LP-Rounding Based Algorithm for Capacitated Uniform Facility Location Problem with Soft Penalties

IF 6.6 1区计算机科学 Q1 Multidisciplinary

Tsinghua Science and Technology Pub Date : 2024-09-11 DOI:10.26599/TST.2024.9010040

Runjie Miao;Chenchen Wu;Jinjiang Yuan

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引用次数: 0

Abstract

Capacitated facility location problem (CFLP) is a classical combinatorial optimization problem that has various applications in operations research, theoretical computer science, and management science. In the CFLP, we have a potential facilities set and a clients set. Each facility has a certain capacity and an open cost, and each client has a spliitable demand that need to be met. The goal is to open some facilities and assign all clients to these open facilities so that the total cost is as low as possible. The CFLP is NP-hard (non-deterministic polynomial-hard), and a large amount of work has been devoted to designing approximation algorithms for CFLP and its variants. Following this vein, we introduce a new variant of CFLP called capacitated uniform facility location problem with soft penalties (CUFLPSP), in which the demand of each client can be partially rejected by paying penalty costs. As a result, we present a linear programming-rounding (LP-rounding) based 5.5122-approximation algorithm for the CUFLPSP.

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基于 LP 轮询的软惩罚容量均匀设施定位问题算法

产能设施定位问题（CFLP）是一个经典的组合优化问题，在运筹学、理论计算机科学和管理科学中有着广泛的应用。在 CFLP 中，我们有一个潜在设施集和一个客户集。每个设施都有一定的容量和开放成本，每个客户都有需要满足的可变需求。我们的目标是开放一些设施，并将所有客户分配到这些开放设施，从而尽可能降低总成本。CFLP 是 NP-hard（非确定性多项式-hard），已有大量工作致力于设计 CFLP 及其变体的近似算法。根据这一思路，我们引入了 CFLP 的一个新变体，称为带软惩罚的有容均匀设施定位问题（CUFLPSP），在该问题中，每个客户的需求都可以通过支付惩罚成本而被部分拒绝。因此，我们针对 CUFLPSP 提出了一种基于线性规划-rounding（LP-rounding）的 5.5122 近似算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Tsinghua Science and Technology COMPUTER SCIENCE, INFORMATION SYSTEMSCOMPU-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

10.20

自引率

10.60%

发文量

2340

期刊介绍： Tsinghua Science and Technology (Tsinghua Sci Technol) started publication in 1996. It is an international academic journal sponsored by Tsinghua University and is published bimonthly. This journal aims at presenting the up-to-date scientific achievements in computer science, electronic engineering, and other IT fields. Contributions all over the world are welcome.