This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. By investigating its Lagrangian dual and primal characterization, we derive a novel convex integer program for MESP and show that its continuous relaxation yields a near-optimal solution. The results motivate us to develop a sampling algorithm and derive its approximation bound for MESP, which improves the best known bound in literature. We then provide an efficient deterministic implementation of the sampling algorithm with the same approximation bound. Besides, we investigate the widely used local search algorithm and prove its first known approximation bound for MESP. The proof techniques further inspire for us an efficient implementation of the local search algorithm. Our numerical experiments demonstrate that these approximation algorithms can efficiently solve medium-size and large-scale instances to near optimality. Finally, we extend the analyses to the A-optimal MESP, for which the objective is to minimize the trace of the inverse of the selected principal submatrix. Funding: This work was supported by the National Science Foundation Division of Information and Intelligent Systems [Grant 2246417] and Division of Civil, Mechanical and Manufacturing Innovation [Grant 2246414]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2023.2488 .
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This content will become publicly available on July 1, 2024
Distributionally Robust Fair Transit Resource Allocation During a Pandemic
This paper studies the distributionally robust fair transit resource allocation model (DrFRAM) under the Wasserstein ambiguity set to optimize the public transit resource allocation during a pandemic. We show that the proposed DrFRAM is highly nonconvex and nonlinear, and it is NP-hard in general. Fortunately, we show that DrFRAM can be reformulated as a mixed integer linear programming (MILP) by leveraging the equivalent representation of distributionally robust optimization and monotonicity properties, binarizing integer variables, and linearizing nonconvex terms. To improve the proposed MILP formulation, we derive stronger ones and develop valid inequalities by exploiting the model structures. Additionally, we develop scenario decomposition methods using different MILP formulations to solve the scenario subproblems and introduce a simple yet effective no one left-based approximation algorithm with a provable approximation guarantee to solve the model to near optimality. Finally, we numerically demonstrate the effectiveness of the proposed approaches and apply them to real-world data provided by the Blacksburg Transit.
History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics.
Funding: This work was supported by the Division of Computing and Communication Foundations [Grant 2153607] and the Division of Civil, Mechanical and Manufacturing Innovation [Grant 2046426].
Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1159 .
more » « less- NSF-PAR ID:
- 10324122
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Transportation Science
- Volume:
- 57
- Issue:
- 4
- ISSN:
- 0041-1655
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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