U.S. Department of Transportation
Federal Highway Administration
1200 New Jersey Avenue, SE
Washington, DC 20590

Skip to content
Facebook iconYouTube iconTwitter iconFlickr iconLinkedInInstagram

Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

This report is an archived publication and may contain dated technical, contact, and link information
Back to Publication List        
Publication Number:  FHWA-HRT-17-104    Date:  June 2018
Publication Number: FHWA-HRT-17-104
Date: June 2018


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




This report presented the results of an FHWA LTPP data analysis project with the objective of using multi-objective optimization to enhance calibration of the MEPDG performance models. The AASHTO recommended single-objective calibration approach was conducted on the MEPDG rutting models for new pavements using the Florida SPS-1 data and overlaid pavements using the Florida SPS-5 data. In the first alternative scenario for multi-objective calibration, SSE and standard deviation of prediction error were simultaneously minimized to reduce the bias and STE (increase model accuracy and precision) at the same time. In the second scenario, the SSE and STE in predicting permanent deformation of SPS-1 and FDOT APT pavement structures were used as separate objective functions to be minimized simultaneously.

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 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 calibration of rutting models for overlaid pavements on Florida 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 (FDOT 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 to choose from.

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 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.


Based on the findings of this study, there are several advantages in adopting a multi-objective calibration approach for pavement design within each State or local highway agency:

The flowchart in figure 42 demonstrates a potential multi-objective calibration framework that highway agencies can adopt for enhanced performance models.

This figure shows a flowchart for implementation of the multi-objective calibration framework devised in this study. The first step is to follow AASHTO recommended procedure for collecting required data. Then, the AASHTOWare™ Pavement ME Design software interface should be used to generate projects and run the software once for each project to generate required files. The material properties, climate, traffic, and response files are generated that will be used by APADS software along with the calibration factor files to provide a rutting prediction. Within the multi-objective calibration code, with every new set of calibration factors and after running APADS, the total calculated performance is extracted from the intermediate files. Then, each one of the objective functions is evaluated by using measured and calculated rut depth values. The multi-objective evolutionary algorithm (MOEA) adjusts the calibration factors in multiple generations to arrive at the final nondominated solution sets. The last step is to select the final calibration factors for design by visualizing the final Pareto-optimal front, using qualitative statistics such as skewness and kurtosis, practicing engineering judgment to select the final factors, observing predicted performance trends, and updating calibration with additional performance data.
Source: FHWA.

Figure 42. Flowchart. Framework for implementation of multi-objective calibration.


Using this multi-objective calibration approach results in a final pool of tradeoff solutions. This way, none of the possible 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.


The following are recommendations for future research into enhancing the multi-objective calibration process:



Federal Highway Administration | 1200 New Jersey Avenue, SE | Washington, DC 20590 | 202-366-4000
Turner-Fairbank Highway Research Center | 6300 Georgetown Pike | McLean, VA | 22101