Efficient Approximations for the Online Dispersion Problem

Chen, Jing; Li, Bo; Li, Yingkai

doi:10.1137/17m1131027

Cited by 3 publications

(1 citation statement)

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“…Jung (2016) developed methodologies for determining the optimal distributions of facilities by including a variety of distance constraints, one of which is related to process safety. Chen et al (2019) proposed the dispersion problem to locate n facilities in a k-dimensional polytope, so that they are far away from each other and from the boundary of the polytope. To the best of our knowledge, our paper is the first study of the facility location games that take the distance requirement and the agents' strategic behavior into consideration for strategyproof mechanism design.…”

Section: Related Workmentioning

confidence: 99%

Two-facility Location Games with Minimum Distance Requirement

Xu¹,

et al. 2021

jair

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We study the mechanism design problem of a social planner for locating two facilities on a line interval [0, 1], where a set of n strategic agents report their locations and a mechanism determines the locations of the two facilities. We consider the requirement of a minimum distance 0 ≤ d ≤ 1 between the two facilities. Given the two facilities are heterogeneous, we model the cost/utility of an agent as the sum of his distances to both facilities. In the heterogeneous two-facility location game to minimize the social cost, we show that the optimal solution can be computed in polynomial time and prove that carefully choosing one optimal solution as output is strategyproof. We also design a strategyproof mechanism minimizing the maximum cost. Given the two facilities are homogeneous, we model the cost/utility of an agent as his distance to the closer facility. In the homogeneous two-facility location game for minimizing the social cost, we show that any deterministic strategyproof mechanism has unbounded approximation ratio. Moreover, in the obnoxious heterogeneous two-facility location game for maximizing the social utility, we propose new deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound (7 − d)/6 for any deterministic strategyproof mechanism. We also design a strategyproof mechanism maximizing the minimum utility. In the obnoxious homogeneous two-facility location game for maximizing the social utility, we propose deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound 4/3. Besides, in the two-facility location game with triple-preference, where each facility may be favorable, obnoxious, indifferent for any agent, we further motivate agents to report both their locations and preferences towards the two facilities truthfully, and design a deterministic group strategyproof mechanism with an approximation ratio 4.

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Section: Related Workmentioning

confidence: 99%

Two-facility Location Games with Minimum Distance Requirement

Xu¹,

et al. 2021

jair

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Two-Facility Location Games with Distance Requirement

Gai

Qian²,

Wu³

2022

Frontiers of Algorithmic Wisdom

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An Efficient Optimization Model and Tabu Search–Based Global Optimization Approach for the Continuous p-Dispersion Problem

Lai,

Lin,

Hao

et al. 2024

INFORMS Journal on Computing

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Continuous p-dispersion problems with and without boundary constraints are NP-hard optimization problems with numerous real-world applications, notably in facility location and circle packing, which are widely studied in mathematics and operations research. In this work, we concentrate on general cases with a nonconvex multiply connected region that are rarely studied in the literature due to their intractability and the absence of an efficient optimization model. Using the penalty function approach, we design a unified and almost everywhere differentiable optimization model for these complex problems and propose a tabu search–based global optimization (TSGO) algorithm for solving them. Computational results over a variety of benchmark instances show that the proposed model works very well, allowing popular local optimization methods (e.g., the quasi-Newton methods and the conjugate gradient methods) to reach high-precision solutions due to the differentiability of the model. These results further demonstrate that the proposed TSGO algorithm is very efficient and significantly outperforms several popular global optimization algorithms in the literature, improving the best-known solutions for several existing instances in a short computational time. Experimental analyses are conducted to show the influence of several key ingredients of the algorithm on computational performance. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72122006, 71821001, and 72471100] Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0089 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0089 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

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Efficient Approximations for the Online Dispersion Problem

Cited by 3 publications

References 51 publications

Two-facility Location Games with Minimum Distance Requirement

Two-facility Location Games with Minimum Distance Requirement

Two-Facility Location Games with Distance Requirement

An Efficient Optimization Model and Tabu Search–Based Global Optimization Approach for the Continuous p-Dispersion Problem

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