Data-driven estimation of travel latency cost functions via inverse optimization in multi-class transportation networks

Abstract

We develop a method to estimate from data travel latency cost functions in multi-class transportation networks, which accommodate different types of vehicles with very different characteristics (e.g., cars and trucks). Leveraging our earlier work on inverse variational inequalities, we develop a data-driven approach to estimate the travel latency cost functions. Extensive numerical experiments using benchmark networks, ranging from moderate-sized to largesized, demonstrate the effectiveness and efficiency of our approach. Index TermsMulti-class transportation network, cost function, Wardrop equilibrium, variational inequality, inverse optimization. I. INTRODUCTIONAssuming all users (drivers) in a transportation network select routes selfishly, the network ends up reaching an equilibrium in terms of link flows, which is known as the Wardrop Equilibrium (WE) [1], an instantiation of the well-known Nash Equilibrium. At the equilibrium, no single driver can "benefit" by rerouting. Mathematically, given travel latency (time) cost functions (we will also simply say cost functions in the sequel) with respect to link (road/arc) flows and an origin-destination (OD) flow demand matrix, finding the WE is formulated as the Traffic Assignment Problem (TAP), which has been well-studied; see, e.g., [2] and the references therein. We will call TAP the forward problem throughout the paper. On the other hand, given an OD demand matrix and the WE, one can seek to "recover" the cost functions, by formulating appropriate inverse problems; see, e.g., [3], [4], [5], among others. Moreover, another version of the inverse problem can be considered: estimating/adjusting the OD demand matrix by assuming that the WE and the cost functions are known (sometimes a "rough" initial OD demand matrix is also available); see, e.g., [6], [7]. In this paper, applying a data-driven approach, we only consider the former version inverse problems, namely, recovering the cost functions from a given OD demand matrix and the corresponding WE, which is of practical importance, as partly shown in [4], [5].

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