Using Multi-Objective Optimization to Enhance Calibration of Performance Models in the Mechanistic-Empirical Pavement Design Guide

EXECUTIVE SUMMARY

The American Association of State Highway and Transportation Officials (AASHTO) has published guidelines to calibrate the pavement performance prediction models used in the AASHTOWare® Pavement Mechanistic–Empirical Design software to local materials–traffic–climate conditions.⁽¹⁾ The AASHTO recommended calibration process consists of several steps to increase accuracy and precision of the calibrated models through single-objective minimization of bias and standard deviation of error. This research project investigated the application of multi-objective optimization to enhance the calibration of the performance models within the Guide for Mechanistic–Empirical Design of New and Rehabilitated Pavement Structures (MEPDG).⁽²⁾

Using a multi-objective optimization approach enables researchers to escape preconception, avoid excessive concentration on only one aspect of the problem, and combine multiple sources of information in an objective manner. This research project devised two scenarios for application of multi-objective optimization to enhance calibration of MEPDG performance models. In the primary multi-objective scenario, mean and standard deviation of prediction error are simultaneously minimized to increase accuracy and precision at the same time. In this manner, the information from a single calibration run is fully implemented, and an additional round of computationally intensive calibration is avoided. In the second scenario, model prediction error on data from Federal Highway Administration’s Long-Term Pavement Performance test sections and error on available accelerated pavement testing (APT) data are treated as independent objective functions to be minimized simultaneously. As a result, the multiple sources of data with different materials–traffic–climate conditions and disparate measurement protocols are combined in an objective manner.

Using this multi-objective calibration approach results in a final pool of tradeoff solutions. This way, none of the viable sets of calibration factors are eliminated prematurely, and all of the nondominated solutions are included in the final tradeoff front. Exploring the final front might reveal unknown aspects of this calibration problem and result in more reasonable calibration coefficients that could not be identified using single-objective approaches. This study demonstrates the application of engineering judgment and qualitative criteria to select reasonable calibration coefficients from the final pool of solutions that result from the multi-objective optimization. More reasonable calibration factors result in a more justifiable pavement design considering multiple aspects of pavement performance.

Although there was no fundamental way to prove whether there was a theoretical conflict between the selected objective functions, the shape of the final nondominated front indicated that the selected objective functions conflicted with one another, and therefore, the application of a multi-objective optimization approach was justified. In the first multi-objective calibration scenario, the simultaneous minimization of bias and standard error (STE) resulted in calibrated models that had higher precision (lower STE) and higher generalization capability (lower difference in bias between calibration and validation data) compared to the single-objective calibration. While this scenario was more successful in the calibration of rutting models for overlaid pavements on Florida Specific Pavement Studies (SPS)-5 data, it did not result in desirable accuracy levels for rutting models on new pavements using Florida SPS-1 data. The results of the second multi-objective scenario demonstrated that incorporation of the disparate source of performance data (Florida Department of Transportation APT data) as a separate objective function has significantly improved the prediction accuracy, precision, and generalization capability of the calibrated rutting model on SPS-1 data.

The qualitative comparison of the calibrated models showed that using the multi-objective approach has resulted in predicted rutting distributions that are more similar in flatness (kurtosis) to the measured rutting distributions. However, the same was not true about skewness. The low goodness-of-fit indicator for scatterplots of predicted versus measured rutting in the case of all calibration approaches reveals that the MEPDG rutting models have an inherent lack of precision that might not be addressed with the calibration process. This is perhaps because the variability in pavement materials has not been captured in these models. The final selected calibration factors for rutting in unbound pavement layers (base and subgrade) were more reasonable in the multi-objective approach, compared to insignificant values achieved through single-objective calibration. Once again, this possibility of applying engineering judgment demonstrates the value of the multi-objective calibration in providing a final pool of solutions from which to choose.

To combine the quantitative and qualitative success metrics of a performance prediction model, the measured and predicted rutting deterioration trends were examined. While the two-objective calibration on SPS-5 data had significantly improved the prediction of rutting deterioration rates compared to the single-objective calibration, the multi-objective calibration results on SPS-1 did not exhibit the same quality. This investigation revealed that simply evaluating the bias and STE is not adequate for a comprehensive evaluation of performance prediction models. Therefore, it is recommended that the comprehensive comparison framework presented in this study be used when selecting suitable performance prediction models.