Surrogate-Based Optimization for Solving a Mixed Integer Network Design Problem

Abstract

This paper considers the bilevel mixed network design problem (MNDP) used in dynamic traffic assignment (DTA) and the simulation-based optimization solution. The upper level of the bilevel MNDP minimizes the network cost in terms of average travel time by the expansion of existing links and the addition of new candidate links. The lower level is a dynamic user-optimal condition that can be formulated as a variational inequality problem. The MNDP simultaneously finds optimal capacity expansions of existing links and new link additions. A surrogate-based optimization (SBO) framework is proposed for solving the MNDP that is characterized by expensive-to-evaluate objective functions. Because simulation was applied to evaluate those objective functions, additional complexity arose from the fine-grained representation of traffic dynamics in large-scale networks, which were not fully considered by the traditional static user equilibrium. SBO methods enjoy both the advantages of simulation in time-varying network performance evaluation and the efficiency of mathematical optimization. To be more specific, SBO produces computational time savings by exploring the input–output mapping surface in a more systematic and efficient way. For demonstrative purposes, a case study was conducted on the large-scale Montgomery County network in Maryland. In this example, a mesoscopic simulation-based DTA model, DTALite, was used to evaluate the system performance in response to various network design strategies. Results showed that the optimal investment with a moderate budget could reduce 17.73% of the network average travel time in the morning peak. The proposed framework is a general approach, which is ready for application to either continuous or discrete network design problems.