Robust Dynamic Continuous Network Design Problem

Typically, the NDP objective function minimizes the total system travel time (TSTT) subject to the conservation of flow conditions and budget constraint or minimizes the TSTT plus the cost converted to equivalent time unit subject to the conservation of flow conditions. The NDP formulations can be classified according to the following four criteria: (a) system-optimal (SO) or user-optimal (UO) behavior, (b) static or dynamic traffic assignment, (c) discrete or continuous investment variable, and (d) deterministic or stochastic parameters. SO behavior is mathematically tractable but unrealistic, whereas UO behavior typically complicates the problem but is more realistic. The static traffic assignment assumes the steady-state condition, whereas the dynamic traffic assignment (DTA) accounts for time dynamics. The discrete investment variable allows entire-lane or new link addition, whereas the continuous investment permits a fraction of lane addition. The continuous investment variable has been used extensively in the literature, with the justification that because most roads in the urban area are already constructed, discrete variables are not practical. The continuous link expansion can be implemented by altering lane width, median, and shoulder area. Also, the continuous NDP can be considered as a possible heuristic for the discrete NDP. Last, the problem parameters typically have been considered deterministic as opposed to stochastic. There is little literature on the DTA-based NDP. Janson showed that the DTA-based NDP model is more desirable than the static model (2). Waller et al. proposed a continuous NDP formulated as a linear programming model (3), in which the users’ route choices are based on the single-destination SO DTA linear programming model with fixed-departure-time O-D demands introduced by Ziliaskopoulos (4). The SO DTA linear programming model propagates traffic according to the cell transmission model (CTM), a traffic flow theoretical model by Daganzo (5). Ukkusuri and Waller proposed a continuous NDP formulated as a linear programming model (6), in which the users’ route choices are based on the UO DTA linear programming model by Ukkusuri (7), also employing Daganzo’s CTM. Jeon et al. employed a genetic algorithm to solve the discrete NDP by allowing either one lane addition or none (8). Waller and Ziliaskopoulos introduced the stochastic SO DTA-based NDP with long-term O-D demand uncertainty (9), formulated as a two-stage stochastic linear program with recourse (SLP2) and a chance-constrained program (CCP). Ukkusuri et al. introduced the UO versions of SLP2 and CCP models (10). Karoonsoontawong and Waller conducted a comprehensive comparison of the SO and UO versions of SLP2 models (11). Karoonsoontawong and Waller also proposed the formulation and exact solution methods for the linear bilevel program of continuous NDP based on the multiorigin single-destination UO DTA, and they developed three metaheuristics for the multiorigin, multidestination, larger-size problem: simulated annealing, genetic algorithm, and Robust Dynamic Continuous Network Design Problem