An Improved Exact $\varepsilon$-Constraint and Cut-and-Solve Combined Method for Biobjective Robust Lane Reservation

This study investigates a new biobjective lanereservation problem, which is to exclusively reserve lanes from an existing transportation network for special transport tasks with given deadlines. The objectives are to minimize the total negative impact on normal traffic due to the reduction of available lanes for general-purpose vehicles and to maximize the robustness of the lane-reservation solution against the uncertainty in link travel times. We first define the robustness for the lanereservation problem and formulate a biobjective mixed-integer linear program. Then, we develop an improved exact ε-constraint and a cut-and-solve combined method to generate its Pareto front. Computational results for an instance based on a real network topology and 220 randomly generated instances with up to 150 nodes, 600 arcs, and 50 tasks demonstrate that the proposed method is able to find the Pareto front and that the proposed cut-and-solve method is more efficient than the direct use of optimization software CPLEX.