} | −1.7505 × 10^{2} | −1.7780 × 10^{2} | 8.8838 × 10^{−1} | Exponential_4 | −1.7101 × 10^{2} | −1.4042 × 10^{2} | −1.5931 × 10^{2} | 7.7148 | |

Exponential_5 | −1.7882 × 10^{2} | −1.7400 × 10^{2} | −1.7725 × 10^{2} | 1.2914 | Exponential_5 | −1.7364 × 10^{2} | −1.2751 × 10^{2} | −1.5552 × 10^{2} | 1.0491 × 10^{1} | |

Exponential_6 | −1.7892 × 10^{2} | −1.7468 × 10^{2} | −1.7757 × 10^{2} | 1.0984 | Exponential_6 | −1.7066 × 10^{2} | −1.4082 × 10^{2} | −1.6037 × 10^{2} | 6.8764 | |

Cosine_1 | −1.7889 × 10^{2} | −1.7626 × 10^{2} | −1.7804 × 10^{2} | 6.7941 × 10^{−1} | Cosine_1 | −1.7102 × 10^{2} | −9.7261 × 10^{1} | −1.4361 × 10^{2} | 1.5506 × 10^{1} | |

Cosine_2 | −1.7888 × 10^{2} | −1.7610 × 10^{2} | −1.7807 × 10^{2} | 6.4727 × 10^{−1} | Cosine_2 | −1.6466 × 10^{2} | −1.1821 × 10^{2} | −1.4021 × 10^{2} | 1.3072 × 10^{1} | |

Cosine_3 | −1.7891 × 10^{2} | −1.7571 × 10^{2} | −1.7791 × 10^{2} | 8.9066 × 10^{−1} | Cosine_3 | −1.6130 × 10^{2} | −1.1206 × 10^{2} | −1.4392 × 10^{2} | 1.3861 × 10^{1} | |

Cosine_4 | −1.7873 × 10^{2} | −1.7465 × 10^{2} | −1.7780 × 10^{2} | 8.3139 × 10^{−1} | Cosine_4 | −1.6327 × 10^{2} | −1.0337 × 10^{2} | −1.3840 × 10^{2} | 1.5854 × 10^{1} | |

${\mathit{f}}_{\mathbf{13}}$ | Straight_1 | 3.9000 × 10^{2} | 4.5949 × 10^{2} | 3.9958 × 10^{2} | 1.3088 × 10^{1} | Straight_1 | 3.9280 × 10^{2} | 3.6620 × 10^{3} | 5.7871 × 10^{2} | 5.8225 × 10^{2} |

Straight_2 | 3.9002 × 10^{2} | 4.8656 × 10^{2} | 4.0653 × 10^{2} | 2.5520 × 10^{1} | Straight_2 | 5.5729 × 10^{2} | 2.9468 × 10^{3} | 8.3659 × 10^{2} | 5.4759 × 10^{2} | |

Threshold_1 | 3.9007 × 10^{2} | 4.0876 × 10^{2} | 3.9979 × 10^{2} | 7.3298 | Threshold_1 | 4.2763 × 10^{2} | 3.9501 × 10^{3} | 8.1099 × 10^{2} | 8.3480 × 10^{2} | |

Threshold_2 | 3.9000 × 10^{2} | 7.9400 × 10^{2} | 4.2759 × 10^{2} | 7.5937 × 10^{1} | Threshold_2 | 4.9760 × 10^{2} | 2.2597 × 10^{3} | 6.9290 × 10^{2} | 3.1747 × 10^{2} | |

Threshold_3 | 3.9012 × 10^{2} | 6.7882 × 10^{2} | 4.0955 × 10^{2} | 5.0771 × 10^{1} | Threshold_3 | 3.9002 × 10^{2} | 2.8846 × 10^{3} | 8.5966 × 10^{2} | 7.8665 × 10^{2} | |

Threshold_4 | 3.9000 × 10^{2} | 4.7366 × 10^{2} | 4.1236 × 10^{2} | 3.1291 × 10^{1} | Threshold_4 | 4.8872 × 10^{2} | 3.5299 × 10^{3} | 9.3974 × 10^{2} | 7.2954 × 10^{2} | |

Exponential_1 | 3.9001 × 10^{2} | 7.8965 × 10^{2} | 4.1481 × 10^{2} | 7.3227 × 10^{1} | Exponential_1 | 3.9200 × 10^{2} | 2.8106 × 10^{3} | 6.1515 × 10^{2} | 4.9085 × 10^{2} | |

Exponential_2 | 3.9007 × 10^{2} | 7.3063 × 10^{2} | 4.1744 × 10^{2} | 6.3802 × 10^{1} | Exponential_2 | 4.7908 × 10^{2} | 8.1095 × 10^{2} | 6.1817 × 10^{2} | 7.2382 × 10^{1} | |

Exponential_3 | 3.9000 × 10^{2} | 9.0772 × 10^{2} | 4.2429 × 10^{2} | 9.6564 × 10^{1} | Exponential_3 | 3.9006 × 10^{2} | 2.9396 × 10^{3} | 6.9200 × 10^{2} | 6.6627 × 10^{2} | |

Exponential_4 | 3.9013 × 10^{2} | 5.4184 × 10^{2} | 4.1655 × 10^{2} | 3.5768 × 10^{1} | Exponential_4 | 4.8828 × 10^{2} | 1.1518 × 10^{3} | 6.4499 × 10^{2} | 1.5060 × 10^{2} | |

Exponential_5 | 3.9000 × 10^{2} | 1.0517 × 10^{3} | 4.4257 × 10^{2} | 1.4997 × 10^{2} | Exponential_5 | 3.9001 × 10^{2} | 2.7678 × 10^{3} | 6.7424 × 10^{2} | 6.4280 × 10^{2} | |

Exponential_6 | 3.9004 × 10^{2} | 4.7407 × 10^{2} | 4.0836 × 10^{2} | 2.6488 × 10^{1} | Exponential_6 | 4.6519 × 10^{2} | 2.0147 × 10^{3} | 6.5145 × 10^{2} | 2.8388 × 10^{2} | |

Cosine_1 | 3.9000 × 10^{2} | 6.1903 × 10^{2} | 4.2205 × 10^{2} | 4.8758 × 10^{1} | Cosine_1 | 4.5850 × 10^{2} | 2.3449 × 10^{3} | 7.1282 × 10^{2} | 3.4454 × 10^{2} | |

Cosine_2 | 3.9002 × 10^{2} | 8.5583 × 10^{2} | 4.1202 × 10^{2} | 8.2736 × 10^{1} | Cosine_2 | 3.9079 × 10^{2} | 3.2281 × 10^{3} | 7.6770 × 10^{2} | 8.2332 × 10^{2} | |

Cosine_3 | 3.9010 × 10^{2} | 8.8341 × 10^{2} | 4.2415 × 10^{2} | 8.8994 × 10^{1} | Cosine_3 | 5.1242 × 10^{2} | 1.8003 × 10^{3} | 7.3318 × 10^{2} | 2.8816 × 10^{2} | |

Cosine_4 | 3.9001 × 10^{2} | 4.0870 × 10^{2} | 3.9875 × 10^{2} | 7.7194 | Cosine_4 | 3.9074 × 10^{2} | 1.1216 × 10^{3} | 5.3644 × 10^{2} | 1.8263 × 10^{2} | |

${\mathit{f}}_{\mathbf{14}}$ | Straight_1 | −3.3000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 2.3198 × 10^{−8} | Straight_1 | −3.2999 × 10^{2} | −3.2784 × 10^{2} | −3.2924 × 10^{2} | 7.3617 × 10^{−1} |

Straight_2 | −3.3000 × 10^{2} | −3.3000 × 10^{2} | −3.3000 × 10^{2} | 6.0514 × 10^{−14} | Straight_2 | −3.3000 × 10^{2} | −3.2801 × 10^{2} | −3.2962 × 10^{2} | 5.9806 × 10^{−1} | |

Threshold_1 | −3.3000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 1.1729 × 10^{−7} | Threshold_1 | −3.2877 × 10^{2} | −3.2057 × 10^{2} | −3.2511 × 10^{2} | 1.7985 | |

Threshold_2 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2997 × 10^{2} | 1.7860 × 10^{−1} | Threshold_2 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2977 × 10^{2} | 4.2082 × 10^{−1} | |

Threshold_3 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2997 × 10^{2} | 1.7859 × 10^{−1} | Threshold_3 | −3.3000 × 10^{2} | −3.2801 × 10^{2} | −3.2974 × 10^{2} | 4.9350 × 10^{−1} | |

Threshold_4 | −3.3000 × 10^{2} | −3.3000 × 10^{2} | −3.3000 × 10^{2} | 1.4154 × 10^{−13} | Threshold_4 | −3.3000 × 10^{2} | −3.2303 × 10^{2} | −3.2718 × 10^{2} | 1.5641 | |

Exponential_1 | −3.3000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 3.0646 × 10^{−8} | Exponential_1 | −3.3000 × 10^{2} | −3.2897 × 10^{2} | −3.2988 × 10^{2} | 3.1104 × 10^{−1} | |

Exponential_2 | −3.3000 × 10^{2} | −3.3000 × 10^{2} | −3.3000 × 10^{2} | 1.0062 × 10^{−13} | Exponential_2 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2983 × 10^{2} | 3.7070 × 10^{−1} | |

Exponential_3 | −3.3000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 1.8858 × 10^{−6} | Exponential_3 | −3.3000 × 10^{2} | −3.2900 × 10^{2} | −3.2990 × 10^{2} | 2.9728 × 10^{−1} | |

Exponential_4 | −3.3000 × 10^{2} | −3.3000 × 10^{2} | −3.3000 × 10^{2} | 1.0934 × 10^{−13} | Exponential_4 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2997 × 10^{2} | 1.7860 × 10^{−1} | |

Exponential_5 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2997 × 10^{2} | 1.7852 × 10^{−1} | Exponential_5 | −3.3000 × 10^{2} | −3.2891 × 10^{2} | −3.2980 × 10^{2} | 3.8883 × 10^{−1} | |

Exponential_6 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2997 × 10^{2} | 1.7860 × 10^{−1} | Exponential_6 | −3.3000 × 10^{2} | −3.2901 × 10^{2} | −3.2987 × 10^{2} | 3.3822 × 10^{−1} | |

Cosine_1 | −3.3000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 4.0641 × 10^{−9} | Cosine_1 | −3.3000 × 10^{2} | −3.2777 × 10^{2} | −3.2947 × 10^{2} | 6.9220 × 10^{−1} | |

Cosine_2 | −3.3000 × 10^{2} | −3.3000 × 10^{2} | −3.3000 × 10^{2} | 2.9464 × 10^{−13} | Cosine_2 | −3.3000 × 10^{2} | −3.2702 × 10^{2} | −3.2920 × 10^{2} | 1.0082 | |

Cosine_3 | −3.3000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 1.5012 × 10^{−11} | Cosine_3 | −3.3000 × 10^{2} | −3.2747 × 10^{2} | −3.2933 × 10^{2} | 7.1582 × 10^{−1} | |

Cosine_4 | −3.3000 × 10^{2} | −3.3000 × 10^{2} | −3.3000 × 10^{2} | 2.0231 × 10^{−13} | Cosine_4 | −3.3000 × 10^{2} | −3.2701 × 10^{2} | −3.2924 × 10^{2} | 9.1373 × 10^{−1} |

No. | Dimension (D) = 30 | Dimension (D) = 100 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Algorithm | Strategy | Min | Max | Mean | SD | Algorithm | Strategy | Min | Max | Mean | SD | |

1 | HS | – | 9.5152 × 10^{−1} | 7.2900 | 3.9526 | 1.8888 | HS | – | 9.8221 × 10^{3} | 1.4318 × 10^{4} | 1.2247 × 10^{4} | 1.1304 × 10^{3} |

IHS | – | 1.8017 × 10^{−7} | 4.5253 × 10^{−7} | 3.4508 × 10^{−7} | 6.9069 × 10^{−8} | IHS | – | 9.3279 × 10^{3} | 1.5282 × 10^{4} | 1.2496 × 10^{4} | 1.2772 × 10^{3} | |

SGHS | – | 7.6930 × 10^{−10} | 1.5045 × 10^{−8} | 5.0535 × 10^{−9} | 3.1296 × 10^{−9} | SGHS | – | 6.6607 × 10^{−1} | 2.7569 | 1.5343 | 4.7765 × 10^{−1} | |

NGHS | – | 1.7413 × 10^{−17} | 2.3048 × 10^{−15} | 3.4620 × 10^{−16} | 4.7004 × 10^{−16} | NGHS | – | 3.0447 × 10^{−4} | 1.3603 × 10^{−3} | 7.4741 × 10^{−4} | 2.1074 × 10^{−4} | |

DANGHS | Exponential_6 | 2.3735 × 10^{−38} | 3.7601 × 10^{−30} | 1.8344 × 10^{−31} | 7.0604 × 10^{−31} | DANGHS | Exponential_6 | 1.6615 × 10^{−16} | 8.0332 × 10^{−14} | 1.2209 × 10^{−14} | 1.9706 × 10^{−14} | |

2 | HS | – | 3.0000 | 1.7000 × 10^{1} | 9.3000 | 3.7162 | HS | – | 8.4840 × 10^{3} | 1.6381 × 10^{4} | 1.2242 × 10^{4} | 1.6586 × 10^{3} |

IHS | – | 0.0000 | 3.0000 | 9.3333 × 10^{−1} | 1.0306 | IHS | – | 1.0060 × 10^{4} | 1.5588 × 10^{4} | 1.2560 × 10^{4} | 1.3116 × 10^{3} | |

SGHS | – | 0.0000 | 0.0000 | 0.0000 | 0.0000 | SGHS | – | 3.0000 | 1.8000 × 10^{1} | 8.7667 | 3.1271 | |

NGHS | – | 0.0000 | 0.0000 | 0.0000 | 0.0000 | NGHS | – | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

DANGHS | Exponential_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | DANGHS | Exponential_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

3 | HS | – | 3.8826 × 10^{−2} | 2.1547 × 10^{−1} | 8.3000 × 10^{−2} | 3.9484 × 10^{−2} | HS | – | 5.2475 × 10^{1} | 6.6253 × 10^{1} | 6.0705 × 10^{1} | 4.1892 |

IHS | – | 1.8454 × 10^{−3} | 2.7586 × 10^{−2} | 3.1832 × 10^{−3} | 4.5541 × 10^{−3} | IHS | – | 5.1429 × 10^{1} | 6.9346 × 10^{1} | 6.0238 × 10^{1} | 4.2859 | |

SGHS | – | 1.2406 × 10^{−4} | 2.3354 × 10^{−4} | 1.6844 × 10^{−4} | 2.7009 × 10^{−5} | SGHS | – | 6.9687 × 10^{−2} | 4.0539 × 10^{−1} | 2.2004 × 10^{−1} | 7.5524 × 10^{−2} | |

NGHS | – | 2.8122 × 10^{−10} | 4.8894 × 10^{−9} | 1.3786 × 10^{−9} | 9.1666 × 10^{−10} | NGHS | – | 8.0120 × 10^{−3} | 1.8302 × 10^{−2} | 1.4477 × 10^{−2} | 2.3050 × 10^{−3} | |

DANGHS | Exponential_6 | 5.1270 × 10^{−23} | 2.5548 × 10^{−17} | 1.9511 × 10^{−18} | 5.5869 × 10^{−18} | DANGHS | Exponential_6 | 1.7326 × 10^{−9} | 2.2346 × 10^{−8} | 7.9778 × 10^{−9} | 5.9706 × 10^{−9} | |

4 | HS | – | 1.3615 × 10^{3} | 8.1756 × 10^{3} | 3.7966 × 10^{3} | 1.4524 × 10^{3} | HS | – | 1.2355 × 10^{5} | 2.2504 × 10^{5} | 1.8030 × 10^{5} | 2.0587 × 10^{4} |

IHS | – | 1.5474 × 10^{3} | 6.0226 × 10^{3} | 3.8475 × 10^{3} | 1.1754 × 10^{3} | IHS | – | 1.2992 × 10^{5} | 2.3481 × 10^{5} | 1.7522 × 10^{5} | 2.7139 × 10^{4} | |

SGHS | – | 2.0150 × 10^{1} | 1.0642 × 10^{2} | 5.2245 × 10^{1} | 2.2107 × 10^{1} | SGHS | – | 1.7856 × 10^{4} | 3.1133 × 10^{4} | 2.2834 × 10^{4} | 2.8349 × 10^{3} | |

NGHS | - | 2.8355 × 10^{1} | 1.4013 × 10^{2} | 6.5269 × 10^{1} | 3.3421 × 10^{1} | NGHS | – | 7.4976 × 10^{3} | 1.2945 × 10^{4} | 9.7007 × 10^{3} | 1.6021 × 10^{3} | |

DANGHS | Threshold_4 | 1.5038 × 10^{1} | 1.5980 × 10^{2} | 6.0249 × 10^{1} | 3.5686 × 10^{1} | DANGHS | Exponential_2 | 4.6763 × 10^{3} | 1.3135 × 10^{4} | 8.6301 × 10^{3} | 1.9698 × 10^{3} | |

5 | HS | – | 1.0212 | 1.1106 | 1.0591 | 2.2096 × 10^{−2} | HS | – | 9.5506 × 10^{1} | 1.4758 × 10^{2} | 1.1631 × 10^{2} | 1.1240 × 10^{1} |

IHS | – | 1.2959 × 10^{−7} | 3.4241 × 10^{−2} | 7.5274 × 10^{−3} | 9.2294 × 10^{−3} | IHS | – | 7.5548 × 10^{1} | 1.4827 × 10^{2} | 1.0997 × 10^{2} | 1.4826 × 10^{1} | |

SGHS | – | 1.7833 × 10^{−2} | 2.3440 × 10^{−1} | 1.0043 × 10^{−1} | 5.1304 × 10^{−2} | SGHS | – | 4.4296 × 10^{−1} | 8.8847 × 10^{−1} | 6.8599 × 10^{−1} | 9.9379 × 10^{−2} | |

NGHS | – | 3.3307 × 10^{−16} | 2.5387 × 10^{−1} | 6.1311 × 10^{−2} | 4.9633 × 10^{−2} | NGHS | – | 1.5343 × 10^{−4} | 9.9663 × 10^{−2} | 1.7168 × 10^{−2} | 2.2003 × 10^{−2} | |

DANGHS | Threshold_4 | 6.6613 × 10^{−16} | 8.0817 × 10^{−2} | 3.1209 × 10^{−2} | 2.3482 × 10^{−2} | DANGHS | Exponential_2 | 3.5352 × 10^{−11} | 4.8906 × 10^{−2} | 6.4754 × 10^{−3} | 9.8313 × 10^{−3} | |

6 | HS | - | 1.9421 × 10^{−2} | 1.3050 | 4.9617 × 10^{−1} | 4.2318 × 10^{−1} | HS | – | 1.0882 × 10^{1} | 1.2567 × 10^{1} | 1.1743 × 10^{1} | 3.8517 × 10^{−1} |

IHS | – | 3.4980 × 10^{−4} | 1.3915 | 2.2199 × 10^{−1} | 3.4543 × 10^{−1} | IHS | – | 1.0987 × 10^{1} | 1.2722 × 10^{1} | 1.1852 × 10^{1} | 4.3446 × 10^{−1} | |

SGHS | – | 1.7703 × 10^{−5} | 4.5526 × 10^{−5} | 3.0830 × 10^{−5} | 6.1683 × 10^{−6} | SGHS | – | 6.3791 × 10^{−2} | 4.5729 × 10^{−1} | 2.4057 × 10^{−1} | 1.2018 × 10^{−1} | |

NGHS | – | 7.7839 × 10^{−10} | 2.0025 × 10^{−8} | 5.7085 × 10^{−9} | 5.2959 × 10^{−9} | NGHS | – | 2.6973 × 10^{−3} | 5.3184 × 10^{−3} | 3.6500 × 10^{−3} | 5.4706 × 10^{−4} | |

DANGHS | Exponential_6 | 4.9294 × 10^{−14} | 2.2338 × 10^{−13} | 9.6308 × 10^{−14} | 3.4392 × 10^{−14} | DANGHS | Exponential_6 | 1.0897 × 10^{−9} | 2.9882 × 10^{−8} | 9.3030 × 10^{−9} | 7.9441 × 10^{−9} | |

7 | HS | – | 9.6358 × 10^{1} | 3.9298 × 10^{2} | 1.8204 × 10^{2} | 5.9631 × 10^{1} | HS | – | 3.2565 × 10^{6} | 9.1894 × 10^{6} | 5.9320 × 10^{6} | 1.2941 × 10^{6} |

IHS | - | 1.7586 × 10^{1} | 2.1565 × 10^{3} | 3.6705 × 10^{2} | 5.5299 × 10^{2} | IHS | – | 4.1100 × 10^{6} | 8.2424 × 10^{6} | 5.7186 × 10^{6} | 1.0494 × 10^{6} | |

SGHS | – | 9.0932 | 2.0293 × 10^{3} | 1.7534 × 10^{2} | 3.7957 × 10^{2} | SGHS | – | 1.0832 × 10^{2} | 2.8592 × 10^{3} | 5.1645 × 10^{2} | 4.7866 × 10^{2} | |

NGHS | – | 6.6756 × 10^{−4} | 2.3003 × 10^{2} | 1.4971 × 10^{1} | 4.0757 × 10^{1} | NGHS | – | 2.1179 × 10^{1} | 1.4411 × 10^{3} | 2.8501 × 10^{2} | 2.8532 × 10^{2} | |

DANGHS | Straight_1 | 9.3515 × 10^{−3} | 2.2089 × 10^{1} | 1.0089 × 10^{1} | 8.7452 | DANGHS | Threshold_3 | 5.6804 × 10^{−2} | 1.1562 × 10^{3} | 6.1559 × 10^{1} | 2.0554 × 10^{2} | |

8 | HS | – | 3.0572 × 10^{−2} | 2.0546 | 4.6448 × 10^{−1} | 6.5390 × 10^{−1} | HS | – | 2.1874 × 10^{2} | 2.8758 × 10^{2} | 2.5192 × 10^{2} | 1.6481 × 10^{1} |

IHS | – | 4.1948 × 10^{−5} | 4.5484 | 1.2420 | 9.8291 × 10^{−1} | IHS | – | 2.0838 × 10^{2} | 2.8193 × 10^{2} | 2.4294 × 10^{2} | 1.8844 × 10^{1} | |

SGHS | – | 3.7300 × 10^{−7} | 9.9498 × 10^{−1} | 1.3267 × 10^{−1} | 3.3822 × 10^{−1} | SGHS | – | 3.2260 × 10^{−2} | 9.1200 | 4.5553 | 2.2588 | |

NGHS | - | 0.0000 | 1.6069 × 10^{−11} | 9.3241 × 10^{−13} | 3.2209 × 10^{−12} | NGHS | – | 1.2729 × 10^{−3} | 1.0102 | 2.1542 × 10^{−1} | 3.9474 × 10^{−1} | |

DANGHS | Threshold_2 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | DANGHS | Exponential_3 | 3.5170 × 10^{−8} | 5.9362 × 10^{−1} | 2.7729 × 10^{−2} | 1.0943 × 10^{−1} | |

9 | HS | – | 6.9691 | 3.8058 × 10^{1} | 1.8422 × 10^{1} | 6.8471 | HS | – | 4.5568 × 10^{3} | 6.9091 × 10^{3} | 5.7964 × 10^{3} | 5.5601 × 10^{2} |

IHS | – | 3.8186 × 10^{−4} | 5.2695 × 10^{−1} | 1.7934 × 10^{−2} | 9.4522 × 10^{−2} | IHS | – | 4.2297 × 10^{3} | 6.4098 × 10^{3} | 5.4659 × 10^{3} | 5.5784 × 10^{2} | |

SGHS | – | 2.3563 × 10^{−3} | 3.6545 × 10^{−2} | 1.3771 × 10^{−2} | 7.5711 × 10^{−3} | SGHS | – | 7.2936 | 3.8640 × 10^{1} | 1.5981 × 10^{1} | 7.4744 | |

NGHS | – | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 5.5493 × 10^{−13} | NGHS | – | 3.3819 × 10^{−3} | 6.8492 × 10^{−2} | 1.1069 × 10^{−2} | 1.3684 × 10^{−2} | |

DANGHS | Threshold_2 | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 3.8183 × 10^{−4} | 1.3763 × 10^{−13} | DANGHS | Threshold_2 | 1.2728 × 10^{−3} | 1.2728 × 10^{−3} | 1.2728 × 10^{−3} | 1.4537 × 10^{−9} | |

10 | HS | – | −4.4898 × 10^{2} | −4.3989 × 10^{2} | −4.4573 × 10^{2} | 2.2745 | HS | – | 1.0055 × 10^{4} | 1.6736 × 10^{4} | 1.2963 × 10^{4} | 1.7748 × 10^{3} |

IHS | – | −4.5000 × 10^{2} | −4.4999 × 10^{2} | −4.4999 × 10^{2} | 1.1657 × 10^{−7} | IHS | – | 1.0425 × 10^{4} | 1.4910 × 10^{4} | 1.2856 × 10^{4} | 1.2084 × 10^{3} | |

SGHS | – | −4.5000 × 10^{2} | −4.4999 × 10^{2} | −4.4999 × 10^{2} | 2.7913 × 10^{−9} | SGHS | – | −4.4918 × 10^{2} | −4.4701 × 10^{2} | −4.4841 × 10^{2} | 5.8573 × 10^{−1} | |

NGHS | – | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 6.9619 × 10^{−14} | NGHS | – | −4.5000 × 10^{2} | −4.4999 × 10^{2} | −4.4999 × 10^{2} | 3.0551 × 10^{−4} | |

DANGHS | Exponential_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 5.4916 × 10^{−14} | DANGHS | Threshold_2 | −4.5000 × 10^{2} | −4.5000 × 10^{2} | −4.5000 × 10^{2} | 2.4117 × 10^{−13} | |

11 | HS | – | 1.5142 × 10^{3} | 7.6068 × 10^{3} | 3.4157 × 10^{3} | 1.2671 × 10^{3} | HS | – | 1.4921 × 10^{5} | 2.5525 × 10^{5} | 1.9430 × 10^{5} | 2.3256 × 10^{4} |

IHS | – | 1.0412 × 10^{3} | 7.3312 × 10^{3} | 3.3180 × 10^{3} | 1.3292 × 10^{3} | IHS | – | 1.4941 × 10^{5} | 2.7307 × 10^{5} | 2.0189 × 10^{5} | 2.7108 × 10^{4} | |

SGHS | – | −4.3194 × 10^{2} | −3.2048 × 10^{2} | −3.9763 × 10^{2} | 2.7006 × 10^{1} | SGHS | – | 1.5646 × 10^{4} | 3.5936 × 10^{4} | 2.6350 × 10^{4} | 4.0064 × 10^{3} | |

NGHS | – | −4.2591 × 10^{2} | −1.9340 × 10^{2} | −3.3680 × 10^{2} | 6.4820 × 10^{1} | NGHS | – | 9.0685 × 10^{3} | 1.7976 × 10^{4} | 1.1950 × 10^{4} | 2.0823 × 10^{3} | |

DANGHS | Threshold_4 | −4.4289 × 10^{2} | −2.5392 × 10^{2} | −3.7419 × 10^{2} | 4.4269 × 10^{1} | DANGHS | Exponential_2 | 6.9718 × 10^{3} | 1.7181 × 10^{4} | 1.1471 × 10^{4} | 2.4981 × 10^{3} | |

12 | HS | – | −1.7016 × 10^{2} | −1.3324 × 10^{2} | −1.5876 × 10^{2} | 9.4348 | HS | – | 3.2343 × 10^{3} | 5.9684 × 10^{3} | 4.7002 × 10^{3} | 6.7476 × 10^{2} |

IHS | – | −1.7607 × 10^{2} | −1.3892 × 10^{2} | −1.5831 × 10^{2} | 7.7527 | IHS | – | 3.4934 × 10^{3} | 6.5826 × 10^{3} | 4.8855 × 10^{3} | 8.4393 × 10^{2} | |

SGHS | – | −1.7830 × 10^{2} | −1.7149 × 10^{2} | −1.7583 × 10^{2} | 1.6385 | SGHS | – | −1.3057 × 10^{2} | −1.5099 × 10^{1} | −7.2944 × 10^{1} | 2.8794 × 10^{1} | |

NGHS | – | −1.7913 × 10^{2} | −1.7532 × 10^{2} | −1.7829 × 10^{2} | 6.4615 × 10^{−1} | NGHS | – | −1.5784 × 10^{2} | −1.1939 × 10^{2} | −1.4231 × 10^{2} | 1.0814 × 10^{1} | |

DANGHS | Straight_2 | −1.7894 × 10^{2} | −1.7562 × 10^{2} | −1.7821 × 10^{2} | 7.6813 × 10^{−1} | DANGHS | Exponential_6 | −1.7066 × 10^{2} | −1.4082 × 10^{2} | −1.6037 × 10^{2} | 6.8764 | |

13 | HS | – | 4.7650 × 10^{2} | 2.5184 × 10^{3} | 6.6765 × 10^{2} | 3.6290 × 10^{2} | HS | – | 4.0732 × 10^{6} | 8.7806 × 10^{6} | 6.0785 × 10^{6} | 1.0919 × 10^{6} |

IHS | – | 4.1262 × 10^{2} | 1.7487 × 10^{3} | 5.7845 × 10^{2} | 2.3203 × 10^{2} | IHS | – | 4.5479 × 10^{6} | 8.5517 × 10^{6} | 6.3527 × 10^{6} | 1.2268 × 10^{6} | |

SGHS | – | 3.9001 × 10^{2} | 5.6058 × 10^{2} | 4.6408 × 10^{2} | 4.0896 × 10^{1} | SGHS | – | 6.4618 × 10^{2} | 2.5249 × 10^{3} | 9.7963 × 10^{2} | 4.0336 × 10^{2} | |

NGHS | – | 3.9000 × 10^{2} | 4.0874 × 10^{2} | 3.9494 × 10^{2} | 5.7399 | NGHS | – | 4.6424 × 10^{2} | 1.6001 × 10^{3} | 7.1517 × 10^{2} | 2.9163 × 10^{2} | |

DANGHS | Cosine_4 | 3.9001 × 10^{2} | 4.0870 × 10^{2} | 3.9875 × 10^{2} | 7.7194 | DANGHS | Cosine_4 | 3.9074 × 10^{2} | 1.1216 × 10^{3} | 5.3644 × 10^{2} | 1.8263 × 10^{2} | |

14 | HS | – | −3.2997 × 10^{2} | −3.2788 × 10^{2} | −3.2938 × 10^{2} | 7.4966 × 10^{−1} | HS | – | −9.3948 × 10^{1} | −6.2235 | −5.1541 × 10^{1} | 2.2413 × 10^{1} |

IHS | – | −3.2999 × 10^{2} | −3.2749 × 10^{2} | −3.2897 × 10^{2} | 6.9697 × 10^{−1} | IHS | – | −1.1215 × 10^{2} | −3.3592 × 10^{1} | −6.5372 × 10^{1} | 1.6227 × 10^{1} | |

SGHS | – | 3.9000 × 10^{2} | −3.2901 × 10^{2} | −3.2993 × 10^{2} | 2.4813 × 10^{−1} | SGHS | – | −3.2900 × 10^{2} | −3.2101 × 10^{2} | −3.2614 × 10^{2} | 2.2502 | |

NGHS | – | 3.9000 × 10^{2} | −3.2999 × 10^{2} | −3.2999 × 10^{2} | 1.1444 × 10^{−12} | NGHS | – | 3.9000 × 10^{2} | −3.2798 × 10^{2} | −3.2979 × 10^{2} | 5.4096 × 10^{−1} | |

DANGHS | Straight_2 | 3.9000 × 10^{2} | 3.9000 × 10^{2} | 3.9000 × 10^{2} | 6.0514 × 10^{−14} | DANGHS | Exponential_4 | 3.9000 × 10^{2} | −3.2901 × 10^{2} | −3.2997 × 10^{2} | 1.7860 × 10^{−1} |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chiu, C.-Y.; Shih, P.-C.; Li, X.
A Dynamic Adjusting Novel Global Harmony Search for Continuous Optimization Problems. *Symmetry* **2018**, *10*, 337.
https://doi.org/10.3390/sym10080337

**AMA Style**

Chiu C-Y, Shih P-C, Li X.
A Dynamic Adjusting Novel Global Harmony Search for Continuous Optimization Problems. *Symmetry*. 2018; 10(8):337.
https://doi.org/10.3390/sym10080337

**Chicago/Turabian Style**

Chiu, Chui-Yu, Po-Chou Shih, and Xuechao Li.
2018. "A Dynamic Adjusting Novel Global Harmony Search for Continuous Optimization Problems" *Symmetry* 10, no. 8: 337.
https://doi.org/10.3390/sym10080337