Empirical Study of ConstraintHandling Techniques in the Optimal Synthesis of Mechanisms for Rehabilitation
Abstract
:1. Introduction
2. Optimization Problem Statement
3. ConstraintHandling Techniques in Metaheuristic Algorithms
3.1. Metaheuristic Algorithms
3.1.1. Differential Evolution Algorithm
Algorithm 1 Differential evolution pseudocode.  
1:  Generate an initial population ${X}_{0}$ with $NP$ individuals. 
2:  Evaluate ${X}_{0}$. 
3:  Initialize the best individual ${x}_{best}$. 
4:  $G\leftarrow 0$ 
5:  while$G\le {G}_{max}$do 
6:  for all ${x}_{i}\in {X}_{G}$do 
7:  Generate a child individual ${u}_{i}$ based on (5)–(12). 
8:  Evaluate ${u}_{i}$ and ${U}_{G}\leftarrow {u}_{i}$. 
9:  end for 
10:  Select the new population ${X}_{G+1}$ between ${X}_{G}$ and ${U}_{G}$ according to CHT. 
$[{X}_{G+1},{x}^{\underset{swarm}{best}}]\leftarrow fncCHT({X}_{G},{U}_{G},{x}_{best})$ (This function is associated to the CHT.)  
11:  $G\leftarrow G+1$ 
12:  end while 
3.1.2. Particle Swarm Optimization
Algorithm 2 Particle swarm optimization pseudocode.  
1:  Initialize the swarm position ${u}_{i}\in {U}_{0}$ with $NP$ particles. 
2:  Evaluate the swarm ${U}_{0}$. 
3:  Initialize the best known position ${X}_{0}={U}_{0}$. 
4:  Initialize the best position of the swarm ${x}^{\underset{swarm}{best}}$. 
5:  Initialize the velocity of each particle ${v}_{i}\in {V}_{0}$. 
6:  $G\leftarrow 0$ 
7:  while$G\le {G}_{max}$do 
8:  Update the inertial weight w based on (13). 
9:  for all ${u}_{i}\in {U}_{G}$do 
10:  Update the velocity ${v}_{i}$ based on (14). 
11:  Update the position ${u}_{i}$ based on (15). 
12:  Evaluate ${u}_{i}$. 
13:  end for 
14:  Update the best known position ${X}_{G+1}$ and the best particle in the swarm ${x}^{\underset{swarm}{best}}$ with the use of CHT between ${X}_{G}$ and ${U}_{G}$. 
$[{X}_{G+1},{x}^{\underset{swarm}{best}}]\leftarrow fncCHT({X}_{G},{U}_{G},{x}^{\underset{swarm}{best}})$ (This function is associated to the CHT.)  
15:  $G\leftarrow G+1$ 
16:  end while 
3.1.3. Genetic Algorithm
Algorithm 3 Genetic algorithm pseudocode.  
1:  Generate a initial population ${X}_{0}$ with $NP$ chromosomes. 
2:  Evaluate ${X}_{0}$ 
3:  $G\leftarrow 0$ 
4:  while$G\le {G}_{max}$do 
5:  for all ${x}_{i}\in {X}_{G}$do 
6:  Obtain ${x}_{{r}_{1}}$ and ${x}_{{r}_{2}}$ in ${X}_{G}$ by tournament. 
7:  Generate a child ${v}_{i}$ by (16) 
8:  Generate a mutant ${u}_{i}$ by (17) 
9:  Evaluate ${u}_{i}$ 
10:  end for 
11:  Replace the population ${X}_{G}$ to ${X}_{G+1}$ considering ${X}_{G}$ and ${U}_{G}$ in the CHT.${X}_{G+1}\leftarrow fncCHT({X}_{G},{U}_{G},\sim )$ (This function is associated to the CHT.) 
12:  $G\leftarrow G+1$ 
13:  end while 
3.2. ConstraintHandling Techniques
3.2.1. Penalty Function
Algorithm 4 Penalty function pseudocode. 

3.2.2. Feasibility Rules
 Between two infeasible solutions, the solution with the fewest number of violated constraints is chosen.
 Between a feasible solution and an infeasible one, the feasible solution is chosen.
 Among two feasible solutions, the solution with the best objective function is chosen.
Algorithm 5 Feasibility rules pseudocode. 

Input: $\tilde{a}\in {X}_{G}$ and $\tilde{b}\in {U}_{G}$ 
Output: ${X}_{G+1}$ and ${x}^{best}$

3.2.3. $\u03f5$Constraint Method
Algorithm 6$\u03f5$constraint method pseudocode.  
1:  Function $fncCHT(\tilde{a},\tilde{b},\tilde{c})$ 
Input: $\tilde{a}\in {X}_{G}$ and $\tilde{b}\in {U}_{G}$  
Output: ${X}_{G+1}$ and ${x}^{best}$  
2:  ${X}_{G+1}=\tilde{a}$ and ${x}^{best}=\tilde{c}$ 
3:  for$j=1$ to $NP$ do 
4:  if$rand(0,1)<Pg$then 
5:  $k=0$ 
6:  while $k<Rg$ and $\varphi \left({\tilde{b}}_{j}\right)>\u03f5$ do 
7:  Obtain $\Delta {\tilde{b}}_{j}=\nabla C{\left({\tilde{b}}_{j}\right)}^{1}\Delta C\left({\tilde{b}}_{j}\right)$ 
$\Delta C\left({\tilde{b}}_{j}\right)$ is the constraint vector, $\Delta C{\left({\tilde{b}}_{j}\right)}^{1}$ is the pseudoinverse of the constraint’s derivative obtained by Moore–Penrose pseudoinverse using the singular value decomposition and $Rg$ is the number of attempts to improve the solution.  
8:  Obtain ${u}^{new}={\tilde{b}}_{j}+\Delta {\tilde{b}}_{j}$ 
9:  if$(\overline{J}\left({u}^{new}\right),\varphi \left({u}^{new}\right)){<}_{\u03f5}(\overline{J}\left({\tilde{b}}_{j}\right),\varphi \left({\tilde{b}}_{j}\right))$then 
10:  ${\tilde{b}}_{j}\leftarrow {u}^{new}$ 
11:  else 
12:  $break$ 
13:  end if 
14:  $k=k+1$ 
15:  end while 
16:  end if 
17:  if$(\overline{J}\left({\tilde{b}}_{j}\right),\varphi \left({\tilde{b}}_{j}\right)){<}_{\u03f5}(\overline{J}\left({\tilde{a}}_{j}\right),\varphi \left({\tilde{a}}_{j}\right))$then 
18:  ${X}_{G+1}\leftarrow {b}_{j}$ 
19:  if$(\overline{J}\left({\tilde{b}}_{j}\right),\varphi \left({\tilde{b}}_{j}\right)){<}_{\u03f5}(\overline{J}\left({x}^{best}\right),\varphi \left({x}^{best}\right))$then 
20:  ${x}^{best}\leftarrow {b}_{j}$ 
21:  end if 
22:  end if 
23:  end for 
3.2.4. StochasticRanking
Algorithm 7 Stochastic ranking pseudocode. 

Input: $\tilde{a}\in {X}_{G}$ and $\tilde{b}\in {U}_{G}$ 
Output: ${X}_{G+1}$ and ${x}^{best}$

4. Study Cases in the Mechanism Synthesis for Lower Limb Rehabilitation
4.1. Case 1: FourBar Linkage Mechanism
4.2. Case 2: CamLinkage Mechanism
4.3. Case 3: EightBar Linkage Mechanism
5. Comparative Experimental Study
5.1. Parameter Tuning Conditions of the CHTs in the Algorithms
5.2. Statistical Analysis of the Overall Performance
 The CHT A can be compared to the CHT B if their CHTs are different, and the algorithms that implement such CHTs are the same. On the contrary, they cannot be compared.
 The statistical measure from the thirty executions of the CHT A is better than the CHT B for the same algorithm if the former presents less value than the latter. When this happens, the CHT A obtains the point (a win) in favor. Thus, the maximum number of points for comparing each CHT is 150 (three CHT comparisons per five measures per ten algorithms).
 The CHT with the highest number of points is the best constrainthandling technique.
5.3. Statistical Analysis of the CHT Behavior through Metrics
 The feasibility probability (FP) is obtained by dividing the number of feasible executions by the total number of executions. FP is in the range of $[0,1]$, where 0 represents that there are not feasible solutions, and 1 represents that all found solutions are feasible.
 The convergence probability (P) is obtained by dividing the number of successful executions by the total number of executions. The successful solutions are defined as the solutions x close to the best solution ${x}^{*}$ in the objective function space. Therefore, a satisfactory solution can be determined by $\overline{J}\left(x\right)\overline{J}\left({x}^{*}\right)\le \overline{e}$, where the best executions per each study case is shown in Table A7, Table A8 and Table A9 of Appendix C. The value of $\overline{e}$ is related to the bias region in the synthesis problem where the mechanism executes a suitable rehabilitation routine.For the fourbar mechanism, $\overline{J}\left({x}^{*}\right)=0.0021$ and $\overline{e}=0.0018$ are considered; for the camlinkage mechanism, $\overline{J}\left({x}^{*}\right)=0.6540$ and $\overline{e}=0.5931$ are chosen; and for the eightbar linkage mechanism, $\overline{J}\left({x}^{*}\right)=1.2054\times {10}^{4}$ and $\overline{e}=0.0011$ are selected. The P metric value is in the interval $[0,1]$, where a higher value (the best P metric) implies that all executions converge to the region. The metric is related to the reliability of an algorithm to find successful solutions.
 AFES is the average number of function evaluations required for each successful execution. Successful execution is considered when it finds the first solution in the bias region $\overline{e}$. If successful executions are not found, NonSuccessful Executions (NSE) are accounted for. The best result in the AFES metric is first related to the minimum value in NSE and then to the lower values of the AFES. This metric indicates a convergence speed measure to the bias region $\overline{e}$.
 Successful performance (SP) divides the AFES by P. The best result in the SP metric is first related to the minimum value in NSE and then to the lower values of the SP.
 EVALS counts the number of evaluations an algorithm needs to find the first feasible solution in every execution. Lower evaluations mean a low computational cost to reach a feasible solution; therefore, this is preferred. This metric is presented with the use of statistics.
 The Progress Ratio (PR) measures the improvement capability of an algorithm inside the feasible region in every execution. This metric is calculated by (86) where ${\overline{J}}_{min}\left({G}_{ff}\right)$ is the value of the objective function of the first feasible solution, and ${\overline{J}}_{min}\left(MCN\right)$ is the value of the objective function of the best feasible solution in the algorithm execution. It is assumed in (86) that ${\overline{J}}_{min}\left(MCN\right)>0$ is fulfilled. A higher value in this metric is preferred and also presented by using statistics.$$PR=\leftln\sqrt{\frac{{\overline{J}}_{min}\left({G}_{ff}\right)}{{\overline{J}}_{min}\left(MCN\right)}}\right$$
 The FR had one of the best performance and the best one of the search for feasible solutions and satisfactory regions for the three study cases, respectively, because this constrainthandling technique has a high probability value in the FP and P metrics. The relationship between the AFES and P gave by SP is the best among the CHTs. Therefore, among the studied CHTs, the Feasibility Rules technique is the most reliable one for the synthesis of mechanisms for rehabilitation.
 The PF can be considered the second option for solving mechanism synthesis for rehabilitation problems because it showed a suitable performance to find satisfactory solutions (P and SP metrics) compared to StochasticRanking and $\u03f5$constraint. This establishes acceptable reliability to find feasible solutions (FP metric).
 $\u03f5$ C method presented the best performance in the search for feasible regions as shown in FP. Inside the feasible region, this CHT produces improved solutions based on the PR metric. Nevertheless, the probability of this CHT to search for satisfactory solutions was low (P and SP metrics). This behavior is attributed to the gradientbased mutation where fast convergence to feasible local regions is promoted.
 SR is the less reliable CHT because some algorithm executions can not find feasible solutions (FP metric). This presents a low performance in the search for suitable solutions (P metric).
5.4. Evaluation of the Obtained Mechanisms
6. Conclusions
 Through the statistical analysis, we observed that the feasibility rules present the best overall performance for the solution of the three mechanism synthesis cases under study. This is because the feasibility rules show a high probability of convergence towards feasible solutions and satisfactory regions based on the performance metrics studied in this work.
 In the solution of mechanism synthesis problems for rehabilitation, there exists a high probability that the search capability of an algorithm is improved by incorporating the FR because, in most of the algorithms reviewed in this work, the FR enhanced the quality and consistency of results.
 The penalty functions can be used as the second option for solving mechanism synthesis for rehabilitation problems. These establish acceptable reliability to find feasible solutions based on the performance metrics.
 The $\u03f5$constraint method and stochasticranking presented the worst overall performance in the solution of the mechanism synthesis for lower limb rehabilitation. This feature is due to the mechanism synthesis problem, which presents a complex search space and wide, with highly nonlinear functions (multimodality), several design variables, and feasible regions that are difficult to find. The $\u03f5$constraint presents a fast convergence to feasible local regions because the gradientbased mutation increases the speed in the search of feasible solutions.
 We confirmed that all study cases for the assessment of the obtained mechanisms, by using the feasibility rules and the worst CHT, presented different tradeoffs in the design goals of the mechanism synthesis problem for lower limb rehabilitation. Nevertheless, FR can endow the algorithm with a better search capability to find reliable results through different executions with a high probability of finding the best overall performance.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Precision Points for Synthesis of Mechanisms
Appendix A.1. Precision Points for the Case 1: FourBar Linkage Mechanism
i  ${\overline{\mathit{x}}}_{\mathit{P}}^{\mathit{i}}$ [m]  ${\overline{\mathit{y}}}_{\mathit{P}}^{\mathit{i}}$ [m] 

1  0.7429  0.1880 
2  0.6551  0.1573 
3  0.6014  0.1388 
4  0.5189  0.1149 
5  0.4159  0.1012 
6  0.3001  0.1074 
7  0.1964  0.1375 
8  0.1639  0.1662 
9  0.1605  0.2003 
10  0.1934  0.2256 
11  0.2619  0.2251 
12  0.4201  0.1808 
13  0.6474  0.1607 
14  0.7429  0.1880 
Appendix A.2. Precision Points for Case 2: CamLinkage Mechanism
i  ${\overline{\mathit{x}}}_{\mathit{P}}^{\mathit{i}}$ [m]  ${\overline{\mathit{y}}}_{\mathit{P}}^{\mathit{i}}$ [m]  i  ${\overline{\mathit{x}}}_{\mathit{P}}^{\mathit{i}}$ [m]  ${\overline{\mathit{y}}}_{\mathit{P}}^{\mathit{i}}$ [m]  i  ${\overline{\mathit{x}}}_{\mathit{P}}^{\mathit{i}}$ [m]  ${\overline{\mathit{y}}}_{\mathit{P}}^{\mathit{i}}$ [m]  

1  −0.3159  −0.7259  2  −0.3054  −0.7295  3  −0.2956  −0.7326  4  −0.2850  −0.7357 
5  −0.2730  −0.7388  6  −0.2596  −0.7421  7  −0.2455  −0.7453  8  −0.2307  −0.7484 
9  −0.2172  −0.7509  10  −0.2019  −0.7540  11  −0.1885  −0.7567  12  −0.1738  −0.7596 
13  −0.1612  −0.7623  14  −0.1479  −0.7650  15  −0.1345  −0.7677  16  −0.1225  −0.7703 
17  −0.1112  −0.7726  18  −0.0984  −0.7750  19  −0.0870  −0.7772  20  −0.0748  −0.7792 
21  −0.0633  −0.7810  22  −0.0517  −0.7826  23  −0.0401  −0.7840  24  −0.0285  −0.7853 
25  −0.0162  −0.7862  26  −0.0045  −0.7870  27  0.0079  −0.7875  28  0.0196  −0.7879 
29  0.0306  −0.7881  30  0.0431  −0.7880  31  0.0548  −0.7876  32  0.0672  −0.7871 
33  0.0789  −0.7863  34  0.0913  −0.7853  35  0.1023  −0.7842  36  0.1139  −0.7827 
37  0.1262  −0.7810  38  0.1378  −0.7791  39  0.1500  −0.7768  40  0.1622  −0.7743 
41  0.1757  −0.7713  42  0.1884  −0.7681  43  0.2017  −0.7644  44  0.2143  −0.7607 
45  0.2280  −0.7562  46  0.2403  −0.7518  47  0.2538  −0.7466  48  0.2652  −0.7418 
49  0.2777  −0.7360  50  0.2894  −0.7301  51  0.3008  −0.7238  52  0.3107  −0.7174 
53  0.3203  −0.7106  54  0.3282  −0.7037  55  0.3352  −0.6964  56  0.3400  −0.6894 
57  0.3436  −0.6819  58  0.3456  −0.6743  59  0.3465  −0.6662  60  0.3442  −0.6590 
61  0.3408  −0.6514  62  0.3356  −0.6443  63  0.3279  −0.6379  64  0.3185  −0.6320 
65  0.3075  −0.6279  66  0.2956  −0.6243  67  0.2810  −0.6230  68  0.2664  −0.6224 
69  0.2499  −0.6241  70  0.2322  −0.6269  71  0.2145  −0.6312  72  0.1955  −0.6366 
73  0.1756  −0.6431  74  0.1540  −0.6505  75  0.1330  −0.6582  76  0.1107  −0.6668 
77  0.0880  −0.6752  78  0.0627  −0.6844  79  0.0380  −0.6931  80  0.0140  −0.7012 
81  −0.0130  −0.7095  82  −0.0388  −0.7168  83  −0.0657  −0.7235  84  −0.0932  −0.7292 
85  −0.1199  −0.7340  86  −0.1476  −0.7372  87  −0.1723  −0.7397  88  −0.1978  −0.7406 
89  −0.2227  −0.7402  90  −0.2449  −0.7388  91  −0.2669  −0.7360  92  −0.2841  −0.7333 
93  −0.2996  −0.7298  94  −0.3130  −0.7261  95  −0.3217  −0.7237  96  −0.3288  −0.7212 
97  −0.3321  −0.7200  98  −0.3322  −0.7202  99  −0.3296  −0.7213  100  −0.3232  −0.7238 
101  −0.3167  −0.7262 
Appendix A.3. Precision Points for Case 3: EightBar Linkage Mechanism
i  ${\overline{\mathit{x}}}_{\mathit{E}}^{\mathit{i}}$ [m]  ${\overline{\mathit{y}}}_{\mathit{E}}^{\mathit{i}}$ [m]  i  ${\overline{\mathit{x}}}_{\mathit{E}}^{\mathit{i}}$ [m]  ${\overline{\mathit{y}}}_{\mathit{E}}^{\mathit{i}}$ [m] 

1  0  0  11  0.25  0 
2  0.025  0  12  0.275  0 
3  0.05  0  13  0.3  0 
4  0.075  0  14  0.291  0.0513 
5  0.1  0  15  0.2591  0.1029 
6  0.125  0  16  0.2094  0.1377 
7  0.15  0  17  0.15  0.15 
8  0.1750  0  18  0.0906  0.1377 
9  0.2  0  19  0.0409  0.1029 
10  0.225  0  20  0.009  0.0513 
Appendix B. Parameter Tuning
Appendix B.1. Parameter Tuning of the Case 1: FourBar Linkage Mechanism
Algorithm  CHT  Parameters 

DER1B  DEB  $CR=0.95$, ${F}_{min}=0.13$, ${F}_{max}=0.95$ 
SR  $CR=0.91$, ${F}_{min}=0.23$, ${F}_{max}=0.96$, $Pf=0.15$  
$\u03f5$ C  $CR=0.89$, ${F}_{min}=0.20$, ${F}_{max}=0.81$, $Pg=0.07$, $Tc=590$, $Rg=5$, $cp=6$  
PF  $CR=0.95$, ${F}_{min}=0.17$, ${F}_{max}=0.91$  
DER1E  DEB  $CR=0.99$, ${F}_{min}=0.23$, ${F}_{max}=0.86$ 
SR  $CR=0.96$, ${F}_{min}=0.47$, ${F}_{max}=0.90$, $Pf=0.05$  
$\u03f5$ C  $CR=0.88$, ${F}_{min}=0.14$, ${F}_{max}=0.87$, $Pg=0.03$, $Tc=430$, $Rg=3$, $cp=10$  
PF  $CR=0.97$, ${F}_{min}=0.06$, ${F}_{max}=0.95$  
DEB1B  DEB  $CR=0.76$, ${F}_{min}=0.50$, ${F}_{max}=0.66$ 
SR  $CR=0.97$, ${F}_{min}=0.23$, ${F}_{max}=0.97$, $Pf=0.18$  
$\u03f5$ C  $CR=0.83$, ${F}_{min}=0.50$, ${F}_{max}=0.50$, $Pg=0.08$, $Tc=490$, $Rg=3$, $cp=6$  
PF  $CR=0.67$, ${F}_{min}=0.59$, ${F}_{max}=0.61$  
DEB1E  DEB  $CR=0.89$, ${F}_{min}=0.48$, ${F}_{max}=0.77$ 
SR  $CR=0.91$, ${F}_{min}=0.57$, ${F}_{max}=0.74$, $Pf=0.30$  
$\u03f5$ C  $CR=0.95$, ${F}_{min}=0.32$, ${F}_{max}=0.85$, $Pg=0.09$, $Tc=400$, $Rg=3$, $cp=5$  
PF  $CR=0.91$, ${F}_{min}=0.52$, ${F}_{max}=0.77$  
DECR  DEB  ${F}_{min}=0.26$, ${F}_{max}=0.98$, ${K}_{min}=0.91$, ${K}_{max}=0.99$ 
SR  ${F}_{min}=0.48$, ${F}_{max}=0.79$, ${K}_{min}=0.13$, ${K}_{max}=0.87$, $Pf=0.42$  
$\u03f5$ C  ${F}_{min}=0.15$, ${F}_{max}=0.89$, ${K}_{min}=0.82$, ${K}_{max}=0.96$, $Pg=0.10$, $Tc=550$, $Rg=5$, $cp=3$  
PF  ${F}_{min}=0.23$, ${F}_{max}=0.93$, ${K}_{min}=0.88$, ${K}_{max}=0.98$  
DECB  DEB  ${F}_{min}=0.44$, ${F}_{max}=0.97$, ${K}_{min}=0.48$, ${K}_{max}=1$ 
SR  ${F}_{min}=0.29$, ${F}_{max}=0.91$, ${K}_{min}=0.29$, ${K}_{max}=0.69$, $Pf=0.40$  
$\u03f5$ C  ${F}_{min}=0.36$, ${F}_{max}=0.75$, ${K}_{min}=0.20$, ${K}_{max}=0.85$, $Pg=0.05$, $Tc=430$, $Rg=5$, $cp=10$  
PF  ${F}_{min}=0.53$, ${F}_{max}=0.89$, ${K}_{min}=0.34$, ${K}_{max}=0.98$  
DECR1B  DEB  $CR=0.92$, ${F}_{min}=0.41$, ${F}_{max}=0.76$, ${K}_{min}=0.95$, ${K}_{max}=0.95$ 
SR  $CR=0.96$, ${F}_{min}=0.46$, ${F}_{max}=0.89$, ${K}_{min}=0.46$, ${K}_{max}=0.72$, $Pf=0.12$  
$\u03f5$ C  $CR=0.97$, ${F}_{min}=0.11$, ${F}_{max}=0.99$, ${K}_{min}=0.56$, ${K}_{max}=0.56$, $Pg=0.08$, $Tc=700$, $Rg=2$, $cp=7$  
PF  $CR=0.92$, ${F}_{min}=0.33$, ${F}_{max}=0.84$, ${K}_{min}=0.96$, ${K}_{max}=0.97$  
DECR1E  DEB  $CR=0.92$, ${F}_{min}=0.32$, ${F}_{max}=0.72$, ${K}_{min}=0.29$, ${K}_{max}=0.77$ 
SR  $CR=0.95$, ${F}_{min}=0.06$, ${F}_{max}=0.99$, ${K}_{min}=0.08$, ${K}_{max}=0.26$, $Pf=0.01$  
$\u03f5$ C  $CR=0.96$, ${F}_{min}=0.08$, ${F}_{max}=0.94$, ${K}_{min}=0.42$, ${K}_{max}=0.87$, $Pg=0.06$, $Tc=740$, $Rg=3$, $cp=9$  
PF  $CR=0.39$, ${F}_{min}=0.44$, ${F}_{max}=0.51$, ${K}_{min}=0.46$, ${K}_{max}=0.65$  
GA  DEB  $CR=0.80$, $MR=0.06$ 
SR  $CR=0.23$, $Pf=0.20$, $MR=0.05$  
$\u03f5$ C  $CR=1$, $Pg=0.05$, $Tc=610$, $Rg=4$, $cp=8$, $MR=0.08$  
PF  $CR=0.83$, $MR=0.11$  
PSO  DEB  ${v}_{max}=0.01$, $C1=1.29$, $C2=2.04$ 
SR  $Pf=0.69$, ${v}_{max}=0.01$, $C1=2.22$, $C2=1.06$  
$\u03f5$ C  $Pg=0.05$, $Tc=610$, $Rg=4$, $cp=8$, ${v}_{max}=0.01$, $C1=1.10$, $C2=1.79$  
PF  ${v}_{min}=0.05$, ${v}_{max}=0.17$, $C1=2.04$, $C2=1.06$ 
Appendix B.2. Parameter Tuning of Case 2: CamLinkage Mechanism
Algorithm  CHT  Parameters 

DER1B  DEB  $CR=0.87$, ${F}_{min}=0.51$, ${F}_{max}=0.53$ 
SR  $CR=0.91$, ${F}_{min}=0.46$, ${F}_{max}=0.70$, $Pf=0.52$  
$\u03f5$ C  $CR=0.92$, ${F}_{min}=0.53$, ${F}_{max}=0.56$, $Pg=0.04$, $Tc=430$, $Rg=5$, $cp=9$  
PF  $CR=0.93$, ${F}_{min}=0.52$, ${F}_{max}=0.63$  
DER1E  DEB  $CR=0.94$, ${F}_{min}=0.47$, ${F}_{max}=0.58$ 
SR  $CR=0.98$, ${F}_{min}=0.56$, ${F}_{max}=0.75$, $Pf=0.50$  
$\u03f5$ C  $CR=0.99$, ${F}_{min}=0.51$, ${F}_{max}=0.66$, $Pg=0.09$, $Tc=230$, $Rg=5$, $cp=6$  
PF  $CR=0.88$, ${F}_{min}=0.25$, ${F}_{max}=0.43$  
DEB1B  DEB  $CR=0.88$, ${F}_{min}=0.80$, ${F}_{max}=0.87$ 
SR  $CR=0.99$, ${F}_{min}=0.62$, ${F}_{max}=0.75$, $Pf=0.49$  
$\u03f5$ C  $CR=0.92$, ${F}_{min}=0.59$, ${F}_{max}=0.61$, $Pg=0.05$, $Tc=380$, $Rg=2$, $cp=8$  
PF  $CR=0.90$, ${F}_{min}=0.63$, ${F}_{max}=0.87$  
DEB1E  DEB  $CR=0.83$, ${F}_{min}=0.11$, ${F}_{max}=0.98$ 
SR  $CR=0.95$, ${F}_{min}=0.65$, ${F}_{max}=0.70$, $Pf=0.50$  
$\u03f5$ C  $CR=0.92$, ${F}_{min}=0.55$, ${F}_{max}=0.61$, $Pg=0.06$, $Tc=370$, $Rg=2$, $cp=8$  
PF  $CR=0.92$, ${F}_{min}=0.65$, ${F}_{max}=0.73$  
DECR  DEB  ${F}_{min}=0.68$, ${F}_{max}=0.79$, ${K}_{min}=0.85$, ${K}_{max}=0.92$ 
SR  ${F}_{min}=0.61$, ${F}_{max}=0.68$, ${K}_{min}=0.31$, ${K}_{max}=0.35$, $Pf=0.50$  
$\u03f5$ C  ${F}_{min}=0.52$, ${F}_{max}=0.62$, ${K}_{min}=0.27$, ${K}_{max}=0.38$, $Pg=0.06$, $Tc=520$, $Rg=2$, $cp=6$  
PF  ${F}_{min}=0.24$, ${F}_{max}=0.90$, ${K}_{min}=0.93$, ${K}_{max}=0.95$  
DECB  DEB  ${F}_{min}=0.74$, ${F}_{max}=0.78$, ${K}_{min}=0.55$, ${K}_{max}=0.78$ 
SR  ${F}_{min}=0.49$, ${F}_{max}=0.66$, ${K}_{min}=0.24$, ${K}_{max}=0.58$, $Pf=0.51$  
$\u03f5$ C  ${F}_{min}=0.51$, ${F}_{max}=0.63$, ${K}_{min}=0.05$, ${K}_{max}=0.45$, $Pg=0.09$, $Tc=340$, $Rg=2$, $cp=6$  
PF  ${F}_{min}=0.49$, ${F}_{max}=0.78$, ${K}_{min}=0.34$, ${K}_{max}=0.53$  
DECR1B  DEB  $CR=0.97$, ${F}_{min}=0.37$, ${F}_{max}=0.73$, ${K}_{min}=0.77$, ${K}_{max}=0.98$ 
SR  $CR=0.98$, ${F}_{min}=0.51$, ${F}_{max}=0.82$, ${K}_{min}=0.10$, ${K}_{max}=0.13$, $Pf=0.45$  
$\u03f5$ C  $CR=0.97$, ${F}_{min}=0.55$, ${F}_{max}=0.64$, ${K}_{min}=0.05$, ${K}_{max}=0.67$, $Pg=0.06$, $Tc=420$, $Rg=4$, $cp=6$  
PF  $CR=0.93$, ${F}_{min}=0.55$, ${F}_{max}=0.63$, ${K}_{min}=0.84$, ${K}_{max}=0.93$  
DECR1E  DEB  $CR=0.99$, ${F}_{min}=0.47$, ${F}_{max}=0.75$, ${K}_{min}=0.84$, ${K}_{max}=0.86$ 
SR  $CR=0.92$, ${F}_{min}=0.58$, ${F}_{max}=0.68$, ${K}_{min}=0.25$, ${K}_{max}=0.65$, $Pf=0.49$  
$\u03f5$ C  $CR=0.94$, ${F}_{min}=0.54$, ${F}_{max}=0.67$, ${K}_{min}=0.08$, ${K}_{max}=0.61$, $Pg=0.09$, $Tc=720$, $Rg=5$, $cp=6$  
PF  $CR=1.00$, ${F}_{min}=0.38$, ${F}_{max}=0.74$, ${K}_{min}=0.70$, ${K}_{max}=1.00$  
GA  DEB  $CR=0.98$, $MR=0.11$ 
SR  $CR=0.57$, $Pf=0.12$, $MR=0.17$  
$\u03f5$ C  $CR=1$, $Pg=0.08$, $Tc=640$, $Rg=4$, $cp=6$, $MR=0.14$  
PF  $CR=0.38$, $MR=0.29$  
PSO  DEB  ${v}_{min}=0.05$, ${v}_{max}=0.24$, $C1=0.29$, $C2=3.12$ 
SR  $Pf=0.48$, ${v}_{min}=0.04$, ${v}_{max}=0.23$, $C1=1.60$, $C2=1.07$  
$\u03f5$ C  $Pg=0.06$, $Tc=600$, $Rg=2$, $cp=2$, ${v}_{min}=0.04$, ${v}_{max}=0.26$, $C1=1.90$, $C2=0.86$  
PF  ${v}_{min}=0.12$, ${v}_{max}=0.34$, $C1=2.47$, $C2=0.34$ 
Appendix B.3. Parameter Tuning of Study Case 3: EightBar Linkage Mechanism
Algorithm  CHT  Parameters 

DER1B  DEB  $CR=0.84$, ${F}_{min}=0.20$, ${F}_{max}=0.65$ 
SR  $CR=0.48$, ${F}_{min}=0.33$, ${F}_{max}=0.80$, $Pf=0.15$  
$\u03f5$ C  $CR=0.35$, ${F}_{min}=0.02$, ${F}_{max}=0.15$, $Pg=0.02$, $Tc=340$, $Rg=3$, $cp=3$  
PF  $CR=0.02$, ${F}_{min}=0.53$, ${F}_{max}=0.76$, $Pg=0.05$, $Rg=2$  
DER1E  DEB  $CR=0.88$, ${F}_{min}=0.08$, ${F}_{max}=0.23$ 
SR  $CR=0.40$, ${F}_{min}=0.36$, ${F}_{max}=0.86$, $Pf=0.15$  
$\u03f5$ C  $CR=0.51$, ${F}_{min}=0.04$, ${F}_{max}=0.24$, $Pg=0.01$, $Tc=510$, $Rg=3$, $cp=7$  
PF  $CR=0.85$, ${F}_{min}=0.43$, ${F}_{max}=0.61$, $Pg=0.06$, $Rg=2$  
DEB1B  DEB  $CR=0.51$, ${F}_{min}=0.09$, ${F}_{max}=0.95$ 
SR  $CR=0.45$, ${F}_{min}=0.16$, ${F}_{max}=0.93$, $Pf=0.15$  
$\u03f5$ C  $CR=0.33$, ${F}_{max}=0.21$, $Pg=0.08$, $Tc=370$, $Rg=4$, $cp=10$  
PF  $CR=0.87$, ${F}_{min}=0.04$, ${F}_{max}=0.34$, $Pg=0.07$, $Rg=1$  
DEB1E  DEB  $CR=0.98$, ${F}_{min}=0.09$, ${F}_{max}=1$ 
SR  $CR=0.43$, ${F}_{min}=0.45$, ${F}_{max}=0.75$, $Pf=0.30$  
$\u03f5$ C  $CR=0.29$, ${F}_{min}=0.03$, ${F}_{max}=0.20$, $Pg=0.04$, $Tc=490$, $Rg=5$, $cp=3$  
PF  $CR=0.78$, ${F}_{min}=0.21$, ${F}_{max}=0.77$, $Pg=0.04$, $Rg=4$  
DECR  DEB  ${F}_{min}=0.21$, ${F}_{max}=0.98$, ${K}_{min}=0.71$, ${K}_{max}=0.98$ 
SR  ${F}_{min}=0.12$, ${F}_{max}=0.85$, ${K}_{min}=0.23$, ${K}_{max}=0.32$, $Pf=0.19$  
$\u03f5$ C  ${F}_{min}=0.07$, ${F}_{max}=0.41$, ${K}_{min}=0.53$, ${K}_{max}=0.64$, $Pg=0.04$, $Tc=310$, $Rg=4$, $cp=7$  
PF  ${F}_{min}=0.53$, ${F}_{max}=0.99$, ${K}_{min}=0.50$, ${K}_{max}=0.64$, $Pg=0.05$, $Rg=3$  
DECB  DEB  ${F}_{min}=0.20$, ${F}_{max}=0.93$, ${K}_{min}=0.01$, ${K}_{max}=0.91$ 
SR  ${F}_{min}=0.10$, ${F}_{max}=0.84$, ${K}_{min}=0.33$, ${K}_{max}=0.71$, $Pf=0.16$  
$\u03f5$ C  ${F}_{min}=0.11$, ${F}_{max}=0.35$, ${K}_{min}=0.11$, ${K}_{max}=0.98$, $Pg=0.02$, $Tc=500$, $Rg=2$, $cp=2$  
PF  ${F}_{min}=0.18$, ${F}_{max}=0.30$, ${K}_{min}=0.57$, ${K}_{max}=0.73$, $Pg=0.06$, $Rg=2$  
DECR1B  DEB  $CR=0.06$, ${F}_{max}=0.71$, ${K}_{min}=0.81$, ${K}_{max}=0.99$ 
SR  $CR=0.41$, ${F}_{min}=0.23$, ${F}_{max}=0.94$, ${K}_{min}=0.30$, ${K}_{max}=0.82$, $Pf=0.19$  
$\u03f5$ C  $CR=0.35$, ${F}_{min}=0.05$, ${F}_{max}=0.15$, ${K}_{min}=0.17$, ${K}_{max}=0.17$, $Pg=0.04$, $Tc=290$, $Rg=5$, $cp=10$  
PF  $CR=0.52$, ${F}_{min}=0.01$, ${F}_{max}=0.28$, ${K}_{min}=0.44$, ${K}_{max}=0.54$, $Pg=0.04$, $Rg=3$  
DECR1E  DEB  $CR=0.75$, ${F}_{min}=0.12$, ${F}_{max}=0.13$, ${K}_{min}=0.84$, ${K}_{max}=1$ 
SR  $CR=0.55$, ${F}_{min}=0.20$, ${F}_{max}=0.78$, ${K}_{min}=0.53$, ${K}_{max}=0.84$, $Pf=0.17$  
$\u03f5$ C  $CR=0.34$, ${F}_{min}=0.07$, ${F}_{max}=0.11$, ${K}_{min}=0.36$, ${K}_{max}=0.42$, $Pg=0.04$, $Tc=720$, $Rg=4$, $cp=5$  
PF  $CR=0.68$, ${F}_{min}=0.05$, ${F}_{max}=0.53$, ${K}_{min}=0.54$, ${K}_{max}=0.90$, $Pg=0.09$, $Rg=3$  
GA  DEB  $CR=0.97$, $MR=0.01$ 
SR  $CR=0.34$, $MR=0.02$  
$\u03f5$ C  $CR=0.94$, $Pg=0.08$, $Tc=350$, $Rg=2$, $cp=4$, $MR=0.01$  
PF  $CR=0.27$, $MR=0.03$  
PSO  DEB  ${v}_{min}=0.00$, ${v}_{max}=0.01$, $C1=0.80$, $C2=2.21$ 
SR  $Pf=0.30$, ${v}_{min}=0.00$, ${v}_{max}=0.08$, $C1=1.40$, $C2=2.04$  
$\u03f5$ C  $Pg=0.08$, $Tc=3773$, $Rg=4$, $cp=8$, ${v}_{min}=0.00$, ${v}_{max}=0.17$, $C1=2.20$, $C2=0.84$  
PF  $Pg=0.01$, $Rg=1$, ${v}_{min}=0.20$, ${v}_{max}=0.23$, $C1=1.66$, $C2=1.25$ 
Appendix C. Descriptive Statistics of the Overall Performance
Appendix C.1. Descriptive Statistics for the Case 1: FourBar Linkage Mechanism
CHT  Algorithm  Mean  std  Median  Minimum  Maximum 

FR  DER1B  $0.01296$  $0.005642$  $0.01244$  $0.003271$  $0.02423$ 
FR  DER1E  $0.01298$  $0.006134$  $0.0123$  $0.003282$  $0.02401$ 
FR  DEB1B  $0.03273$  $0.009165$  $0.03411$  $0.01517$  $0.05649$ 
FR  DEB1E  $\mathbf{0}.\mathbf{01037}$  $0.005054$  $\mathbf{0}.\mathbf{009278}$  $0.003184$  $\mathbf{0}.\mathbf{02038}$ 
FR  CR  $0.03024$  $0.03444$  $0.01922$  $\mathbf{0}.\mathbf{002098}$  $0.1306$ 
FR  DECB  $0.02672$  $0.01009$  $0.03212$  $0.004001$  $0.04514$ 
FR  DECR1B  $0.02253$  $0.006748$  $0.02359$  $0.0119$  $0.03175$ 
FR  DECR1E  $0.0156$  $0.004565$  $0.01666$  $0.007841$  $0.02277$ 
FR  GA  $0.03255$  $0.01192$  $0.03667$  $0.007953$  $0.05098$ 
FR  PSO  $0.03674$  $0.01234$  $0.03682$  $0.006861$  $0.0626$ 
SR  DER1B  $0.04564$  $0.01582$  $0.04094$  $0.0148$  $0.09932$ 
SR  DER1E  $7.262$  $13.89$  $0.04702$  $0.02393$  $44.38$ 
SR  DEB1B  $0.5216$  $1.512$  $0.04276$  $0.01174$  $7.343$ 
SR  DEB1E  $0.7596$  $1.715$  $0.1027$  $0.02227$  $6.513$ 
SR  CR  $87.61$  $91.56$  $60.56$  $0.03306$  $301.4$ 
SR  DECB  $0.4961$  $0.1162$  $0.5248$  $0.235$  $0.6868$ 
SR  DECR1B  $51.32$  $184.1$  $0.1216$  $0.03939$  1004 
SR  DECR1E  $0.02671$  $0.01325$  $0.02941$  $0.003726$  $0.04865$ 
SR  GA  $0.2966$  $0.02964$  $0.2934$  $0.256$  $0.3475$ 
SR  PSO  $0.1187$  $0.09226$  $0.07567$  $0.05316$  $0.4158$ 
$\u03f5$ C  DER1B  $0.02942$  $0.007475$  $0.03029$  $0.005715$  $0.03749$ 
$\u03f5$ C  DER1E  $0.01729$  $0.01095$  $0.01764$  $0.002085$  $0.03321$ 
$\u03f5$ C  DEB1B  $0.04082$  $0.01317$  $0.04182$  $0.01743$  $0.05896$ 
$\u03f5$ C  DEB1E  $0.0286$  $0.01351$  $0.02925$  $0.004001$  $0.05625$ 
$\u03f5$ C  CR  $0.03108$  $0.006818$  $0.03157$  $0.01884$  $0.0462$ 
$\u03f5$ C  DECB  $0.03389$  $0.01216$  $0.03374$  $0.01447$  $0.06199$ 
$\u03f5$ C  DECR1B  $0.03121$  $0.007929$  $0.03368$  $0.01265$  $0.04719$ 
$\u03f5$ C  DECR1E  $0.0315$  $0.006558$  $0.03454$  $0.01178$  $0.03626$ 
$\u03f5$ C  GA  $0.03387$  $0.01013$  $0.03524$  $0.00771$  $0.04701$ 
$\u03f5$ C  PSO  $0.03464$  $0.009985$  $0.03127$  $0.01969$  $0.05899$ 
PF  DER1B  $0.02611$  $0.005129$  $0.02606$  $0.01551$  $0.03761$ 
PF  DER1E  $0.01265$  $0.004983$  $0.01281$  $0.003099$  $0.02219$ 
PF  DEB1B  $0.02822$  $0.0111$  $0.02901$  $0.008141$  $0.06079$ 
PF  DEB1E  $0.03803$  $0.01028$  $0.03771$  $0.01184$  $0.05553$ 
PF  CR  $0.02607$  $0.01001$  $0.0293$  $0.005715$  $0.03949$ 
PF  DECB  $0.01989$  $0.01117$  $0.01766$  $0.004001$  $0.03941$ 
PF  DECR1B  $0.03768$  $\mathbf{0}.\mathbf{001529}$  $0.03785$  $0.0353$  $0.04146$ 
PF  DECR1E  $0.01371$  $0.00562$  $0.01297$  $0.005481$  $0.025$ 
PF  GA  $0.2107$  $0.02938$  $0.2136$  $0.1417$  $0.2513$ 
PF  PSO  $0.03619$  $0.01384$  $0.03593$  $0.01575$  $0.06243$ 
Appendix C.2. Descriptive Statistics for Study Case 2: CamLinkage Mechanism
CHT  Algorithm  Mean  std  Median  Minimum  Maximum 

FR  DER1B  $0.7253$  $0.09932$  $0.673$  $0.6597$  $0.9351$ 
FR  DER1E  $0.7259$  $0.08588$  $0.6727$  $0.6613$  $0.8963$ 
FR  DEB1B  $2.45$  $2.111$  $1.006$  $\mathbf{0}.\mathbf{6557}$  $6.614$ 
FR  DEB1E  $1.497$  $1.024$  $1.11$  $0.7351$  $5.727$ 
FR  CR  $0.7242$  $0.0778$  $0.6811$  $0.6729$  $0.9079$ 
FR  DECB  $1.552$  $1.611$  $0.8419$  $0.6701$  $5.734$ 
FR  DECR1B  $0.8583$  $0.4566$  $0.6928$  $0.6648$  $3.206$ 
FR  DECR1E  $0.8033$  $0.3489$  $0.6752$  $0.6634$  $2.594$ 
FR  GA  $7.932$  $5.341$  $7.413$  $1.713$  $22.22$ 
FR  PSO  $4.023$  $2.485$  $3.088$  $1.701$  $10.51$ 
SR  DER1B  $3.98\times {10}^{6}$  $1.217\times {10}^{7}$  $0.7733$  $0.6758$  $4.334\times {10}^{7}$ 
SR  DER1E  $0.9158$  $0.8067$  $0.678$  $0.6561$  $4.822$ 
SR  DEB1B  $4.475$  $6.158$  $2.524$  $0.7182$  $29.66$ 
SR  DEB1E  $4.578$  $3.676$  $3.113$  $0.9298$  $14.62$ 
SR  CR  $0.7209$  $0.07337$  $0.6729$  $0.6592$  $\mathbf{0}.\mathbf{8956}$ 
SR  DECB  $2.318$  $2.059$  $1.168$  $0.7212$  $8.189$ 
SR  DECR1B  $\mathbf{0}.\mathbf{6932}$  $\mathbf{0}.\mathbf{06188}$  $0.6745$  $0.6676$  $0.9003$ 
SR  DECR1E  $2.247$  $0.5756$  $2.305$  $1.286$  $3.097$ 
SR  GA  $4.043$  $2.889$  $2.61$  $1.852$  $13.68$ 
SR  PSO  $7.455$  $8.686$  $3.739$  $1.501$  $33.68$ 
$\u03f5$ C  DER1B  $1.783$  $0.5594$  $1.602$  $0.8771$  $3.155$ 
$\u03f5$ C  DER1E  $2.423$  $0.5487$  $2.443$  $1.396$  $4.675$ 
$\u03f5$ C  DEB1B  $2.914$  $1.678$  $2.723$  $0.887$  $6.619$ 
$\u03f5$ C  DEB1E  $3.084$  $2.389$  $2.545$  $0.7588$  $10.64$ 
$\u03f5$ C  CR  $2.559$  $0.266$  $2.558$  $1.692$  $3.106$ 
$\u03f5$ C  DECB  $3.911$  $2.732$  $2.965$  $2.253$  $13.26$ 
$\u03f5$ C  DECR1B  $5.566$  $1.927$  $4.807$  $3.266$  $9.281$ 
$\u03f5$ C  DECR1E  $5.051$  $1.1$  $5.002$  $2.951$  $7.233$ 
$\u03f5$ C  GA  $5.01$  $2.443$  $3.715$  $2.38$  $10.7$ 
$\u03f5$ C  PSO  $2.773$  $0.8773$  $2.532$  $1.825$  $6.639$ 
PF  DER1B  $0.7117$  $0.07392$  $\mathbf{0}.\mathbf{669}$  $0.6656$  $0.8965$ 
PF  DER1E  $0.9899$  $0.182$  $0.9877$  $0.7517$  $1.539$ 
PF  DEB1B  $3.621$  $3.049$  $2.184$  $0.6752$  $10.26$ 
PF  DEB1E  $1.636$  $1.477$  $0.926$  $0.6808$  $5.991$ 
PF  CR  $0.7895$  $0.3857$  $0.6878$  $0.6799$  $2.788$ 
PF  DECB  $2.472$  $2.941$  $0.8362$  $0.6606$  $10.12$ 
PF  DECR1B  $0.7817$  $0.1013$  $0.8168$  $0.6697$  $0.9375$ 
PF  DECR1E  $0.8034$  $0.1227$  $0.774$  $0.6809$  $1.072$ 
PF  GA  $2.446$  $0.4424$  $2.301$  $2.088$  $3.758$ 
PF  PSO  $1.799$  $0.6056$  $1.621$  $1.028$  3 
Appendix C.3. Descriptive Statistics for the Case 3: EightBar Linkage Mechanism
CHT  Algorithm  Mean  std  Median  Minimum  Maximum 

FR  DER1B  $\mathbf{0}.\mathbf{001525}$  $\mathbf{0}.\mathbf{0004962}$  $0.001405$  $0.0007166$  $\mathbf{0}.\mathbf{002662}$ 
FR  DER1E  $0.002575$  $0.001006$  $0.002563$  $0.0007069$  $0.005309$ 
FR  DEB1B  $0.00315$  $0.001883$  $0.002815$  $0.0005762$  $0.0107$ 
FR  DEB1E  $0.002491$  $0.001148$  $0.002239$  $0.0009604$  $0.004837$ 
FR  CR  $0.01321$  $0.009235$  $0.01462$  $0.0001903$  $0.02864$ 
FR  DECB  $8.333\times {10}^{15}$  $3.79\times {10}^{15}$  $1\times {10}^{16}$  $0.1895$  $1\times {10}^{16}$ 
FR  DECR1B  $0.00966$  $0.001957$  $0.009238$  $0.0066$  $0.01404$ 
FR  DECR1E  $3.333\times {10}^{14}$  $1.826\times {10}^{15}$  $0.02744$  $0.01085$  $1\times {10}^{16}$ 
FR  GA  $0.01943$  $0.01749$  $0.01586$  $0.002204$  $0.0732$ 
FR  PSO  $1.333\times {10}^{15}$  $3.457\times {10}^{15}$  $0.2493$  $0.09734$  $1\times {10}^{16}$ 
SR  DER1B  $6\times {10}^{15}$  $4.983\times {10}^{15}$  $1\times {10}^{16}$  $0.5789$  $1\times {10}^{16}$ 
SR  DER1E  $1\times {10}^{16}$  2454  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
SR  DEB1B  $0.06065$  $0.04348$  $0.03995$  $0.01126$  $0.1604$ 
SR  DEB1E  $1\times {10}^{16}$  2506  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
SR  CR  $0.0136$  $0.008586$  $0.01399$  $\mathbf{0}.\mathbf{0001884}$  $0.02977$ 
SR  DECB  $1\times {10}^{16}$  $833.3$  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
SR  DECR1B  $0.02013$  $0.0101$  $0.02329$  $0.0006199$  $0.03406$ 
SR  DECR1E  $1\times {10}^{16}$  1598  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
SR  GA  $0.01858$  $0.01994$  $0.01138$  $0.001002$  $0.07766$ 
SR  PSO  $1\times {10}^{15}$  $3.051\times {10}^{15}$  $0.107$  $0.03381$  $1\times {10}^{16}$ 
$\u03f5$ C  DER1B  $0.01442$  $0.009972$  $0.0153$  $0.0005622$  $0.03068$ 
$\u03f5$ C  DER1E  $0.003982$  $0.001845$  $0.003714$  $0.001142$  $0.009192$ 
$\u03f5$ C  DEB1B  $2.333\times {10}^{15}$  $4.302\times {10}^{15}$  $0.0382$  $0.00842$  $1\times {10}^{16}$ 
$\u03f5$ C  DEB1E  $0.005852$  $0.00337$  $0.006034$  $0.001077$  $0.01249$ 
$\u03f5$ C  CR  $0.01856$  $0.009206$  $0.02236$  $0.0006742$  $0.03008$ 
$\u03f5$ C  DECB  $0.02113$  $0.006483$  $0.02121$  $0.006247$  $0.02996$ 
$\u03f5$ C  DECR1B  $0.0139$  $0.007828$  $0.01407$  $0.0004182$  $0.0269$ 
$\u03f5$ C  DECR1E  $0.008319$  $0.003387$  $0.008318$  $0.003046$  $0.01597$ 
$\u03f5$ C  GA  $0.03706$  $0.0432$  $0.02497$  $0.00161$  $0.2009$ 
$\u03f5$ C  PSO  $0.03373$  $0.009459$  $0.03339$  $0.01327$  $0.05506$ 
PF  DER1B  $0.002417$  $0.002739$  $\mathbf{0}.\mathbf{001362}$  $0.0006484$  $0.01144$ 
PF  DER1E  $0.002131$  $0.0008177$  $0.001843$  $0.001185$  $0.004332$ 
PF  DEB1B  $0.005953$  $0.004698$  $0.003834$  $0.001046$  $0.01781$ 
PF  DEB1E  $0.005379$  $0.002734$  $0.005059$  $0.001756$  $0.01551$ 
PF  CR  $0.04953$  $0.02291$  $0.04997$  $0.0015$  $0.1098$ 
PF  DECB  $1\times {10}^{16}$  1172  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
PF  DECR1B  $0.03493$  $0.004417$  $0.03614$  $0.02261$  $0.04204$ 
PF  DECR1E  $1\times {10}^{16}$  $451.7$  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
PF  GA  $1\times {10}^{16}$  $105.7$  $1\times {10}^{16}$  $1\times {10}^{16}$  $1\times {10}^{16}$ 
PF  PSO  $0.04157$  $0.01425$  $0.03784$  $0.01316$  $0.0727$ 
Appendix D. Inferential Statistics of the Overall Performance
Appendix D.1. Ranks Achieved by the Friedman Test
Ranks  

Algorithm  CHT  Study Case 1  Study Case 2  Study Case 3 
DER1B  FR  $1.1$  $1.7$  $1.6$ 
DER1B  SR  $3.8$  $2.8$  4 
DER1B  $\u03f5$ C  $2.8$  $3.8$  $2.7$ 
DER1B  PF  $2.3$  $1.6$  $1.7$ 
Statistic  67  59  66  
pvalue  $2.24\times {10}^{14}$  $9.43\times {10}^{13}$  $2.83\times {10}^{14}$  
DER1E  FR  $1.9$  $1.5$  $1.9$ 
DER1E  SR  4  $1.7$  4 
DER1E  $\u03f5$ C  $2.3$  $3.9$  $2.6$ 
DER1E  PF  $1.9$  $2.9$  $1.5$ 
Statistic  53  71  64  
pvalue  $1.51\times {10}^{11}$  $3.18\times {10}^{15}$  $6.87\times {10}^{14}$  
DEB1B  FR  $2.2$  2  $1.3$ 
DEB1B  SR  $3.2$  $2.5$  $3.5$ 
DEB1B  $\u03f5$ C  3  $2.9$  $3.5$ 
DEB1B  PF  $1.6$  $2.6$  $1.7$ 
Statistic  29  $6.5$  73  
pvalue  $2.67\times {10}^{6}$  $8.89\times {10}^{2}$  $7.82\times {10}^{16}$  
DEB1E  FR  $1.2$  $1.8$  $1.3$ 
DEB1E  SR  $3.8$  $3.5$  4 
DEB1E  $\u03f5$ C  $2.1$  3  $2.4$ 
DEB1E  PF  $2.9$  $1.7$  $2.3$ 
Statistic  71  39  69  
pvalue  $2.93\times {10}^{15}$  $1.48\times {10}^{8}$  $8.18\times {10}^{15}$  
DECR  FR  $1.6$  2  2 
DECR  SR  $3.9$  $1.6$  $1.9$ 
DECR  $\u03f5$ C  $2.5$  4  $2.4$ 
DECR  PF  2  $2.4$  $3.7$ 
Statistic  56  57  35  
pvalue  $5.01\times {10}^{12}$  $2.67\times {10}^{12}$  $1.24\times {10}^{7}$  
DECB  FR  $1.9$  $1.8$  $2.3$ 
DECB  SR  4  $2.6$  $3.1$ 
DECB  $\u03f5$ C  $2.5$  $3.4$  1 
DECB  PF  $1.6$  $2.3$  $3.6$ 
Statistic  61  24  69  
pvalue  $3.81\times {10}^{13}$  $2.10\times {10}^{5}$  $5.52\times {10}^{15}$  
DER1B  FR  $1.2$  $2.5$  $1.5$ 
DER1B  SR  4  $1.3$  $2.5$ 
DER1B  $\u03f5$ C  2  4  $2.1$ 
DER1B  PF  $2.9$  $2.3$  $3.9$ 
Statistic  80  69  58  
pvalue  $3.01\times {10}^{17}$  $7.41\times {10}^{15}$  $1.67\times {10}^{12}$  
DER1E  FR  $2.1$  $1.3$  2 
DER1E  SR  $2.9$  3  4 
DER1E  $\u03f5$ C  $3.5$  4  1 
DER1E  PF  $1.5$  $1.7$  3 
Statistic  42  80  88  
pvalue  $4.34\times {10}^{9}$  $2.47\times {10}^{17}$  $7.04\times {10}^{19}$  
GA  FR  $1.6$  $3.3$  $1.8$ 
GA  SR  4  $2.2$  $1.8$ 
GA  $\u03f5$ C  $1.4$  $3.1$  $2.4$ 
GA  PF  3  $1.4$  4 
Statistic  81  42  58  
pvalue  $1.73\times {10}^{17}$  $4.69\times {10}^{09}$  $1.88\times {10}^{12}$  
PSO  FR  $2.1$  $2.9$  $3.8$ 
PSO  SR  4  $3.2$  3 
PSO  $\u03f5$ C  $1.9$  $2.5$  $1.3$ 
PSO  PF  2  $1.4$  $1.8$ 
Statistic  52  33  68  
pvalue  $2.82\times {10}^{11}$  $2.98\times {10}^{7}$  $1.12\times {10}^{14}$ 
Appendix D.2. Multiple Comparison Friedman Test
Hypotesis  Study Case 1  Study Case 2  Study Case 3  

Alg. A + CHT vs. Alg B + CHT  pValue  z  Win  pValue  z  Win  pValue  z  Win 
DER1B FR vs. DER1B SR  $\mathbf{7}.\mathbf{99}\times {\mathbf{10}}^{\mathbf{15}}$  −8  A  $\mathbf{2}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{03}}$  −3.4  A  $\mathbf{3}.\mathbf{61}\times {\mathbf{10}}^{\mathbf{12}}$  −7.2  A 
DER1B FR vs. DER1B EC  $\mathbf{2}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{06}}$  −5  A  $\mathbf{7}.\mathbf{77}\times {\mathbf{10}}^{\mathbf{10}}$  −6.4  A  $\mathbf{4}.\mathbf{12}\times {\mathbf{10}}^{\mathbf{03}}$  −3.2  A 
DER1B FR vs. DER1B PF  $\mathbf{2}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{03}}$  −3.4  A  $8.41\times {10}^{01}$  0.2  −  $6.89\times {10}^{01}$  −0.4  − 
DER1B SR vs. DER1B EC  $\mathbf{5}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{03}}$  3  B  $\mathbf{5}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{03}}$  −3  A  $\mathbf{2}.\mathbf{53}\times {\mathbf{10}}^{\mathbf{04}}$  4  B 
DER1B SR vs. DER1B PF  $\mathbf{1}.\mathbf{69}\times {\mathbf{10}}^{\mathbf{05}}$  4.6  B  $\mathbf{1}.\mathbf{27}\times {\mathbf{10}}^{\mathbf{03}}$  3.6  B  $\mathbf{5}.\mathbf{23}\times {\mathbf{10}}^{\mathbf{11}}$  6.8  B 
DER1B EC vs. DER1B PF  $1.10\times {10}^{01}$  1.6  −  $\mathbf{2}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{10}}$  6.6  B  $\mathbf{1}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{02}}$  2.8  B 
DER1E FR vs. DER1E SR  $\mathbf{2}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{09}}$  −6.2  A  $4.84\times {10}^{01}$  −0.7  −  $\mathbf{2}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{09}}$  −6.2  A 
DER1E FR vs. DER1E EC  $6.90\times {10}^{01}$  −1.1  −  $\mathbf{8}.\mathbf{17}\times {\mathbf{10}}^{\mathbf{13}}$  −7.4  A  $1.15\times {10}^{01}$  −1.9  − 
DER1E FR vs. DER1E PF  $9.20\times {10}^{01}$  0.1  −  $\mathbf{6}.\mathbf{83}\times {\mathbf{10}}^{\mathbf{05}}$  −4.3  A  $1.94\times {10}^{01}$  1.3  − 
DER1E SR vs. DER1E EC  $\mathbf{1}.\mathbf{36}\times {\mathbf{10}}^{\mathbf{06}}$  5.1  B  $\mathbf{1}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{10}}$  −6.7  A  $\mathbf{6}.\mathbf{83}\times {\mathbf{10}}^{\mathbf{05}}$  4.3  B 
DER1E SR vs. DER1E PF  $\mathbf{1}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{09}}$  6.3  B  $\mathbf{9}.\mathbf{55}\times {\mathbf{10}}^{\mathbf{04}}$  −3.6  A  $\mathbf{3}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{13}}$  7.5  B 
DER1E EC vs. DER1E PF  $6.90\times {10}^{01}$  1.2  −  $\mathbf{3}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{03}}$  3.1  B  $\mathbf{4}.\mathbf{12}\times {\mathbf{10}}^{\mathbf{03}}$  3.2  B 
DEB1B FR vs. DEB1B SR  $\mathbf{1}.\mathbf{08}\times {\mathbf{10}}^{\mathbf{02}}$  −3  A  $6.46\times {10}^{01}$  −1.4  −  $\mathbf{2}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{10}}$  −6.6  A 
DEB1B FR vs. DEB1B EC  $\mathbf{2}.\mathbf{80}\times {\mathbf{10}}^{\mathbf{02}}$  −2.6  A  $7.45\times {10}^{02}$  −2.5  −  $\mathbf{2}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{10}}$  −6.6  A 
DEB1B FR vs. DEB1B PF  $2.19\times {10}^{01}$  1.6  −  $4.46\times {10}^{01}$  −1.7  −  $4.60\times {10}^{01}$  −1.2  − 
DEB1B SR vs. DEB1B EC  $6.89\times {10}^{01}$  0.4  −  $8.14\times {10}^{01}$  −1.1  −  1  0  − 
DEB1B SR vs. DEB1B PF  $\mathbf{2}.\mathbf{53}\times {\mathbf{10}}^{\mathbf{05}}$  4.6  B  $8.47\times {10}^{01}$  −0.3  −  $\mathbf{2}.\mathbf{67}\times {\mathbf{10}}^{\mathbf{07}}$  5.4  B 
DEB1B EC vs. DEB1B PF  $\mathbf{1}.\mathbf{33}\times {\mathbf{10}}^{\mathbf{04}}$  4.2  B  $8.47\times {10}^{01}$  0.8  −  $\mathbf{2}.\mathbf{67}\times {\mathbf{10}}^{\mathbf{07}}$  5.4  B 
DEB1E FR vs. DEB1E SR  $\mathbf{7}.\mathbf{99}\times {\mathbf{10}}^{\mathbf{15}}$  −8  A  $\mathbf{4}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{06}}$  −4.9  A  $\mathbf{1}.\mathbf{33}\times {\mathbf{10}}^{\mathbf{15}}$  −8.2  A 
DEB1E FR vs. DEB1E EC  $\mathbf{2}.\mathbf{08}\times {\mathbf{10}}^{\mathbf{02}}$  −2.7  A  $\mathbf{2}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{03}}$  −3.4  A  $\mathbf{1}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{03}}$  −3.5  A 
DEB1E FR vs. DEB1E PF  $\mathbf{5}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{07}}$  −5.3  A  $7.64\times {10}^{01}$  0.3  −  $\mathbf{3}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{03}}$  −3.1  A 
DEB1E SR vs. DEB1E EC  $\mathbf{5}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{07}}$  5.3  B  $2.67\times {10}^{01}$  1.5  −  $\mathbf{1}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{05}}$  4.7  B 
DEB1E SR vs. DEB1E PF  $\mathbf{2}.\mathbf{08}\times {\mathbf{10}}^{\mathbf{02}}$  2.7  B  $\mathbf{1}.\mathbf{20}\times {\mathbf{10}}^{\mathbf{06}}$  5.2  B  $\mathbf{1}.\mathbf{70}\times {\mathbf{10}}^{\mathbf{06}}$  5.1  B 
DEB1E EC vs. DEB1E PF  $\mathbf{2}.\mathbf{08}\times {\mathbf{10}}^{\mathbf{02}}$  −2.6  A  $\mathbf{8}.\mathbf{62}\times {\mathbf{10}}^{\mathbf{04}}$  3.7  B  $6.89\times {10}^{01}$  0.4  − 
DECR FR vs. DECR SR  $\mathbf{3}.\mathbf{12}\times {\mathbf{10}}^{\mathbf{11}}$  −6.9  A  $4.60\times {10}^{01}$  1.1  −  $8.41\times {10}^{01}$  0.2  − 
DECR FR vs. DECR EC  $\mathbf{3}.\mathbf{73}\times {\mathbf{10}}^{\mathbf{02}}$  −2.5  A  $\mathbf{1}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{08}}$  −5.9  A  $4.85\times {10}^{01}$  −1.2  − 
DECR FR vs. DECR PF  $3.17\times {10}^{01}$  −1  −  $4.60\times {10}^{01}$  −1.2  −  $\mathbf{2}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{06}}$  −5  A 
DECR SR vs. DECR EC  $\mathbf{4}.\mathbf{33}\times {\mathbf{10}}^{\mathbf{05}}$  4.4  B  $\mathbf{1}.\mathbf{54}\times {\mathbf{10}}^{\mathbf{11}}$  −7  A  $4.85\times {10}^{01}$  −1.4  − 
DECR SR vs. DECR PF  $\mathbf{1}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{08}}$  5.9  B  $6.43\times {10}^{02}$  −2.3  −  $\mathbf{1}.\mathbf{20}\times {\mathbf{10}}^{\mathbf{06}}$  −5.2  A 
DECR EC vs. DECR PF  $2.67\times {10}^{01}$  1.5  −  $\mathbf{1}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{05}}$  4.7  B  $\mathbf{5}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{04}}$  −3.8  A 
DECB FR vs. DECB SR  $\mathbf{2}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{09}}$  −6.2  A  $\mathbf{4}.\mathbf{97}\times {\mathbf{10}}^{\mathbf{02}}$  −2.5  A  $\mathbf{3}.\mathbf{28}\times {\mathbf{10}}^{\mathbf{02}}$  −2.4  A 
DECB FR vs. DECB EC  $2.19\times {10}^{01}$  −1.6  −  $\mathbf{9}.\mathbf{52}\times {\mathbf{10}}^{\mathbf{06}}$  −4.8  A  $\mathbf{3}.\mathbf{85}\times {\mathbf{10}}^{\mathbf{04}}$  3.9  B 
DECB FR vs. DECB PF  $3.17\times {10}^{01}$  1  −  $2.67\times {10}^{01}$  −1.5  −  $\mathbf{3}.\mathbf{85}\times {\mathbf{10}}^{\mathbf{04}}$  −3.9  A 
DECB SR vs. DECB EC  $\mathbf{1}.\mathbf{69}\times {\mathbf{10}}^{\mathbf{05}}$  4.6  B  $6.43\times {10}^{02}$  −2.3  −  $\mathbf{1}.\mathbf{49}\times {\mathbf{10}}^{\mathbf{09}}$  6.3  B 
DECB SR vs. DECB PF  $\mathbf{3}.\mathbf{61}\times {\mathbf{10}}^{\mathbf{12}}$  7.2  B  $3.17\times {10}^{01}$  1  −  $1.34\times {10}^{01}$  −1.5  − 
DECB EC vs. DECB PF  $\mathbf{2}.\mathbf{80}\times {\mathbf{10}}^{\mathbf{02}}$  2.6  B  $\mathbf{4}.\mathbf{83}\times {\mathbf{10}}^{\mathbf{03}}$  3.3  B  $\mathbf{3}.\mathbf{73}\times {\mathbf{10}}^{\mathbf{14}}$  −7.8  A 
DECR1B FR vs. DECR1B SR  $\mathbf{0}$  −8.5  A  $\mathbf{9}.\mathbf{55}\times {\mathbf{10}}^{\mathbf{04}}$  3.6  B  $\mathbf{1}.\mathbf{12}\times {\mathbf{10}}^{\mathbf{02}}$  −2.9  A 
DECR1B FR vs. DECR1B EC  $\mathbf{1}.\mathbf{64}\times {\mathbf{10}}^{\mathbf{02}}$  −2.4  A  $\mathbf{1}.\mathbf{69}\times {\mathbf{10}}^{\mathbf{05}}$  −4.6  A  $1.44\times {10}^{01}$  −1.8  − 
DECR1B FR vs. DECR1B PF  $\mathbf{1}.\mathbf{36}\times {\mathbf{10}}^{\mathbf{06}}$  −5.1  A  $5.49\times {10}^{01}$  0.6  −  $\mathbf{1}.\mathbf{73}\times {\mathbf{10}}^{\mathbf{12}}$  −7.3  A 
DECR1B SR vs. DECR1B EC  $\mathbf{5}.\mathbf{30}\times {\mathbf{10}}^{\mathbf{09}}$  6.1  B  $\mathbf{1}.\mathbf{33}\times {\mathbf{10}}^{\mathbf{15}}$  −8.2  A  $2.71\times {10}^{01}$  1.1  − 
DECR1B SR vs. DECR1B PF  $\mathbf{2}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{03}}$  3.4  B  $\mathbf{5}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{03}}$  −3  A  $\mathbf{4}.\mathbf{33}\times {\mathbf{10}}^{\mathbf{05}}$  −4.4  A 
DECR1B EC vs. DECR1B PF  $\mathbf{1}.\mathbf{39}\times {\mathbf{10}}^{\mathbf{02}}$  −2.7  A  $\mathbf{9}.\mathbf{96}\times {\mathbf{10}}^{\mathbf{07}}$  5.2  B  $\mathbf{1}.\mathbf{90}\times {\mathbf{10}}^{\mathbf{07}}$  −5.5  A 
DECR1E FR vs. DECR1E SR  $\mathbf{4}.\mathbf{92}\times {\mathbf{10}}^{\mathbf{02}}$  −2.4  A  $\mathbf{3}.\mathbf{83}\times {\mathbf{10}}^{\mathbf{06}}$  −4.9  A  $\mathbf{9}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{09}}$  −6  A 
DECR1E FR vs. DECR1E EC  $\mathbf{5}.\mathbf{41}\times {\mathbf{10}}^{\mathbf{05}}$  −4.4  A  $\mathbf{7}.\mathbf{99}\times {\mathbf{10}}^{\mathbf{15}}$  −8  A  $\mathbf{7}.\mathbf{46}\times {\mathbf{10}}^{\mathbf{03}}$  2.9  B 
DECR1E FR vs. DECR1E PF  $1.10\times {10}^{01}$  1.6  −  $2.71\times {10}^{01}$  −1.1  −  $\mathbf{7}.\mathbf{46}\times {\mathbf{10}}^{\mathbf{03}}$  −2.9  A 
DECR1E SR vs. DECR1E EC  $9.10\times {10}^{02}$  −2  −  $\mathbf{3}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{03}}$  −3.1  A  $\mathbf{0}$  8.9  B 
DECR1E SR vs. DECR1E PF  $\mathbf{2}.\mathbf{53}\times {\mathbf{10}}^{\mathbf{04}}$  4  B  $\mathbf{4}.\mathbf{34}\times {\mathbf{10}}^{\mathbf{04}}$  3.8  B  $\mathbf{5}.\mathbf{81}\times {\mathbf{10}}^{\mathbf{03}}$  3.1  B 
DECR1E EC vs. DECR1E PF  $\mathbf{1}.\mathbf{18}\times {\mathbf{10}}^{\mathbf{08}}$  6  B  $\mathbf{2}.\mathbf{60}\times {\mathbf{10}}^{\mathbf{11}}$  6.9  B  $\mathbf{2}.\mathbf{65}\times {\mathbf{10}}^{\mathbf{08}}$  −5.8  A 
GA FR vs. GA SR  $\mathbf{1}.\mathbf{44}\times {\mathbf{10}}^{\mathbf{12}}$  −7.3  A  $\mathbf{2}.\mathbf{70}\times {\mathbf{10}}^{\mathbf{03}}$  3.4  B  $9.20\times {10}^{01}$  0.1  − 
GA FR vs. GA EC  $6.89\times {10}^{01}$  0.4  −  $4.24\times {10}^{01}$  0.8  −  $2.67\times {10}^{01}$  −1.6  − 
GA FR vs. GA PF  $\mathbf{5}.\mathbf{12}\times {\mathbf{10}}^{\mathbf{05}}$  −4.3  A  $\mathbf{3}.\mathbf{98}\times {\mathbf{10}}^{\mathbf{08}}$  5.8  B  $\mathbf{4}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{10}}$  −6.5  A 
GA SR vs. GA EC  $\mathbf{8}.\mathbf{13}\times {\mathbf{10}}^{\mathbf{14}}$  7.7  B  $\mathbf{2}.\mathbf{80}\times {\mathbf{10}}^{\mathbf{02}}$  −2.6  A  $2.67\times {10}^{01}$  −1.7  − 
GA SR vs. GA PF  $\mathbf{5}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{03}}$  3  B  $\mathbf{3}.\mathbf{28}\times {\mathbf{10}}^{\mathbf{02}}$  2.4  B  $\mathbf{2}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{10}}$  −6.6  A 
GA EC vs. GA PF  $\mathbf{1}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{05}}$  −4.7  A  $\mathbf{2}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{06}}$  5  B  $\mathbf{3}.\mathbf{83}\times {\mathbf{10}}^{\mathbf{06}}$  −4.9  A 
PSO FR vs. PSO SR  $\mathbf{1}.\mathbf{52}\times {\mathbf{10}}^{\mathbf{07}}$  −5.5  A  $4.84\times {10}^{01}$  −0.7  −  $\mathbf{4}.\mathbf{29}\times {\mathbf{10}}^{\mathbf{02}}$  2.3  B 
PSO FR vs. PSO EC  1  0.7  −  $3.87\times {10}^{01}$  1.3  −  $\mathbf{8}.\mathbf{17}\times {\mathbf{10}}^{\mathbf{13}}$  7.4  B 
PSO FR vs. PSO PF  1  0.4  −  $\mathbf{2}.\mathbf{11}\times {\mathbf{10}}^{\mathbf{05}}$  4.6  B  $\mathbf{1}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{08}}$  5.9  B 
PSO SR vs. PSO EC  $\mathbf{3}.\mathbf{39}\times {\mathbf{10}}^{\mathbf{09}}$  6.2  B  $1.37\times {10}^{01}$  2  −  $\mathbf{1}.\mathbf{36}\times {\mathbf{10}}^{\mathbf{06}}$  5.1  B 
PSO SR vs. PSO PF  $\mathbf{1}.\mathbf{82}\times {\mathbf{10}}^{\mathbf{08}}$  5.9  B  $\mathbf{6}.\mathbf{95}\times {\mathbf{10}}^{\mathbf{07}}$  5.3  B  $\mathbf{9}.\mathbf{55}\times {\mathbf{10}}^{\mathbf{04}}$  3.6  B 
PSO EC vs. PSO PF  1  −0.3  −  $\mathbf{3}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{03}}$  3.3  B  $1.34\times {10}^{01}$  −1.5  − 
Appendix E. Performance Metrics of the CHT Behavior
Appendix E.1. FP Metric
Study Case 1  Study Case 2  Study Case 3  

FR  SR  $\mathit{\u03f5}$ C  PF  FR  SR  $\mathit{\u03f5}$ C  PF  FR  SR  $\mathit{\u03f5}$ C  PF  
DER1B  1  1  1  1  1  $0.87$  1  1  1  $0.33$  1  1 
DER1E  1  $0.57$  1  1  1  1  1  1  1  0  1  1 
DEB1B  1  $0.83$  1  1  1  1  1  1  1  1  $0.77$  1 
DEB1E  1  $0.73$  1  1  1  1  1  1  1  0  1  1 
DECR  1  $0.1$  1  1  1  1  1  1  1  1  1  1 
DECB  1  1  1  1  1  1  1  1  $0.17$  0  1  0 
DECR1B  1  $0.6$  1  1  1  1  1  1  1  1  1  1 
DECR1E  1  1  1  1  1  1  1  1  $0.97$  0  1  0 
GA  1  1  1  1  1  1  1  1  1  1  1  0 
PSO  1  1  1  1  1  1  1  1  $0.87$  $0.9$  1  1 
Mean  $\mathbf{1}$  $0.78$  $\mathbf{1}$  $\mathbf{1}$  $\mathbf{1}$  $0.99$  $\mathbf{1}$  1  $0.9$  $0.52$  $\mathbf{0}.\mathbf{98}$  $0.7$ 
Appendix E.2. P Metric
Study Case 1  Study Case 2  Study Case 3  

FR  SR  $\mathit{\u03f5}$ C  PF  FR  SR  $\mathit{\u03f5}$ C  PF  FR  SR  $\mathit{\u03f5}$ C  PF  
DER1B  $0.067$  0  $0.033$  0  1  $0.87$  $0.33$  1  $0.57$  0  $0.17$  $0.6$ 
DER1E  $0.17$  0  $0.3$  $0.13$  1  $0.93$  $0.033$  $0.97$  $0.17$  0  $0.067$  $0.2$ 
DEB1B  0  0  0  0  $0.6$  $0.3$  $0.17$  $0.43$  $0.13$  0  0  $0.1$ 
DEB1E  $0.17$  0  $0.067$  0  $0.7$  $0.1$  $0.27$  $0.73$  $0.17$  0  $0.033$  0 
DECR  $0.1$  0  0  $0.1$  1  1  0  $0.97$  $0.2$  $0.1$  $0.1$  0 
DECB  $0.033$  0  0  $0.13$  $0.77$  $0.53$  0  $0.73$  0  0  0  0 
DECR1B  0  0  0  0  $0.97$  1  0  1  0  $0.1$  $0.1$  0 
DECR1E  0  $0.1$  0  $0.067$  $0.97$  $0.1$  0  1  0  0  0  0 
GA  0  0  0  0  0  0  0  0  0  $0.033$  0  0 
PSO  0  0  0  0  0  0  0  $0.27$  0  0  0  0 
Mean  $\mathbf{0}.\mathbf{053}$  $0.01$  $0.04$  $0.043$  $0.7$  $0.48$  $0.08$  $\mathbf{0}.\mathbf{71}$  $\mathbf{0}.\mathbf{12}$  $0.023$  $0.047$  $0.09$ 
Appendix E.3. AFES Metric
Study Case 1  Study Case 2  Study Case 3  

FR/NSE  SR/NSE  $\mathit{\u03f5}$ C/NSE  PF/NSE  FR/NSE  SR/NSE  $\mathit{\u03f5}$ C/NSE  PF/NSE  FR/NSE  SR/NSE  $\mathit{\u03f5}$ C/NSE  PF/NSE  
DER1B  $4.976\times {10}^{6}$    $3.885\times {10}^{6}$    $2.222\times {10}^{6}$  $1.551\times {10}^{6}$  $1.98\times {10}^{5}$  $2.29\times {10}^{6}$  $2.391\times {10}^{7}$    $2.395\times {10}^{7}$  $2.377\times {10}^{7}$ 
DER1E  $4.92\times {10}^{6}$    $4.974\times {10}^{6}$  $4.947\times {10}^{6}$  $2.325\times {10}^{6}$  $6.587\times {10}^{5}$  $1.998\times {10}^{5}$  $2.352\times {10}^{6}$  $2.396\times {10}^{7}$    $2.347\times {10}^{7}$  $2.389\times {10}^{7}$ 
DEB1B          $2.161\times {10}^{6}$  $1.397\times {10}^{6}$  $1.836\times {10}^{5}$  $2.103\times {10}^{6}$  $2.375\times {10}^{7}$      $2.377\times {10}^{7}$ 
DEB1E  $4.973\times {10}^{6}$    $4.581\times {10}^{6}$    $2.337\times {10}^{6}$  $1.008\times {10}^{5}$  $1.963\times {10}^{5}$  $2.219\times {10}^{6}$  $2.396\times {10}^{7}$    $2.392\times {10}^{7}$   
DECR  $4.809\times {10}^{6}$      $5\times {10}^{6}$  $2.196\times {10}^{6}$  $2.181\times {10}^{6}$    $2.325\times {10}^{6}$  $2.399\times {10}^{7}$  $2.392\times {10}^{7}$  $2.396\times {10}^{7}$   
DECB  $4.119\times {10}^{6}$      $4.648\times {10}^{6}$  $2.276\times {10}^{6}$  $2.106\times {10}^{6}$    $2.247\times {10}^{6}$         
DECR1B          $2.253\times {10}^{6}$  $2.147\times {10}^{6}$    $2.147\times {10}^{6}$    $5.907\times {10}^{6}$  $2.4\times {10}^{7}$   
DECR1E    $5.91\times {10}^{5}$    $4.951\times {10}^{6}$  $2.221\times {10}^{6}$  $7.68\times {10}^{5}$    $2.301\times {10}^{6}$         
GA                    $2.372\times {10}^{7}$     
PSO                $2.381\times {10}^{6}$         
Mean  $\mathbf{4}.\mathbf{8}\times {\mathbf{10}}^{\mathbf{6}}/\mathbf{5}$  $5.9\times {10}^{5}/9$  $4.5\times {10}^{6}/7$  $4.9\times {10}^{6}/6$  $2.2\times {10}^{6}/2$  $1.4\times {10}^{6}/2$  $1.9\times {10}^{5}/6$  $\mathbf{2}.\mathbf{3}\times {\mathbf{10}}^{\mathbf{6}}/\mathbf{1}$  $2.391\times {10}^{7}/5$  $1.8\times {10}^{7}/7$  $\mathbf{2}.\mathbf{386}\times {\mathbf{10}}^{\mathbf{7}}/\mathbf{5}$  $2.38\times {10}^{7}/7$ 
Appendix E.4. SP Metric
Study Case 1  Study Case 2  Study Case 3  

FR/NSE  SR/NSE  $\mathit{\u03f5}$ C/NSE  PF/NSE  FR/NSE  SR/NSE  $\mathit{\u03f5}$ C/NSE  PF/NSE  FR/NSE  SR/NSE  $\mathit{\u03f5}$ C/NSE  PF/NSE  
DER1B  $7.464\times {10}^{7}$    $1.165\times {10}^{8}$    $2.222\times {10}^{6}$  $1.79\times {10}^{6}$  $5.941\times {10}^{5}$  $2.29\times {10}^{6}$  $4.219\times {10}^{7}$    $1.437\times {10}^{8}$  $3.961\times {10}^{7}$ 
DER1E  $2.952\times {10}^{7}$    $1.658\times {10}^{7}$  $3.71\times {10}^{7}$  $2.325\times {10}^{6}$  $7.058\times {10}^{5}$  $5.993\times {10}^{6}$  $2.433\times {10}^{6}$  $1.437\times {10}^{8}$    $3.52\times {10}^{8}$  $1.194\times {10}^{8}$ 
DEB1B          $3.601\times {10}^{6}$  $4.656\times {10}^{6}$  $1.101\times {10}^{6}$  $4.854\times {10}^{6}$  $1.781\times {10}^{8}$      $2.377\times {10}^{8}$ 
DEB1E  $2.984\times {10}^{7}$    $6.871\times {10}^{7}$    $3.339\times {10}^{6}$  $1.008\times {10}^{6}$  $7.362\times {10}^{5}$  $3.026\times {10}^{6}$  $1.438\times {10}^{8}$    $7.176\times {10}^{8}$   
DECR  $4.809\times {10}^{7}$      $5\times {10}^{7}$  $2.196\times {10}^{6}$  $2.181\times {10}^{6}$    $2.405\times {10}^{6}$  $1.2\times {10}^{8}$  $2.392\times {10}^{8}$  $2.396\times {10}^{8}$   
DECB  $1.236\times {10}^{8}$      $3.486\times {10}^{7}$  $2.969\times {10}^{6}$  $3.949\times {10}^{6}$    $3.064\times {10}^{6}$         
DECR1B          $2.331\times {10}^{6}$  $2.147\times {10}^{6}$    $2.147\times {10}^{6}$    $5.907\times {10}^{7}$  $2.4\times {10}^{8}$   
DECR1E    $5.91\times {10}^{6}$    $7.427\times {10}^{7}$  $2.298\times {10}^{6}$  $7.68\times {10}^{6}$    $2.301\times {10}^{6}$         
GA                    $7.117\times {10}^{8}$     
PSO                $8.93\times {10}^{6}$         
Mean  $\mathbf{6}.\mathbf{1}\times {\mathbf{10}}^{\mathbf{7}}/\mathbf{5}$  $5.9\times {10}^{6}/9$  $6.7\times {10}^{7}/7$  $4.9\times {10}^{7}/6$  $2.7\times {10}^{6}/2$  $3\times {10}^{6}/2$  $2.1\times {10}^{6}/6$  $\mathbf{3}.\mathbf{5}\times {\mathbf{10}}^{\mathbf{6}}/\mathbf{1}$  $\mathbf{1}.\mathbf{25}\times {\mathbf{10}}^{\mathbf{8}}/\mathbf{5}$  $3.4\times {10}^{8}/7$  $3.4\times {10}^{8}/5$  $1.3\times {10}^{8}/7$ 
Appendix E.5. EVALS Metric: Descriptive Statistics
Appendix E.5.1. Descriptive Statistics for Study Case 1: FourBar Linkage Mechanism
CHT  Algorithm  Mean  std  Median  Minimum  Maximum  IS 

FR  DER1B  200  0  200  200  200  0 
FR  DER1E  200  0  200  200  200  0 
FR  DEB1B  200  0  200  200  200  0 
FR  DEB1E  200  0  200  200  200  0 
FR  DECR  200  0  200  200  200  0 
FR  DECB  200  0  200  200  200  0 
FR  DECR1B  200  0  200  200  200  0 
FR  DECR1E  200  0  200  200  200  0 
FR  GA  200  0  200  200  200  0 
FR  PSO  200  0  200  200  200  0 
SR  DER1B  200  0  200  200  200  0 
SR  DER1E  200  0  200  200  200  0 
SR  DEB1B  200  0  200  200  200  0 
SR  DEB1E  200  0  200  200  200  0 
SR  DECR  200  0  200  200  200  0 
SR  DECB  200  0  200  200  200  0 
SR  DECR1B  200  0  200  200  200  0 
SR  DECR1E  200  0  200  200  200  0 
SR  GA  200  0  200  200  200  0 
SR  PSO  200  0  200  200  200  0 
$\u03f5C$  DER1B  200  0  200  200  200  0 
$\u03f5C$  DER1E  200  0  200  200  200  0 
$\u03f5C$  DEB1B  200  0  200  200  200  0 
$\u03f5C$  DEB1E  200  0  200  200  200  0 
$\u03f5C$  DECR  200  0  200  200  200  0 
$\u03f5C$  DECB  200  0  200  200  200  0 
$\u03f5C$  DECR1B  200  0  200  200  200  0 
$\u03f5C$  DECR1E  200  0  200  200  200  0 
$\u03f5C$  GA  200  0  200  200  200  0 
$\u03f5C$  PSO  200  0  200  200  200  0 
PF  DER1B  200  0  200  200  200  0 
PF  DER1E  200  0  200  200  200  0 
PF  DEB1B  200  0  200  200  200  0 
PF  DEB1E  200  0  200  200  200  0 
PF  DECR  200  0  200  200  200  0 
PF  DECB  200  0  200  200  200  0 
PF  DECR1B  200  0  200  200  200  0 
PF  DECR1E  200  0  200  200  200  0 
PF  GA  200  0  200  200  200  0 
PF  PSO  200  0  200  200  200  0 
Appendix E.5.2. Descriptive Statistics for Study Case 2: CamLinkage Mechanism
CHT  Algorithm  Mean  std  Median  Minimum  Maximum  IS 

FR  DER1B  1836  1915  960  240  6120  0 
FR  DER1E  1796  1088  1440  360  3600  0 
FR  DEB1B  1844  1711  1320  240  6720  0 
FR  DEB1E  1232  $641.2$  1140  240  2640  0 
FR  DECR  1432  1160  1140  240  5040  0 
FR  DECB  1144  $798.3$  840  240  3240  0 
FR  DECR1B  1676  1139  1440  240  4200  0 
FR  DECR1E  1752  1525  1140  240  6120  0 
FR  GA  1392  $804.4$  1320  240  3000  0 
FR  PSO  1604  1382  1200  240  5880  0 
SR  DER1B  4716  4616  2820  240  $1.584\times {10}^{4}$  0 
SR  DER1E  2740  2040  2280  480  9000  0 
SR  DEB1B  1952  2291  1200  240  $1.032\times {10}^{4}$  0 
SR  DEB1E  2016  1660  1740  240  6120  0 
SR  DECR  3036  2027  3240  240  7800  0 
SR  DECB  2448  2228  1800  360  $1.092\times {10}^{4}$  0 
SR  DECR1B  3240  2621  2520  240  9960  0 
SR  DECR1E  2260  1643  1680  240  6000  0 
SR  GA  2096  1663  1680  240  6600  0 
SR  PSO  2660  3709  1800  240  $1.944\times {10}^{4}$  0 
$\u03f5C$  DER1B  6415  5308  5596  245  $1.759\times {10}^{4}$  0 
$\u03f5C$  DER1E  7675  5490  7724  422  $2.033\times {10}^{4}$  0 
$\u03f5C$  DEB1B  2185  1848  1701  245  8232  0 
$\u03f5C$  DEB1E  2894  2330  2381  248  8761  0 
$\u03f5C$  DECR  6501  5848  3458  248  $2.123\times {10}^{4}$  0 
$\u03f5C$  DECB  4521  4713  3065  253  $1.42\times {10}^{4}$  0 
$\u03f5C$  DECR1B  9087  7118  6334  261  $2.154\times {10}^{4}$  0 
$\u03f5C$  DECR1E  9799  $1.014\times {10}^{4}$  6297  271  $3.267\times {10}^{4}$  0 
$\u03f5C$  GA  $1.267\times {10}^{4}$  $1.53\times {10}^{4}$  6227  260  $6.385\times {10}^{4}$  0 
$\u03f5C$  PSO  3250  3580  1729  248  $1.363\times {10}^{4}$  0 
PF  DER1B  2128  1259  1920  240  6000  0 
PF  DER1E  1324  $952.5$  1020  240  4080  0 
PF  DEB1B  1560  $978.4$  1620  240  3600  0 
PF  DEB1E  1380  924  1200  240  4080  0 
PF  DECR  1680  1106  1500  240  3960  0 
PF  DECB  1344  $952.9$  1200  240  3720  0 
PF  DECR1B  2228  1821  1860  240  8640  0 
PF  DECR1E  1572  1481  1020  240  5040  0 
PF  GA  2496  2216  1560  360  7200  0 
PF  PSO  1724  1075  1680  240  4080  0 
Appendix E.5.3. Descriptive Statistics for Study Case 3: EightBar Linkage Mechanism
CHT  Algorithm  Mean  std  Median  Minimum  Maximum  IS 

FR  DER1B  $1.436\times {10}^{4}$  $882.5$  $1.434\times {10}^{4}$  $1.2\times {10}^{4}$  $1.572\times {10}^{4}$  0 
FR  DER1E  $5.526\times {10}^{4}$  6357  $5.55\times {10}^{4}$  $4.152\times {10}^{4}$  $6.696\times {10}^{4}$  0 
FR  DEB1B  $1.256\times {10}^{4}$  1194  $1.296\times {10}^{4}$  9960  $1.428\times {10}^{4}$  0 
FR  DEB1E  $4.278\times {10}^{4}$  4220  $4.35\times {10}^{4}$  $3.54\times {10}^{4}$  $4.848\times {10}^{4}$  0 
FR  DECR  $2.015\times {10}^{5}$  $2.972\times {10}^{4}$  $1.981\times {10}^{5}$  $1.52\times {10}^{5}$  $2.674\times {10}^{5}$  0 
FR  DECB  $2.33\times {10}^{5}$  $2.882\times {10}^{5}$  $4.2\times {10}^{4}$  $2.484\times {10}^{4}$  $6.575\times {10}^{5}$  25 
FR  DECR1B  $3.39\times {10}^{4}$  2550  $3.432\times {10}^{4}$  $2.82\times {10}^{4}$  $3.804\times {10}^{4}$  0 
FR  DECR1E  $3.323\times {10}^{5}$  $8.968\times {10}^{4}$  $3.086\times {10}^{5}$  $2.116\times {10}^{5}$  $6.296\times {10}^{5}$  1 
FR  GA  $2.066\times {10}^{4}$  3400  $2.094\times {10}^{4}$  $1.5\times {10}^{4}$  $2.844\times {10}^{4}$  0 
FR  PSO  $1.156\times {10}^{6}$  $2.641\times {10}^{6}$  $8.31\times {10}^{4}$  $1.248\times {10}^{4}$  $1.184\times {10}^{7}$  4 
SR  DER1B  8952  4006  7620  6960  $2.016\times {10}^{4}$  20 
SR  DER1E            30 
SR  DEB1B  6524  $983.2$  6240  4920  9600  0 
SR  DEB1E            30 
SR  DECR  $1.27\times {10}^{5}$  $1.458\times {10}^{4}$  $1.255\times {10}^{5}$  $9.372\times {10}^{4}$  $1.782\times {10}^{5}$  0 
SR  DECB            30 
SR  DECR1B  9720  $930.6$  9600  7560  $1.164\times {10}^{4}$  0 
SR  DECR1E            30 
SR  GA  $1.686\times {10}^{4}$  2972  $1.662\times {10}^{4}$  $1.068\times {10}^{4}$  $2.256\times {10}^{4}$  0 
SR  PSO  5276  1684  4920  3960  $1.308\times {10}^{4}$  3 
$\u03f5C$  DER1B  $2.442\times {10}^{5}$  $7.438\times {10}^{4}$  $2.443\times {10}^{5}$  $1.279\times {10}^{5}$  $3.818\times {10}^{5}$  0 
$\u03f5C$  DER1E  $2.033\times {10}^{4}$  5100  $2.041\times {10}^{4}$  $1.247\times {10}^{4}$  $2.908\times {10}^{4}$  0 
$\u03f5C$  DEB1B  $1.147\times {10}^{4}$  3487  $1.196\times {10}^{4}$  6783  $1.959\times {10}^{4}$  7 
$\u03f5C$  DEB1E  $1.552\times {10}^{4}$  2467  $1.559\times {10}^{4}$  $1.077\times {10}^{4}$  $2.161\times {10}^{4}$  0 
$\u03f5C$  DECR  $1.019\times {10}^{5}$  $3.323\times {10}^{4}$  $1.049\times {10}^{5}$  $3.351\times {10}^{4}$  $1.699\times {10}^{5}$  0 
$\u03f5C$  DECB  $2.874\times {10}^{4}$  $1.847\times {10}^{4}$  $2.289\times {10}^{4}$  8345  $8.51\times {10}^{4}$  0 
$\u03f5C$  DECR1B  $4.015\times {10}^{4}$  8020  $3.933\times {10}^{4}$  $2.658\times {10}^{4}$  $5.523\times {10}^{4}$  0 
$\u03f5C$  DECR1E  $1.863\times {10}^{4}$  3388  $1.949\times {10}^{4}$  8640  $2.342\times {10}^{4}$  0 
$\u03f5C$  GA  $2.451\times {10}^{4}$  5107  $2.464\times {10}^{4}$  $1.258\times {10}^{4}$  $3.403\times {10}^{4}$  0 
$\u03f5C$  PSO  $1.872\times {10}^{4}$  6898  $1.745\times {10}^{4}$  $1.02\times {10}^{4}$  $4.117\times {10}^{4}$  0 
PF  DER1B  $1.386\times {10}^{4}$  1404  $1.404\times {10}^{4}$  $1.104\times {10}^{4}$  $1.716\times {10}^{4}$  0 
PF  DER1E  $3.556\times {10}^{4}$  2830  $3.594\times {10}^{4}$  $2.916\times {10}^{4}$  $4.008\times {10}^{4}$  0 
PF  DEB1B  $1.399\times {10}^{4}$  1423  $1.392\times {10}^{4}$  $1.14\times {10}^{4}$  $1.764\times {10}^{4}$  0 
PF  DEB1E  $2.794\times {10}^{4}$  3584  $2.766\times {10}^{4}$  $2.124\times {10}^{4}$  $3.828\times {10}^{4}$  0 
PF  DECR  $1.295\times {10}^{6}$  $2.591\times {10}^{5}$  $1.257\times {10}^{6}$  $7.696\times {10}^{5}$  $1.818\times {10}^{6}$  0 
PF  DECB            30 
PF  DECR1B  $8.422\times {10}^{4}$  $1.001\times {10}^{4}$  $8.436\times {10}^{4}$  $6.624\times {10}^{4}$  $1.021\times {10}^{5}$  0 
PF  DECR1E            30 
PF  GA            30 
PF  PSO  $1.807\times {10}^{7}$  $7.56\times {10}^{5}$  $1.797\times {10}^{7}$  $1.678\times {10}^{7}$  $1.973\times {10}^{7}$  0 
Appendix E.6. EVALS Metric: Inferential Statistics
Appendix E.6.1. Ranks Achieved by the Friedman Test
Ranks  

Algorithms  CHT  Study Case 1  Study Case 2  Study Case 3 
DER1B  FR  $2.5$  $1.8$  2 
DER1B  SR  $2.5$  $2.7$  $3.1$ 
DER1B  $\u03f5$ C  $2.5$  $3.1$  $3.3$ 
DER1B  PF  $2.5$  $2.4$  $1.6$ 
Statistic  $Inf$  15  24  
pvalue  $Inf$  $1.63\times {10}^{3}$  $2.23\times {10}^{5}$  
DER1E  FR  $2.5$  $2.3$  3 
DER1E  SR  $2.5$  $2.6$  4 
DER1E  $\u03f5$ C  $2.5$  $3.4$  1 
DER1E  PF  $2.5$  $1.7$  2 
Statistic  $Inf$  28  $Inf$  
pvalue  $Inf$  $3.56\times {10}^{6}$  $Inf$  
DEB1B  FR  $2.5$  $2.7$  $2.6$ 
DEB1B  SR  $2.5$  1  $2.3$ 
DEB1B  $\u03f5$ C  $2.5$  $2.9$  $2.7$ 
DEB1B  PF  $2.5$  $3.4$  $2.4$ 
Statistic  $Inf$  48  $1.5$  
pvalue  $Inf$  $1.71\times {10}^{10}$  $6.82\times {10}^{1}$  
DEB1E  FR  $2.5$  $2.2$  3 
DEB1E  SR  $2.5$  $2.5$  4 
DEB1E  $\u03f5$ C  $2.5$  $3.1$  1 
DEB1E  PF  $2.5$  $2.2$  2 
Statistic  $Inf$  11  $Inf$  
pvalue  $Inf$  $1.19\times {10}^{2}$  $Inf$  
DECR  FR  $2.5$  $1.8$  3 
DECR  SR  $2.5$  $2.8$  $1.8$ 
DECR  $\u03f5$ C  $2.5$  $3.2$  $1.2$ 
DECR  PF  $2.5$  $2.1$  4 
Statistic  $Inf$  23  84  
pvalue  $Inf$  $4.94\times {10}^{5}$  $5.29\times {10}^{18}$  
DECB  FR  $2.5$  2  2 
DECB  SR  $2.5$  $2.8$  3 
DECB  $\u03f5$ C  $2.5$  3  1 
DECB  PF  $2.5$  $2.3$  4 
Statistic  $Inf$  11  $Inf$  
pvalue  $Inf$  $1.38\times {10}^{2}$  $Inf$  
DER1B  FR  $2.5$  $1.8$  $2.2$ 
DER1B  SR  $2.5$  $2.4$  1 
DER1B  $\u03f5$ C  $2.5$  $3.5$  $2.8$ 
DER1B  PF  $2.5$  $2.2$  4 
Statistic  $Inf$  29  84  
pvalue  $Inf$  $2.14\times {10}^{6}$  $5.29\times {10}^{18}$  
DER1E  FR  $2.5$  $2.2$  2 
DER1E  SR  $2.5$  $2.5$  3 
DER1E  $\u03f5$ C  $2.5$  3  1 
DER1E  PF  $2.5$  $2.3$  4 
Statistic  $Inf$  $7.8$  $Inf$  
pvalue  $Inf$  $5.04\times {10}^{2}$  $Inf$  
GA  FR  $2.5$  2  $2.1$ 
GA  SR  $2.5$  $2.2$  $1.2$ 
GA  $\u03f5$ C  $2.5$  $3.2$  $2.7$ 
GA  PF  $2.5$  $2.6$  4 
Statistic  $Inf$  16  $Inf$  
pvalue  $Inf$  $9.78\times {10}^{4}$  $Inf$  
PSO  FR  $2.5$  $2.3$  3 
PSO  SR  $2.5$  $2.5$  $1.3$ 
PSO  $\u03f5$ C  $2.5$  $2.7$  2 
PSO  PF  $2.5$  $2.5$  $3.8$ 
Statistic  $Inf$  $1.6$  70  
pvalue  $Inf$  $6.60\times {10}^{1}$  $4.71\times {10}^{15}$ 
Appendix E.6.2. Multiple Comparison Friedman Test
Algorithms  Study Case 1  Study Case 2  Study Case 3  

Alg. A + CHT vs. Alg B + CHT  pValue  z  Win  pValue  z  Win  pValue  z  Win 
DER1B FR vs. DER1B SR  1  0    $\mathbf{4}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{2}}$  −2.7  A  $\mathbf{1}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{5}}$  −3.3  A 
DER1B FR vs. DER1B $\u03f5$ C  1  0    $\mathbf{1}.\mathbf{06}\times {\mathbf{10}}^{\mathbf{3}}$  −3.8  A  $\mathbf{1}.\mathbf{24}\times {\mathbf{10}}^{\mathbf{4}}$  −4.1  A 
DER1B FR vs. DER1B PF  1  0    $2.16\times {10}^{1}$  −1.8    $3.17\times {10}^{1}$  1   
DER1B SR vs. DER1B $\u03f5$ C  1  0    $5.43\times {10}^{1}$  −1.1    $\mathbf{0}$  −0.8  A 
DER1B SR vs. DER1B PF  1  0    $5.43\times {10}^{1}$  0.85    $\mathbf{4}.\mathbf{31}\times {\mathbf{10}}^{\mathbf{4}}$  4.3  B 
DER1B $\u03f5$ C vs. DER1B PF  1  0    $2.05\times {10}^{1}$  2    $\mathbf{1}.\mathbf{70}\times {\mathbf{10}}^{\mathbf{6}}$  5.1  B 
DER1E FR vs. DER1E SR  1  0    $4.24\times {10}^{1}$  −0.8    $\mathbf{0}$  −3  A 
DER1E FR vs. DER1E $\u03f5$ C  1  0    $\mathbf{6}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{3}}$  −3.2  A  $\mathbf{9}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{9}}$  6  B 
DER1E FR vs. DER1E PF  1  0    $9.10\times {10}^{2}$  2    $\mathbf{8}.\mathbf{10}\times {\mathbf{10}}^{\mathbf{3}}$  3  B 
DER1E SR vs. DER1E $\u03f5$ C  1  0    $\mathbf{4}.\mathbf{92}\times {\mathbf{10}}^{\mathbf{2}}$  −2.4  A  $\mathbf{8}.\mathbf{10}\times {\mathbf{10}}^{\mathbf{3}}$  9  B 
DER1E SR vs. DER1E PF  1  0    $\mathbf{2}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{2}}$  2.8  B  $\mathbf{9}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{9}}$  6  B 
DER1E $\u03f5$ C vs. DER1E PF  1  0    $\mathbf{1}.\mathbf{20}\times {\mathbf{10}}^{\mathbf{6}}$  5.2  B  $\mathbf{8}.\mathbf{10}\times {\mathbf{10}}^{\mathbf{3}}$  −3  A 
DEB1B FR vs. DEB1B SR  1  0    1  0.85    $\mathbf{2}.\mathbf{21}\times {\mathbf{10}}^{\mathbf{6}}$  5.1  B 
DEB1B FR vs. DEB1B $\u03f5$ C  1  0    1  −0.15    $\mathbf{4}.\mathbf{89}\times {\mathbf{10}}^{\mathbf{2}}$  −0.55  A 
DEB1B FR vs. DEB1B PF  1  0    1  0.7    $5.74\times {10}^{2}$  −1.9   
DEB1B SR vs. DEB1B $\u03f5$ C  1  0    1  −1    $\mathbf{1}.\mathbf{53}\times {\mathbf{10}}^{\mathbf{2}}$  −5.6  A 
DEB1B SR vs. DEB1B PF  1  0    1  −0.15    $\mathbf{2}.\mathbf{19}\times {\mathbf{10}}^{\mathbf{11}}$  −6.9  A 
DEB1B $\u03f5$ C vs. DEB1B PF  1  0    1  0.85    $\mathbf{1}.\mathbf{33}\times {\mathbf{10}}^{\mathbf{4}}$  −1.4  A 
DEB1E FR vs. DEB1E SR  1  0    1  −0.95    $\mathbf{0}$  −3  A 
DEB1E FR vs. DEB1E $\u03f5$ C  1  0    $\mathbf{2}.\mathbf{24}\times {\mathbf{10}}^{\mathbf{2}}$  −2.9  A  $\mathbf{9}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{9}}$  6  B 
DEB1E FR vs. DEB1E PF  1  0    1  −0.15    $\mathbf{8}.\mathbf{10}\times {\mathbf{10}}^{\mathbf{3}}$  3  B 
DEB1E SR vs. DEB1E $\u03f5$ C  1  0    $2.05\times {10}^{1}$  −1.9    $\mathbf{8}.\mathbf{10}\times {\mathbf{10}}^{\mathbf{3}}$  9  B 
DEB1E SR vs. DEB1E PF  1  0    1  0.8    $\mathbf{9}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{9}}$  6  B 
DEB1E $\u03f5$ C vs. DEB1E PF  1  0    $\mathbf{2}.\mathbf{98}\times {\mathbf{10}}^{\mathbf{2}}$  2.7  B  $\mathbf{8}.\mathbf{10}\times {\mathbf{10}}^{\mathbf{3}}$  −3  A 
DECR FR vs. DECR SR  1  0    $\mathbf{1}.\mathbf{27}\times {\mathbf{10}}^{\mathbf{2}}$  −3  A  $\mathbf{6}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{4}}$  3.7  B 
DECR FR vs. DECR $\u03f5$ C  1  0    $\mathbf{1}.\mathbf{60}\times {\mathbf{10}}^{\mathbf{4}}$  −4.2  A  $\mathbf{4}.\mathbf{63}\times {\mathbf{10}}^{\mathbf{7}}$  5.3  B 
DECR FR vs. DECR PF  1  0    $4.23\times {10}^{1}$  −0.85    $\mathbf{5}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{3}}$  −3  A 
DECR SR vs. DECR $\u03f5$ C  1  0    $4.23\times {10}^{1}$  −1.2    $1.10\times {10}^{1}$  1.6   
DECR SR vs. DECR PF  1  0    $1.07\times {10}^{1}$  2.1    $\mathbf{1}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{10}}$  −6.7  A 
DECR $\u03f5$ C vs. DECR PF  1  0    $\mathbf{4}.\mathbf{04}\times {\mathbf{10}}^{\mathbf{3}}$  3.4  B  $\mathbf{0}$  −8.3  A 
DECB FR vs. DECB SR  1  0    $1.07\times {10}^{1}$  −2.3    $\mathbf{1}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{3}}$  −3  A 
DECB FR vs. DECB $\u03f5$ C  1  0    $\mathbf{1}.\mathbf{91}\times {\mathbf{10}}^{\mathbf{2}}$  −3  A  $\mathbf{4}.\mathbf{55}\times {\mathbf{10}}^{\mathbf{2}}$  3  B 
DECB FR vs. DECB PF  1  0    $6.84\times {10}^{1}$  −0.95    $\mathbf{4}.\mathbf{02}\times {\mathbf{10}}^{\mathbf{10}}$  −6  A 
DECB SR vs. DECB $\u03f5$ C  1  0    $6.84\times {10}^{1}$  −0.65    $\mathbf{1}.\mathbf{52}\times {\mathbf{10}}^{\mathbf{7}}$  6  B 
DECB SR vs. DECB PF  1  0    $5.31\times {10}^{1}$  1.4    $\mathbf{5}.\mathbf{40}\times {\mathbf{10}}^{\mathbf{3}}$  −3  A 
DECB $\u03f5$ C vs. DECB PF  1  0    $1.82\times {10}^{1}$  2    $\mathbf{0}$  −9  A 
DECR1B FR vs. DECR1B SR  1  0    $2.40\times {10}^{1}$  −1.7    $\mathbf{6}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{4}}$  3.7  B 
DECR1B FR vs. DECR1B $\u03f5$ C  1  0    $\mathbf{2}.\mathbf{65}\times {\mathbf{10}}^{\mathbf{6}}$  −5  A  $1.10\times {10}^{1}$  −1.6   
DECR1B FR vs. DECR1B PF  1  0    $6.35\times {10}^{1}$  −1    $\mathbf{5}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{7}}$  −5.3  A 
DECR1B SR vs. DECR1B $\u03f5$ C  1  0    $\mathbf{3}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{3}}$  −3.3  A  $\mathbf{5}.\mathbf{79}\times {\mathbf{10}}^{\mathbf{7}}$  −5.3  A 
DECR1B SR vs. DECR1B PF  1  0    $6.35\times {10}^{1}$  0.75    $\mathbf{0}$  −9  A 
DECR1B $\u03f5$ C vs. DECR1B PF  1  0    $\mathbf{2}.\mathbf{56}\times {\mathbf{10}}^{\mathbf{4}}$  4.1  B  $\mathbf{6}.\mathbf{47}\times {\mathbf{10}}^{\mathbf{4}}$  −3.7  A 
DECR1E FR vs. DECR1E SR  1  0    1  −0.95    $\mathbf{1}.\mathbf{45}\times {\mathbf{10}}^{\mathbf{8}}$  −3  A 
DECR1E FR vs. DECR1E $\u03f5$ C  1  0    $6.46\times {10}^{2}$  −2.6    $\mathbf{5}.\mathbf{81}\times {\mathbf{10}}^{\mathbf{3}}$  3  B 
DECR1E FR vs. DECR1E PF  1  0    1  −0.3    $\mathbf{0}$  −6  A 
DECR1E SR vs. DECR1E $\u03f5$ C  1  0    $4.38\times {10}^{1}$  −1.6    $\mathbf{5}.\mathbf{81}\times {\mathbf{10}}^{\mathbf{3}}$  6  B 
DECR1E SR vs. DECR1E PF  1  0    1  0.65    $\mathbf{5}.\mathbf{81}\times {\mathbf{10}}^{\mathbf{3}}$  −3  A 
DECR1E $\u03f5$ C vs. DECR1E PF  1  0    $1.22\times {10}^{1}$  2.2    $\mathbf{5}.\mathbf{30}\times {\mathbf{10}}^{\mathbf{9}}$  −9  A 
GA FR vs. GA SR  1  0    $5.16\times {10}^{01}$  −0.65    $\mathbf{1}.\mathbf{39}\times {\mathbf{10}}^{\mathbf{02}}$  2.7  B 
GA FR vs. GA EC  1  0    $\mathbf{1}.\mathbf{29}\times {\mathbf{10}}^{\mathbf{03}}$  −3.7  A  $9.89\times {10}^{02}$  −1.6   
GA FR vs. GA PF  1  0    $1.61\times {10}^{01}$  −2.    $\mathbf{1}.\mathbf{08}\times {\mathbf{10}}^{\mathbf{09}}$  −5.6  A 
GA SR vs. GA EC  1  0    $\mathbf{1}.\mathbf{14}\times {\mathbf{10}}^{\mathbf{02}}$  −3.1  A  $\mathbf{5}.\mathbf{45}\times {\mathbf{10}}^{\mathbf{05}}$  −4.4  A 
GA SR vs. GA PF  1  0    $3.23\times {10}^{01}$  −1.4    $\mathbf{7}.\mathbf{87}\times {\mathbf{10}}^{\mathbf{04}}$  −8.3  A 
GA EC vs. GA PF  1  0   