Construction and solution of a multi-objective hierarchical fuzzy optimization model for fire station location considering risk levels

doi:10.11947/j.AGCS.2026.20260070

Abstract

Abstract:

Optimizing fire station location to improve emergency rescue efficiency is an urgent issue in urban development. This study investigates fire station location from three aspects: model construction, solution, and evaluation, aiming to optimize the spatial layout of fire stations. Firstly, based on differences in station attributes and fire response demands, we classify risk levels and set corresponding response times. Considering factors such as cost, coverage rate, and response timeliness, we adopt a multi-objective hierarchical optimization modeling approach to establish a two-level objective function of quantity and distance. Secondly, using the road network, we define a path distance measure and replace traditional linear constraints with fuzzy nonlinear membership functions, thereby constructing a fuzzy multi-objective hierarchical location model based on path distance, named R-NLSM. Finally, the fuzzy membership functions are embedded into both genetic algorithm (GA) and particle swarm optimization (PSO) algorithms, and the two algorithms are employed to solve the model. Experimental results show that the overall response coverage rate increases by 16.69 percentage points after optimization, demonstrating the effectiveness and stability of the proposed model. Moreover, the model improves the matching between different risk levels and fire rescue efficiency, and ensures timely response for highrisk demand points. This work provides a methodological reference and technical pathway for fire station location and layout optimization.

Key words: fire station, risk level, multi-objective hierarchical optimization, nonlinear fuzzy membership, improved genetic algorithm

CLC Number:

P208

Lin Liu, Dongmei Pei, Wanwu Li, Xiutao Tang, Bin Wu, Yan Jin. Construction and solution of a multi-objective hierarchical fuzzy optimization model for fire station location considering risk levels[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(7): 1293-1305.

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References 29

[1]	马小林, 昌伟伟. 基于事故致因链的天津港“8.12”火灾爆炸事故分析[J]. 安全, 2022, 43(5): 56-61.
	Ma Xiaolin, Chang Weiwei. Analysis on Tianjin Port “8.12” fire and explosion accident based on accident causation chains[J]. Safety & Security, 2022, 43(5): 56-61.
[2]	太原冰雕馆“10•1”重大火灾事故51人被追责[J]. 中国消防, 2021(10): 39.
	51 people held accountable for the major fire accident at Taiyuan Ice Sculpture Hall on October 1[J]. China Fire Protection, 2021 (10): 39.
[3]	肖方. 强化责任担当抓好贯彻落实坚决遏制重特大火灾事故切实维护人民群众生命财产安全[J]. 中国消防, 2022(2): 7-9.
	Xiao Fang. Strengthen responsibility and commitment, implement thoroughly, resolutely curb major and extraordinarily serious fire accidents, and effectively safeguard the safety of people's lives and property[J]. China Fire, 2022(2): 7-9.
[4]	Ma Chengye, Song Mingxing, Zeng Weitao, et al. Enhancing urban emergency response: a Euclidean distance-based framework for optimizing rescue facility layouts[J]. Sustainable Cities and Society, 2025, 118: 106006.
[5]	Chen Yulong, Yao Jing, Wang Shaohua, et al. Location optimization of urban fire stations considering the variations in fire service demands: a bi-objective coverage model[J]. International Journal of Digital Earth, 2025, 18(1): 2454386.
[6]	Zhu Jingjing, Xu Xiangdong, Yang Xin. Spatial accessibility measurement of urban fire stations considering multi-path characteristic of road networks[J]. Journal of Transport Geography, 2025, 126: 104248.
[7]	徐志标, 萧颖莹. 基于火灾风险评估的城市消防设施选址优化研究——以广东省高州市中心城区为例[J]. 上海城市规划, 2020(6): 117-123.
	Xu Zhibiao, Xiao Yingying. Location optimization of urban fire facilities based on fire risk assessment: a case study of urban center in Gaozhou, Guangdong[J]. Shanghai Urban Planning Review, 2020(6): 117-123.
[8]	He Qize, Xue Lin, Yang Yun, et al. Research on Chinese fire station optimal location model based on fire risk statistics: case study in Shanghai[J]. Applied Sciences, 2024, 14(5): 2052.
[9]	裴冬梅. 基于模糊隶属度函数的消防设施布局多目标优化及求解[D]. 青岛: 山东科技大学, 2023: 1-77.
	Pei Dongmei. Multi-objective optimization and solution of fire facilities layout based on fuzzy membership function[D]. Qingdao: Shandong University of Science and Technology, 2023: 1-77.
[10]	Drezner Z, Brimberg J, Schöbel A. Dispersed starting solutions in facility location: the case of the planar P-median problem[J]. Computers & Operations Research, 2024, 169: 106726.
[11]	Zhang Yao, Wang Shaohua, Liang Haojian, et al. Dual hybrid frameworks combining graph convolutional network with decoding for covering location problem[J]. iScience, 2024, 27(5): 109803.
[12]	Ma Xiaoya, Zhang Xiaoyu, Zhao Xiang. Service coverage optimization for facility location: considering line-of-sight coverage in continuous demand space[J]. International Journal of Geographical Information Science, 2023, 37(7): 1496-1519.
[13]	Mu Wangshu, Li Changfeng. Optimization of urban greenway route using a coverage maximization model for lines[J]. Computers, Environment and Urban Systems, 2024, 112: 102155.
[14]	刘勇, 刘宇轩, 马良. 基于算子学习的多目标深度强化学习模型求解消防设施选址问题[J]. 计算机应用研究, 2025, 42(2): 477-485.
	Liu Yong, Liu Yuxuan, Ma Liang. Multi-objective deep reinforcement learning model based on operator learning for solving fire facility location problems[J]. Application Research of Computers, 2025, 42(2): 477-485.
[15]	尚春剑, 宁爱兵, 彭大江, 等. P-中心选址问题的一种降阶回溯算法[J]. 计算机应用研究, 2021, 38(03): 734-737.
	Shang Chunjian, Ning Aibing, Peng Dajiang, et al. Backtracking algorithm with reduction for P-center location problem[J]. Application Research of Computers, 2021, 38(3): 734-737, 769.
[16]	Yao Jing, Zhang Xiaoxiang, Murray A T. Location optimization of urban fire stations: access and service coverage[J]. Computers, Environment and Urban Systems, 2019, 73: 184-190.
[17]	Chen Mengmeng, Wang Kai, Yuan Yingfeng, et al. A POIs based method for location optimization of urban fire station: a case study in Zhengzhou city[J]. Fire, 2023, 6(2): 58.
[18]	谢小川, 许建梅, 黎明. 基于海象算法的模糊多目标高校校区微型消防站选址优化[J]. 四川大学学报(自然科学版), 2025, 62(6): 1385-1398.
	Xie Xiaochuan, Xu Jianmei, Li Ming. Fuzzy multi-objective optimization for micro fire station location on university campuses using the walrus algorithm[J]. Journal of Sichuan University (Natural Science Edition), 2025, 62(6): 1385-1398.
[19]	Han Bing, Hu Mingxing, Zheng Jiemin, et al. Site selection of fire stations in large cities based on actual spatiotemporal demands: a case study of Nanjing city[J]. ISPRS International Journal of Geo-Information, 2021, 10(8): 542.
[20]	王雅荣, 赵海鹏, 周慰涛, 等. 整合多因素影响的城市消防站布局优化实践[J]. 消防科学与技术, 2024, 43(4): 551-556.
	Wang Yarong, Zhao Haipeng, Zhou Weitao, et al. Practice of optimizing the layout of urban fire stations by integrating multiple factors[J]. Fire Science and Technology, 2024, 43(4): 551-556.
[21]	陈振, 王伟贤, 李卓群, 等. 基于多因子约束P中值模型的充电桩布局优化研究[J]. 北京交通大学学报, 2021, 45(3): 93-99.
	Chen Zhen, Wang Weixian, Li Zhuoqun, et al. Study on optimization of charging pile layout based on multi-factor constrained P-median model[J]. Journal of Beijing Jiaotong University, 2021, 45(3): 93-99.
[22]	Jiang Yuncheng, Lü Aifeng, Yan Zhigang, et al. A GIS-based multi-criterion decision-making method to select city fire brigade: a case study of Wuhan, China[J]. ISPRS International Journal of Geo-Information, 2021, 10(11): 777.
[23]	于志金, 徐澜, 陈霜霜, 等. 基于模型交点法的城市消防站布局规划[J]. 中国安全科学学报, 2022, 32(10): 178-185.
	Yu Zhijin, Xu Lan, Chen Shuangshuang, et al. Research on urban fire station layout planning based on model intersection method[J]. China Safety Science Journal, 2022, 32(10): 178-185.
[24]	Shahparvari S, Fadaki M, Chhetri P. Spatial accessibility of fire stations for enhancing operational response in Melbourne[J]. Fire Safety Journal, 2020, 117: 103149.
[25]	Levin M S. P-center problem[J]. Journal of Communications Technology and Electronics, 2025, 70(7): 360-387.
[26]	Nyimbili P H, Erden T. GIS-based fuzzy multi-criteria approach for optimal site selection of fire stations in Istanbul, Turkey[J]. Socio-Economic Planning Sciences, 2020, 71: 100860.
[27]	Yu Wenhao, Chen Yujie, Guan Menglin. Hierarchical siting of macro fire station and micro fire station[J]. Environment and Planning B: Urban Analytics and City Science, 2021, 48(7): 1972-1988.
[28]	He Junjie, Guan Xin, Lu Houjun, et al. Research on multi-objective hierarchical site selection coverage of fire station[J]. PLoS One, 2024, 19(12): e0309731.
[29]	Zuo Chenyu, Xu Yifan, Ding Lingfang, et al. ST-Map: an interactive map for discovering spatial and temporal patterns in bibliographic data[J]. Journal of Geodesy and Geoinformation Science, 2024, 7(1): 3-15.

火灾风险因子	POI类型
易燃易爆类	加气站，加油站，生产、储存及销售易燃易爆品的工厂及企业等
人群脆弱类	医院及诊所、养老院、各类学校及幼儿园等婴幼儿服务场所
重要场所类	县（区）及以上政府机关、公检法部门、科研单位、图书馆、博物馆、档案馆、外国派驻机构、历史文化遗迹等
人员密集类	市场和商场等经营场所，娱乐场所，酒店，机场、火车站、汽车站等交通枢纽
一般消防类	办公楼区，居民区，除化工厂外的公司企业、产业园区、体育休闲服务场所、生活服务场所4类之外的其他POI点

因素	权重	归一化权重
易燃易爆类	1.626	0.3
人群脆弱类	1.220	0.2
重要场所类	0.850	0.2
人员密集类	1.016	0.2
一般消防类	0.610	0.1

火灾风险等级	到达时间限制/min	火灾地点距离限制/km
A	[4，5)	[4，5)
B	[5，10)	[5，10)
C	[10，20]	[10，20]

λ取值	响应覆盖率/（%）
λ取值	A级	B级	C级	总体
1.0	70.40	66.22	51.27	61.86
1.5	87.79	77.62	54.59	69.00
2.0	100.00	92.23	61.21	83.13
2.5	98.67	67.65	61.43	68.69
3.0	98.61	72.23	58.39	70.39

风险等级	GA算法优化后覆盖率				PSO算法优化后覆盖率
风险等级	MCLP	P-center	P-median	R-NLSM	MCLP	P-center	P-median	R-NLSM
A	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00
B	90.51	93.62	89.99	92.23	78.88	84.67	89.69	90.42
C	47.87	50.70	53.10	61.21	60.15	57.53	58.41	59.56
所有	80.21	80.59	79.24	83.13	74.83	77.53	80.29	81.55