摘要
我国城市义务教育学校采用单校划片或多校划片的方式确定招生范围,落实就近入学的法律要求.针对现有学校分区问题模型未考虑空间连续约束,构建空间连续约束单校划片和多校划片问题的整型规划模型.单校划片模型在满足学额、空间连续等分区约束的前提下,最小化学生入学距离;并在基本模型的基础上,将学额硬约束修改为软约束进一步改进模型.考虑到多校划片问题的复杂度极高,将该问题分解为学校分组和学生分派两个子问题求解.针对学校分组问题构建了基本模型和分区学额软约束模型.使用两个案例区对模型进行测试,结果表明:所设计的模型能够高效求解多校划片问题,也适用于一定规模的单校划片问题,其中软约束模型更容易求解.
School districting has been widely introduced for compulsory education.According to a new policy issued by the China Ministry of Education in 2016,a school district should consist of multiple schools for cities with uneven provision of compulsory schools.It aims to stabilize the apartment price in ‘hot＇school districts,and also to appease the public criticism on the phenomenon of school choice.This paper proposes several integer programming formulations for solving both single-school and multi-school districting problems.The basic model for classical single school districting is to minimize the total traveling distance of students while satisfying the constraints on districts such as spatial contiguity and school quotas.Two rewritten models convert the‘hard＇constraints on school quotas as‘soft＇constraints and minimize the over quotas as well as the total traveling distance.Due to the problem complexity of multi-school districting,it is solved by two sub-problems：school grouping problem and student assigning problem.Similar to single school districting,the basic model and two rewritten models are proposed for student assigning problem.The newly proposed models are tested on two regions.The model results show that the multi-school districting problem can be solved efficiently with optimal solutions,and the classical single-school districting problem can be solved efficiently with optimal or near-optimal solutions.We also find that the problem models with‘soft＇constraints have an advantage that can be solved more efficiently.
作者
孔云峰
朱艳芳
王玉璟
KONG Yunfeng ZHU Yanfang WANG Yujing(Key Laboratory of Geospatial Technology for the Middle and Lower Yellow River Regions, Ministry of Education, Henan University, Henan Kaifeng 475004, China College of Computer and Information Engineering, Henan University, Henan Kaifeng 475004, China)
出处
《河南大学学报（自然科学版）》
CAS
2017年第5期514-521,共8页
Journal of Henan University:Natural Science
基金
国家自然科学基金项目(41401461)
关键词
学校分区问题
多校划片
整型规划
空间连续约束
school districting problem
multi-school distrieting
integer programming
spatial contiguity
