Travel Time Modeling Using Non-Linear Multi-Objective Fuzzy Optimization Approach

Travel time is an important performance measure in transportation network modeling. Providing accurate real-time information to travelers contributes to the reduction in day to day travel time variance and improves trip planning performance. The fuzzy set theory method is an essential contribution to transportation planning decision processes. The fuzzy optimization technique plays a vital role in transportation modeling with vague parameters. The present study aims to show the possibility of a non-linear fuzzy mathematical model to capture travel time information for transportation system users. Therefore, drivers can make informed decisions about their travel. The non-linear fuzzy mathematical model was introduced in multi-objective mathematical modeling to incorporate more than one objective in the design process. This helps engineers/analysts in the decision process. In this study, a fuzzy mathematical model is proposed to maximize the satisfaction levels considering minimal travel time and variability. The proposed mathematical model is applied to archived speed data from weigh-in-motion (WIM) sensors from multi-region in the State of Ohio in order for the model to capture the uncertainties for a wide range of variations such as vehicle drivers, weather, roadway, etc. The optimal solution has been identified using multi-objective fuzzy programming along with hyperbolic membership function. Fuzzy membership includes a range of satisfaction values between 1 (represents the maximum satisfaction level) and 0 (represents no association in the model). The results from the non-linear fuzzy model show better fitting of travel time variation compared to the linear membership function that has been used in past research. A linear membership function is not a suitable representation in many practical situations because it does not represent the real distribution of the data. The non-linear membership function describes the uncertainty and reflects the fuzziness of the actual situation of the data. The enhanced multi-objective fuzzy mathematical model may have an impact on the decision-maker travel behavior such as route choice and departure time. The experimental results exhibit the model’s capability to represent stochastic travel times and help decision-makers to solve problems with incomplete information under uncertain events.