Lagrangean decomposition: A model yielding stronger lagrangean bounds
Mathematical Programming: Series A and B
Lagrangian decomposition for integer nonlinear programming with linear constraints
Mathematical Programming: Series A and B
Solving makespan minimization problems with Lagrangean decomposition
Discrete Applied Mathematics
Genetic search methods in air traffic control
Computers and Operations Research
Lagrangian decomposition of block-separable mixed-integer all-quadratic programs
Mathematical Programming: Series A and B
Receding horizon control for aircraft arrival sequencing and scheduling
IEEE Transactions on Intelligent Transportation Systems
Dynamic network flow model for short-term air traffic flow management
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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An algorithm for optimal arrival flight sequencing and spacing in a near-terminal area is proposed. The optimization problem and algorithm proposed in this paper are developed for a decision-support tool for air-traffic control, which uses discrete delay times as optimization variables. The algorithm is applicable to various scenarios with situational and operational constraints such as maximum position shift (MPS) constraints or different sets of discrete delay times, depending on aircraft types or approaching routes. The proposed algorithm is based on a branch-and-bound algorithm with linear programming (LP) and Lagrangian dual decomposition. We formulate the sequencing and scheduling problem as LP with linear matrix inequalities (LMIs), which allows computing the lower bound of the cost for the best first search in the branch-and-bound algorithm and propose Lagrangian dual decomposition for computational efficiency. The proposed algorithm is analyzed and validated through illustrative air-traffic scenarios with various operational constraints, and the simulation results show that the computation time can be significantly reduced using the proposed Lagrangian dual-decomposition method.