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Unmanned aerial vehicles or drones are widely used or proposed to carry out various tasks in low-altitude airspace. To safely integrate drone traffic into congested airspace, the current concept of operations for drone traffic management will reserve a static traffic volume for the whole planned trajectory, which is safe but inefficient. In this paper, we propose a dynamic traffic volume reservation method for the drone traffic management system based on a multiscale A* algorithm. The planning airspace is represented as a multiresolution grid world, where the resolution will be coarse for the area on the far side. Therefore, each drone only needs to reserve a temporary traffic volume along the finest flight path in its local area, which helps release the airspace back to others. Moreover, the multiscale A* can run nearly in real-time due to a much smaller search space, which enables dynamically rolling planning to consider updated information. To handle the infeasible corner cases of the multiscale algorithm, a hybrid strategy is further developed, which can maintain a similar optimal level to the classic A* algorithm while still running nearly in real-time. The presented numerical results support the advantages of the proposed approach. 

This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process and develops an efficient search algorithm that is able to solve practical instances of the MIP model faster than commercial solvers. The formulation is novel for it directly maximizes the Gini reduction, an effective split selection criterion that has never been modeled in a mathematical program for its nonconvexity. The proposed approach differs from other optimal classification tree models in that it does not attempt to optimize the whole tree; therefore, the flexibility of the recursive partitioning scheme is retained, and the optimization model is more amenable. The approach is implemented in an open-source R package named bsnsing. Benchmarking experiments on 75 open data sets suggest that bsnsing trees are the most capable of discriminating new cases compared with trees trained by other decision tree codes including the rpart, C50, party, and tree packages in R. Compared with other optimal decision tree packages, including DL8.5, OSDT, GOSDT, and indirectly more, bsnsing stands out in its training speed, ease of use, and broader applicability without losing in prediction accuracy. History: Accepted by RamRamesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported by the National Science Foundation Division of Civil, MechanicalandManufacturing Innovation [Grant 1944068]. Supplemental Material: Data are available at https://doi.org/10.1287/ijoc.2022.1225 . 

The p-center location problem in an area is an important yet very difficult problem in location science. The objective is to determine the location of p hubs within a service area so that the distance from any point in the area to its nearest hub is as small as possible. While effective heuristic methods exist for finding good feasible solutions, research work that probes the lower bound of the problem’s objective value is still limited. This paper presents an iterative solution framework along with two optimization-based heuristics for computing and improving the lower bound, which is at the core of the problem’s difficulty. One method obtains the lower bound via solving the discrete version of the Euclidean p-center problem, and the other via solving a relatively easier clustering problem. Both methods have been validated in various test cases, and their performances can serve as a benchmark for future methodological improvements.

 

This paper introduces several means to expedite a known Voronoi heuristic method for solving a continuousp‐center location problem, which is to cover a polygon withpcircles such that no circle's center lies outside the polygon, no circle's center drops inside a polygonal hole, and the radius of the largest circle is as small as possible. A key step in the Voronoi heuristic is the repeated task of determining the constrained minimum covering circle (CMCC), but the best‐known method for this task is brute‐force and inefficient. This paper develops an improved method by exploiting the convexity of a related subproblem and employing an optimized search procedure. The algorithmic enhancements help to drastically reduce the effort required for finding the CMCC, and in turn, significantly expedite the solution of thep‐center problem. On a realistic‐scale test case, the proposed algorithm ran 400× faster than the literature benchmark.