基于交通网络的乡村中小学优化布局

doi:10.12082/dqxxkx.2020.190443

地球信息科学学报 ›› 2020, Vol. 22 ›› Issue (5): 1120-1132.doi: 10.12082/dqxxkx.2020.190443

• “空间综合人文学与社会科学”专辑 • 上一篇下一篇

基于交通网络的乡村中小学优化布局

陈玉龙^1,², 赖志柱³, 王铮^2,^3,^*()

1.河南大学黄河文明与可持续发展研究中心暨黄河文明传承与现代文明建设河南省协同创新中心,开封 475001
2.河南大学环境与规划学院,开封 475004
3.华东师范大学地理信息科学教育部重点实验室,上海 200241

收稿日期:2019-08-13 修回日期:2019-12-07 出版日期:2020-05-25 发布日期:2020-07-25
通讯作者: 王铮 E-mail:wangzheng@casipm.ac.cn
作者简介:陈玉龙（1989— ）,男,河南栾川人,博士,讲师,主要从事地理计算研究。E-mail:chenyulong0203@163.com
基金资助:
国家自然科学基金项目(41671396)

Optimization of Rural Primary and Secondary School Location based on Traffic Network

CHEN Yulong^1,², LAI Zhizhu³, WANG Zheng^2,^3,^*()

1. Key Research Institute of Yellow River Civilization and Sustainable Development & Collaborative Innovation Center on Yellow River Civilization of Henan Province, Henan University, Kaifeng 475001, China
2. College of Environment and Planning, Henan University, Kaifeng 475004, China
3. Key Laboratory of Geographical Information Science, Ministry of Education of China, East China Normal University, Shanghai 200241, China

Received:2019-08-13 Revised:2019-12-07 Online:2020-05-25 Published:2020-07-25
Contact: WANG Zheng E-mail:wangzheng@casipm.ac.cn
Supported by:
National Natural Science Foundation of China(41671396)

摘要/Abstract

摘要：

合理规划中小学布局是优化教育资源配置、提高办学效益以及实现教育均衡发展的重要途径。本研究针对中国乡村建设的需要和中国多山的地理环境,考虑山地环境对乡村中小学选址的影响,构建多山环境下乡村中小学的区位模型,运用地理信息科学方法,以Visual Studio. Net 2010为开发平台,使用C#语言和ArcGIS Engine 10.0组件库,同时结合MATLAB编程,开发出基于交通网络的乡村中小学区位优化系统。最后将系统应用于贵州省某镇的小学布局优化中,分别在只考虑已有道路、假设道路可升级、假设道路可新建或升级3种情景下,通过改进的模拟退火算法,确定新建学校的最佳位置,以及新道路的修建和原有道路的升级情况,从而得到不同情景下各居民点学生的上学耗时。结果表明,交通网络对乡村中小学布局优化具有重要影响,改善交通网络条件能够有效提高学生的就学效率上学速度。

关键词: 乡村中小学, 交通网络, 学校布局, 区位优化, 山区, 多目标设施区位-网络设计模型, 模拟退火算法, 贵州省

Abstract:

The rational planning of school location is an important way to optimize the allocation of educational resources, improve the efficiency of school running and realize the balanced development of education. The accessibility must be considered in optimizing the location of rural schools, which is an important difference from the location of urban schools. Many scholars have studied the location problem of rural schools, but most of them have neglected the impact of transportation network conditions on the location of schools. On the basis of previous studies, this study will consider the impact of traffic network on the optimization location of primary schools in mountainous environment. The object of this study is to minimize the total transportation costs for students, construction costs for new schools, construction and upgrade costs for roads on a traffic network. We regard a set of villages as demand nodes exists in a geographical region, a set of roads as transfer links. The road links in the network contain existing and new potential road links. A set of schools exists in the region and it is clearly desired to locate a set of new schools, to construct new road links, to improve the existing road links such that the total investment costs (including the travel costs for students, construction costs for school facilities, construction and upgrading costs for roads) are minimized. Thus, a multi-objective optimization model for this problem is proposed. The multi-objective facility location-network design model constructed in this paper is an extension of FLNDP problem, and also belongs to NP-hard problem. In order to facilitate the model application, this study use geographic information science method, take Visual Studio. Net 2010 as the development platform, use C# language, MATLAB language and ArcGIS Engine 10 component library to develop a location optimization system of rural primary and secondary school based on transportation network. Finally, the system is applied to the optimization of the primary school location of a town in Guizhou province. Aiming at the location optimization problem of rural primary, this paper considers three scenarios (only consider the existing road, assume that the road can be upgraded and the road can be built or upgraded) which are different from the problem of urban primary school location. In geographic calculation, this paper explores an improved multi-objective simulated annealing algorithm to determine the best location of new schools, as well as the construction of new roads and the upgrading of existing roads.

Key words: rural primary and high school, traffic network, school location, location optimization, mountain area, multi-objective facility location network design model, simulated annealing algorithm, Guizhou

陈玉龙, 赖志柱, 王铮. 基于交通网络的乡村中小学优化布局[J]. 地球信息科学学报, 2020, 22(5): 1120-1132.DOI:10.12082/dqxxkx.2020.190443

CHEN Yulong, LAI Zhizhu, WANG Zheng. Optimization of Rural Primary and Secondary School Location based on Traffic Network[J]. Journal of Geo-information Science, 2020, 22(5): 1120-1132.DOI:10.12082/dqxxkx.2020.190443

图/表 13

图1

图2

表1

图3

图4

图5

表2

情景1 Pareto最优解对应的方案及目标值"

方案编号	新建设施个数 $(p)$	设施选址位置	旅行成本（第一目标值）	设施建设成本（第二目标值）
1	$1$	1	1 642 335	400 000
2	$1$	15	1 488 424	450 000
3	$2$	1,22	1 495 064	800 000
4	$2$	1,15	1 331 460	850 000
5	$2$	15,21	1 315 524	900 000
6	$2$	15,17	1 303 802	1 000 000
7	$3$	15,17,21	1 130 902	1 450 000
8	$3$	1,15,21	1 158 560	1 300 000
9	$3$	1,11,22	1 379 636	1 200 000
10	$3$	1,11,15	1 216 032	1 250 000
11	$3$	9,15,17	1 121 438	1 550 000
12	$3$	1,15,17	1 146 838	1 400 000

表2

图6

表3

情景2 Pareto最优解对应的方案及目标值"

方案编号	新建设施个数 $(p)$	设施选址位置	旅行成本（第一目标值）	建设成本（第二目标值）
1	$1$	15	1 295 687	559 000
2	$1$	15	1 132 810	787 155
3	$1$	15	1 068 135	890 765
4	$1$	15	1 002 049	991 840
5	$1$	15	864 630	1 271 470
6	$1$	15	807 618	1 431 305
7	$2$	15,17	1 000 392	1 267 605
8	$2$	15,17	855 648	1 466 570
9	$2$	15,17	742 158	1 687 960
10	$2$	15,17	713 800	1 736 255
11	$2$	15,17	655 768	1 865 215
12	$2$	15,17	622 996	1 981 305
13	$2$	15,17	610 746	2 078 610
14	$2$	15,17	593 241	2 195 025
15	$2$	15,17	553 786	2 313 000
16	$3$	1,15,17	857 898	1 712 325
17	$3$	1,15,17	750 337	1 874 305
18	$3$	1,15,17	692 305	2 003 265
19	$3$	1,15,17	580 291	2 118 835
20	$3$	1,15,17	548 536	2 199 760
21	$3$	1,15,17	536 285	2 297 065
22	$3$	1,15,17	508 400	2 458 200

表3

图7

表4

情景3 Pareto最优解对应的方案及目标值"

方案编号	新建设施个数 $(p)$	设施选址位置	旅行成本（第一目标值）	建设成本（第二目标值）
1	$1$	15	969 011	1 049 911
2	$1$	15	909 984	1 176 466
3	$1$	15	797 970	1 292 036
4	$1$	15	764 372	1 420 996
5	$1$	15	752 155	1 479 340
6	$1$	15	720 408	1 560 265
7	$1$	15	689 716	1 781 031
8	$2$	15,17	861 953	1 458 445
9	$2$	15,17	805 014	1 580 320
10	$2$	15,17	717 808	1 753 675
11	$2$	15,17	650 227	1 782 035
12	$2$	15,17	567 661	1 932 035
13	$2$	15,17	549 277	2 012 960
14	$2$	15,17	521 388	2 174 095
15	$2$	15,17	506 368	2 292 070
16	$3$	15,17,21	897 560	1 859 931
17	$3$	15,17,21	736 467	2 098 156
18	$3$	15,17,21	646 687	2 308 041
19	$3$	15,17,21	522 456	2 481 955
20	$3$	15,17,21	515 037	2 549 215
21	$3$	15,17,21	400 220	2 724 416
22	$3$	15,17,21	372 331	2 885 551

表4

图8

图9

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算法	NN		MGD		SP		平均时间/s
算法	平均值/个	总和/个	平均值	标准方差	平均值	标准方差	平均时间/s
MOSA	7	216	537.41	246.30	924.29	639.11	84.77
NSGA-II	15	456	276.30	106.20	726.30	315.65	68.62
IMOSA	22	647	130.60	40.12	525.14	170.04	59.53

基于交通网络的乡村中小学优化布局

Optimization of Rural Primary and Secondary School Location based on Traffic Network

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