Figure 1

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Figure 5
![Process flow of the GEP-based model development [44].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/69388d63a2cfbc128b1cffde/j_rams-2025-0143_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKC3522UWU%2F20251212%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251212T092634Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDkaDGV1LWNlbnRyYWwtMSJHMEUCIQC%2BQfKW5N5JBG%2FGTUK1Ddg%2BFHMy7CCph8HJvJRHrnwxLQIgOanKEyn9%2Bo1M2Ux%2FTqFXNo9GIguZfSvTxkZ4ODONHxwqvQUIAhACGgw5NjMxMzQyODk5NDAiDNmcz7mmWd%2ByHyWFXSqaBca2WeDmL0ylQGyAwWbHkxwYhnn9qCr3dXNfeV1UIGFwVVXFTW9J0x8l%2FobHjabimJrNoiuSio73%2BzbZwW7rlyRJpDeiY62uzWn7Tmm2A%2FAy2ChDr%2F%2B0u3rkWr3S9CD2%2Fh0cVlBCMPZCpxTK%2BJbHZoB%2F6TREBwts2XG%2BYOs7rW4fuPBfTFW22LKpXf1SxdA2BCkpcI4mat9907otV0ZLop9qCyCiF%2Belg7JccCC4fiHUITG9%2B4EXhCxvU9qYIDmgXFJaGkjfuwLJSxOPZ72u8vIXlpigJlR%2BDsPEy7VaJc3hoLumUK0wfKkKK9GSrx4tjtDEEa3m%2B2rgq9CISYMqLl2JR9DhBdoXf%2Fw%2F88rw%2FkFmW0ZDaff8WZpKafbCny5KHm4VD8uQvc6GMxULMI319N33AtRNeHv68PkBHXtiaCr9CHT30Pu4TL%2BYuEF%2BJHiBUQm3dSXnZ0MUoBA6F3fMcpeYUjXIuObf%2B2FKiY4rdKxDA%2BQ%2BpL6P2vgyhH7Pfmjn7S1H0yO%2B8bHWSHXSObzpezY1aPFowyWgn9QKjiYKfqZvCltLTUko1QQCj2zsNwVJnyL3RCME0E906K5n4fTgMz0hXegLW69MrNNg0dn4jPNN8cL5mS0D9Ge0qw4rVmZxgDRxWeRr0lzCUC3QXGN3rFchBIKCcUAL7P7UEGam5E2xOvgrDRJChfS6EODwMtnGY06xvELPC0KqQSZnXbpkMIKt1JIv1U5do%2BYE0uqEtU2Y%2Fgifb2a7MmdHpD%2BOZt4t8%2FjtryZCOXrayOsc7KoeBucESjdSsIWpBbOuSFJyIII4ck9TM2jnxmdjYlNtxWBOlLmmDka4y0stOlQz192O3eaipUWYvBLMtZnOnfMEF741RWEGFOQ2b0TwqDCer%2B%2FJBjqxAW4NnZodJUXY96PxpqFzqL6n1pL8JT2lQ4LVr8c4pftcXMAU7ouVfyQPSgVc2lwaSxkXUBj21zT50VxNK4fHtlyFFz4Lz3DTQCYNH%2BCq3PGxqXLTIN170tnl0CApuctAJHBWAwXJya3ZyxeI170LibMcV5TVp4DEYWKlKW7Ltn0zkR3ZFEL58x4ngXcc0qizg9%2FuxM3%2F1uhkmatbLC2l3IA6Io3jpmtXzXmvB%2FDe4Ls77w%3D%3D&X-Amz-Signature=92d40ca6f9b82659d5c9060677b434cde5bcfb0bb0404542c510dbcaf8689029&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 6
![Flowchart of the MEP method [44].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/69388d63a2cfbc128b1cffde/j_rams-2025-0143_fig_006.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKC3522UWU%2F20251212%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251212T092634Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDkaDGV1LWNlbnRyYWwtMSJHMEUCIQC%2BQfKW5N5JBG%2FGTUK1Ddg%2BFHMy7CCph8HJvJRHrnwxLQIgOanKEyn9%2Bo1M2Ux%2FTqFXNo9GIguZfSvTxkZ4ODONHxwqvQUIAhACGgw5NjMxMzQyODk5NDAiDNmcz7mmWd%2ByHyWFXSqaBca2WeDmL0ylQGyAwWbHkxwYhnn9qCr3dXNfeV1UIGFwVVXFTW9J0x8l%2FobHjabimJrNoiuSio73%2BzbZwW7rlyRJpDeiY62uzWn7Tmm2A%2FAy2ChDr%2F%2B0u3rkWr3S9CD2%2Fh0cVlBCMPZCpxTK%2BJbHZoB%2F6TREBwts2XG%2BYOs7rW4fuPBfTFW22LKpXf1SxdA2BCkpcI4mat9907otV0ZLop9qCyCiF%2Belg7JccCC4fiHUITG9%2B4EXhCxvU9qYIDmgXFJaGkjfuwLJSxOPZ72u8vIXlpigJlR%2BDsPEy7VaJc3hoLumUK0wfKkKK9GSrx4tjtDEEa3m%2B2rgq9CISYMqLl2JR9DhBdoXf%2Fw%2F88rw%2FkFmW0ZDaff8WZpKafbCny5KHm4VD8uQvc6GMxULMI319N33AtRNeHv68PkBHXtiaCr9CHT30Pu4TL%2BYuEF%2BJHiBUQm3dSXnZ0MUoBA6F3fMcpeYUjXIuObf%2B2FKiY4rdKxDA%2BQ%2BpL6P2vgyhH7Pfmjn7S1H0yO%2B8bHWSHXSObzpezY1aPFowyWgn9QKjiYKfqZvCltLTUko1QQCj2zsNwVJnyL3RCME0E906K5n4fTgMz0hXegLW69MrNNg0dn4jPNN8cL5mS0D9Ge0qw4rVmZxgDRxWeRr0lzCUC3QXGN3rFchBIKCcUAL7P7UEGam5E2xOvgrDRJChfS6EODwMtnGY06xvELPC0KqQSZnXbpkMIKt1JIv1U5do%2BYE0uqEtU2Y%2Fgifb2a7MmdHpD%2BOZt4t8%2FjtryZCOXrayOsc7KoeBucESjdSsIWpBbOuSFJyIII4ck9TM2jnxmdjYlNtxWBOlLmmDka4y0stOlQz192O3eaipUWYvBLMtZnOnfMEF741RWEGFOQ2b0TwqDCer%2B%2FJBjqxAW4NnZodJUXY96PxpqFzqL6n1pL8JT2lQ4LVr8c4pftcXMAU7ouVfyQPSgVc2lwaSxkXUBj21zT50VxNK4fHtlyFFz4Lz3DTQCYNH%2BCq3PGxqXLTIN170tnl0CApuctAJHBWAwXJya3ZyxeI170LibMcV5TVp4DEYWKlKW7Ltn0zkR3ZFEL58x4ngXcc0qizg9%2FuxM3%2F1uhkmatbLC2l3IA6Io3jpmtXzXmvB%2FDe4Ls77w%3D%3D&X-Amz-Signature=109f2a766e26918a5618d4e9b17a30aa2891f361985c40d9114dc3ed5fec23bb&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
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Findings obtained by statistical analysis
| Metric | Unit | C-S GEP | C-S MEP |
|---|---|---|---|
| RMSE | MPa | 2.066 | 1.588 |
| MAE | MPa | 1.666 | 1.203 |
| R | MPa | 0.900 | 0.982 |
| MAPE | % | 4.119 | 3.026 |
| NSE | MPa | 0.796 | 0.961 |
| PI | — | 1.355 | 1.786 |
| OF | — | 4.269 | 2.522 |
MEP/GEP method parameters
| Groups | Descriptions | Settings |
|---|---|---|
| GEP/MEP sampling | Training records | 286 |
| Validation/test records | 122 | |
| GEP parameters | Error measure | MSE |
| Number of sub-populations | 100 | |
| Sub-population size | 250 | |
| Code length | 50 | |
| Cross-over probability | 0.9 | |
| Number of generations | 250 | |
| Mutation probability | 0.1 | |
| Functions | +, −, ÷, ×, √, ^, ex | |
| MEP parameters | Number of chromosomes | 75 |
| Head size | 10 | |
| Number of genes | 6 | |
| Linking function | Addition | |
| Functions | +, −, ÷, ×, √, ^, ex |