1. Introduction
2. Related Work
3. Methodology
3.1. The Dataset
3.2. Genetic Programming and Tested Flavors
Algorithm 1 Genetic Programming pseudocode. 
1: for $i=1$ to $NumOfGenerations$ (or until an acceptable solution is found) do 
2: if 1st generation then 
3: generate initial population with primitives (variables, constants and elements from the function set) 
4: end if 
5: Calculate fitness (minimize RMSE) of population members 
6: Select n parents from population (based on fitness) 
7: Stochastically apply Genetic operators to generate n offspring 
8: end for 
9: Return best individual (based on fitness) found during search 
3.2.1. GPTIPS V2
3.2.2. neatGP
3.2.3. neatGPLS
3.3. Statistical Analysis: Friedman Test and Critical Difference Diagram
4. Results
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
GP  Genetic Programming 
ML  Machine Learning 
SRM  Symbolic Regression Model 
ANN  Artificial Neural Networks 
SVM  Support Vector Machines 
RF  Random Forest 
BN  Bayesian Networks 
FIS  Fuzzy Inference Systems 
BRR  Bayesian Ridge Regression 
SVR  Support Vector Regression 
LS  Local Search 
NEAT  NeuroEvolution of Augmenting Topologies algorithm 
FlatOE  Flat Operator Equalization 
DE  Driving Event 
RMSE  Root Mean Squared Error 
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Driving Event (id Number in the Feature Vector)  Value (Frequency)  Score for the Travel 

Distance (${x}_{1}$)  7  
Avg. Velocity (${x}_{2}$)  6  
# of acceleration events (${x}_{3}$)  5  
# of sudden starts (${x}_{4}$)  3  8 
# of abrupt lane changes (${x}_{5}$)  2  
# of intense brakes (${x}_{6}$)  7  
# of sudden stops (${x}_{7}$)  0  
# of abrupt steerings (${x}_{8}$)  1 
Parameter  Value  Units 

Population size  100  items 
Max. # of generations  100  items 
Input variables  8  items 
Range of Constants  [−10, 10]  items 
Training instances  180  road trips 
Testing instances  20  road trips 
Crossover probability  85  percentage (%) 
Mutation probability  15  percentage (%) 
Function set  $\times ,,+,\xf7,\sqrt{x},$  functions 
$tanh,exp,log,{x}^{3},$  
$MULT3,ADD3,$  
$negexp,neg,\leftx\right$ 
GPTIPS  

Fold  Best Train  Best Test  Size Best Ind  Avg. Pop. Size 
1  1.1219  1.2211  22  21.1200 
2  1.1168  1.2188  25  22.6067 
3  1.1329  1.0482  22  20.0633 
4  1.0978  1.4509  26  23.6000 
5  1.1479  1.0034  25  22.7067 
6  1.1296  1.1546  24  24.3533 
7  1.1367  1.1857  24  23.2800 
8  1.0650  1.7854  25  23.0167 
9  1.1356  1.3130  23  22.2233 
10  1.0595  1.5560  22  21.1667 
Minimum  1.0595  1.0034  22  20.0633 
Maximum  1.1479  1.7854  26  24.3533 
mean  1.1144  1.2937  23.8000  22.4137 
SD  0.0306  0.2408  1.4757  1.2994 
median  1.1257  1.2199  24.0000  22.6567 
Correlation Coefficient  0.8030  0.2868 
neatGP  

Fold  Best Train  Best Test  Size Best Ind  Avg. Pop. Size 
1  1.2093  1.5795  46  39.1850 
2  1.2584  1.1488  64  45.9650 
3  1.8291  1.9927  183  124.3400 
4  1.3928  1.3015  132  100.0250 
5  1.3064  1.5171  44  27.9500 
6  1.2969  1.9753  61  44.3100 
7  0.8505  1.5701  625  211.0900 
8  1.2261  1.6290  69  54.6200 
9  1.2496  1.9254  66  47.0100 
10  1.2546  1.4381  44  29.5650 
Minimum  0.8505  1.1488  44  27.9500 
Maximum  1.8291  1.9927  625  211.0900 
mean  1.2874  1.6077  133.4000  72.4060 
SD  0.2378  0.2845  178.4204  57.7911 
median  1.2565  1.5748  65.0000  46.4875 
Correlation Coefficient  0.6432  0.6337 
neatGPLS  

Fold  Best Train  Best Test  Size Best Ind  Avg. Pop. Size 
1  1.1690  1.6912  30  11.5900 
2  1.2195  1.1623  40  11.9700 
3  1.1622  1.2626  22  16.0000 
4  1.2188  1.0513  31  18.8400 
5  1.1756  1.5657  29  16.1750 
6  1.1813  1.0310  36  20.1050 
7  1.3758  1.3739  1  3.4200 
8  1.1822  1.1456  18  18.5950 
9  1.1326  1.4899  31  13.2200 
10  1.1917  1.2202  35  16.5700 
Minimum  1.1326  1.0310  1  3.4200 
Maximum  1.3758  1.6912  40  20.1050 
mean  1.2009  1.2994  27.3000  14.6485 
SD  0.0666  0.2236  11.2551  4.8923 
median  1.1818  1.2414  30.5000  16.0875 
Correlation Coefficient  0.7735  0.5012 
GPTIPS  

Fold  Best Train  Best Test  Size Best Ind  Avg. Pop. Size 
1  0.6445  0.7347  22  22.0300 
2  0.6567  0.6591  18  17.7833 
3  0.6474  0.7408  21  21.8767 
4  0.6215  0.9530  23  23.9733 
5  0.6604  0.6833  29  24.4567 
6  0.6491  0.7931  20  18.0233 
7  0.6630  0.5913  22  20.8233 
8  0.6524  0.6400  29  22.3667 
9  0.6402  0.7241  21  19.9933 
10  0.6176  0.9286  23  21.7733 
Minimum  0.6176  0.5913  18  17.7833 
Maximum  0.6630  0.9530  29  24.4567 
mean  0.6453  0.7448  22.8000  21.3100 
SD  0.0153  0.1182  3.5839  2.2205 
median  0.6482  0.7294  22.0000  21.8250 
Correlation Coefficient  0.7505  0.6219 
neatGP  

Fold  Best Train  Best Test  Size Best Ind  Avg. Pop. Size 
1  0.6070  2.6656  234  174.0650 
2  0.5770  0.9034  276  169.5550 
3  0.8056  0.8421  464  266.4800 
4  0.6513  1.1010  176  118.1200 
5  0.4705  0.5493  236  151.3600 
6  0.5038  1.1317  245  160.8900 
7  0.6748  0.7746  159  110.3400 
8  0.7093  0.7463  55  42.1850 
9  0.5284  0.9176  205  146.1850 
10  0.5491  1.4260  139  65.5550 
Minimum  0.4705  0.5493  55  42.1850 
Maximum  0.8056  2.6656  464  266.4800 
mean  0.6077  1.1058  218.9000  140.4735 
SD  0.1034  0.5991  107.1888  62.4507 
median  0.5920  0.9105  219.5000  148.7725 
Correlation Coefficient  0.8805  0.5857 
neatGPLS  

Fold  Best Train  Best Test  Size Best Ind  Avg. Pop. Size 
1  0.6387  0.9852  30  18.9650 
2  0.7240  0.7477  29  16.7000 
3  0.6675  0.7854  28  14.3150 
4  0.6291  0.9384  37  20.5550 
5  0.6321  0.7810  21  16.1550 
6  0.6611  0.7851  41  24.1900 
7  0.7217  0.4519  29  19.7950 
8  0.6337  0.6387  34  19.5900 
9  0.6622  0.9408  29  15.8750 
10  0.6323  1.0198  17  14.0850 
Minimum  0.6291  0.4519  17  14.0850 
Maximum  0.7240  1.0198  41  24.1900 
mean  0.6603  0.8074  29.5000  18.0225 
SD  0.0359  0.1738  6.9960  3.1629 
median  0.6499  0.7852  29.0000  17.8325 
Correlation Coefficient  0.7598  0.3352 
RMSE Testing  Complexity (# of Nodes)  Model 

0.919  37 
$$\begin{array}{cc}\hfill y& =\frac{0.4486\phantom{\rule{0.166667em}{0ex}}{\mathrm{e}}^{1.0\phantom{\rule{0.166667em}{0ex}}{\mathrm{x}}_{1}}\phantom{\rule{0.166667em}{0ex}}\left({\mathrm{x}}_{1}1.0\phantom{\rule{0.166667em}{0ex}}{\mathrm{x}}_{1}\phantom{\rule{0.166667em}{0ex}}\left({\mathrm{x}}_{2}9.9\right)\right)}{{\mathrm{x}}_{2}}0.05036\phantom{\rule{0.166667em}{0ex}}{\mathrm{x}}_{8}\hfill \\ & 0.02518\phantom{\rule{0.166667em}{0ex}}tanh\phantom{\rule{0.166667em}{0ex}}\left(tanh\phantom{\rule{0.166667em}{0ex}}\left({\mathrm{x}}_{4}\right)\right)\phantom{\rule{0.166667em}{0ex}}\left(tanh\phantom{\rule{0.166667em}{0ex}}\left(tanh\phantom{\rule{0.166667em}{0ex}}\left({\mathrm{x}}_{4}\right)\right)1.0\phantom{\rule{0.166667em}{0ex}}{\mathrm{x}}_{1}\phantom{\rule{0.166667em}{0ex}}\left({\mathrm{x}}_{2}9.9\right)\right)\hfill \\ & 0.2356\phantom{\rule{0.166667em}{0ex}}{\mathrm{x}}_{2}+3.443\hfill \end{array}$$

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