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Alternate traffic restriction (ATR) schemes manage traffic congestion by prohibiting a proportion of cars from entering a predetermined ATR area during specific time periods. Under the ATR scheme, Park-and-Ride (P&amp;R) often becomes more popular as travelers can park cars at P&amp;R facilities and avoid driving into the ATR area. This paper proposes a multi-objective bi-level model that jointly optimizes the P&amp;R facility locations and the ATR scheme (the ATR areas and the proportion of restricted private cars). The upper-level model minimizes the total travel cost and total emission cost, and maximizes consumer surplus. The lower-level model characterizes the user equilibrium of travel modes and route choices. The non-dominated sorting genetic algorithm is adapted to solve the proposed multi-objective bi-level model, where a gradient project algorithm is used for solving the lower-level model. Numerical studies are conducted to test and illustrate the applicability of the model and algorithms.

Joint optimisation of park-and-ride facility locations and alternate traffic restriction scheme under equilibrium flows