学校分区问题混合元启发算法研究

中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。针对多校划片这一新的学校分区问题,提出“先学校分组,再学生分派”的策略进行划片,并设计了学校分组线性规划模型和学校分区混合元启发算法。分区算法包括初始解构造、邻域搜索算子、破坏重建扰动、集合划分问题（SPP）建模与求解等基本模块,在多启动迭代局部搜索（ILS）算法框架中进行问题求解。通过多启动、随机搜索、破坏重建扰动等机制提升算法的多样性,并引入SPP模型提升算法的全局寻优能力。选择一个县级市和一个市辖区分别进行学校划片实验,结果表明：混合元启发算法优化性能优异且收敛性好,适用于求解单校划片和多校划片问题;SPP模型在单校划片问题中具有明显的优势。     

MOTS算法在空间分区问题中的应用研究

空间分区问题是将基本的空间单元遵照多个规划准则组合成若干较大簇即空间区域的过程,保证区片的连续性是其空间硬约束条件。近年来,空间分区问题在政治选举区域划分,市政公共设施选址布局,社会紧急服务以及商业销售区域的划分等领域有着十分重要的应用。目前,空间分区问题的研究成果较为零散,缺乏较系统的归纳和总结,而且其应用也大多集中在传统领域。为此,本文对空间分区问题的通用模型进行了总结,并对多目标禁忌搜索算法解决此类问题的流程和核心问题作了详细阐述,最后本文将研究成果应用到江夏区高产农田整理区片自动划分中,并取得了较好的效果。     

利用GIS与线性规划学校最优学区划分

利用运筹学线性规划方法,在GIS软件支持下进行中小学最优学区划分。以就近入学为目标,依据学校、居民点及道路网络构建最优学区划分的整型规划模型,利用ArcGIS 10软件开发了最优学区划分工具。实验表明,优化模型能获得最优目标,且效率较高,所开发的优化工具使用简便,实用性强。     

A non-dominated sorting genetic algorithm for the location and districting planning of earthquake shelters

The improvement of emergency coping capacity is one of the most efficient measures for mitigating disaster impact. Shelter planning is an important strategy to reduce the number of casualties and injuries and facilitate disaster recovery. This study aims to address earthquake shelter location selection and the districting planning of service areas jointly. A bi-objective model is proposed to minimise the total evacuation distance and the total cost, subject to capacity and contiguity constraints. A non-dominated sorting genetic algorithm is developed to tackle the bi-objective model, which involves a multitude of decision variables. To fit the model, the chromosome structure, initialisation process and genetic operators in the algorithm are specifically designed to maintain the contiguity of the service area. And a hybrid strategy of bidirectional multi-point crossover and bidirectional single-point crossover helps promote the diversity of the solutions and accelerate the convergence. Moreover, the Pareto-optimal strategy and feasibility-based rule are combined to obtain trade-offs between objectives. The model and algorithm are validated in a case study of the earthquake shelter location and districting planning problem in Chaoyang District of Beijing, and the results confirm the effectiveness and efficiency of the method.     

An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems

A measure of shape compactness is a numerical quantity representing the degree to which a shape is compact. Ways to provide an accurate measure have been given great attention due to its application in a broad range of GIS problems, such as detecting clustering patterns from remote-sensing images, understanding urban sprawl, and redrawing electoral districts to avoid gerrymandering. In this article, we propose an effective and efficient approach to computing shape compactness based on the moment of inertia (MI), a well-known concept in physics. The mathematical framework and the computer implementation for both raster and vector models are discussed in detail. In addition to computing compactness for a single shape, we propose a computational method that is capable of calculating the variations in compactness as a shape grows or shrinks, which is a typical application found in regionalization problems. We conducted a number of experiments that demonstrate the superiority of the MI over the popular isoperimetric quotient approach in terms of (1) computational efficiency; (2) tolerance of positional uncertainty and irregular boundaries; (3) ability to handle shapes with holes and multiple parts; and (4) applicability and efficacy in districting/zonation/regionalization problems.     

Multi-Objective Analysis of School District Regionalization Alternatives in Connecticut*

This paper demonstrates the utility of multi-objective programming techniques as an aid in educational planning and the limitations to the achievement of any educational objective given the spatial distribution of existing disparities. A case study of Connecticut is used to examine alternative scenarios for the implementation of interdistrict responses to a number of issues facing the state's public education system. A mixed-integer, goal programming model is formulated where the goal constraints are to minimize disparities in: (1) minority enrollments, (2) grand-list/student ratios, (3) student-teacher ratios, and (4) overall enrollment. Results show that the traditional distance-minimizing or transportation-minimizing objectives are in conflict with all other aims of equity and quality of educational opportunities. The geographic distribution of minority students and grand-list property values also limited the reduction of statewide disparities in these goals.