Improving the performance of genetic algorithms for land-use allocation problems

Multi-objective optimization can be used to solve land-use allocation problems involving multiple conflicting objectives. In this paper, we show how genetic algorithms can be improved in order to effectively and efficiently solve multi-objective land-use allocation problems. Our focus lies on improving crossover and mutation operators of the genetic algorithms. We tested a range of different approaches either based on the literature or proposed for the first time. We applied them to a land-use allocation problem in Switzerland including two conflicting objectives: ensuring compact urban development and reducing the loss of agricultural productivity. We compared all approaches by calculating hypervolumes and by analysing the spread of the produced non-dominated fronts. Our results suggest that a combination of different mutation operators, of which at least one includes spatial heuristics, can help to find well-distributed fronts of non-dominated solutions. The tested modified crossover operators did not significantly improve the results. These findings provide a benchmark for multi-objective optimization of land-use allocation problems with promising prospectives for solving complex spatial planning problems.     

An improved artificial bee colony algorithm for optimal land-use allocation

Land-use allocation is of great importance for rapid urban planning and natural resource management. This article presents an improved artificial bee colony (ABC) algorithm to solve the spatial optimization problem. The new approach consists of a heuristic information-based pseudorandom initialization (HIPI) method for initial solutions and pseudorandom search strategy based on a long-chain (LC) mechanism for neighborhood searches; together, these methods substantially improve the search efficiency and quality when handling spatial data in large areas. We evaluated the approach via a series of land-use allocation experiments and compared it with particle swarm optimization (PSO) and genetic algorithm (GA) methods. The experimental results show that the new approach outperforms the current methods in both computing efficiency and optimization quality.     

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。     

Spatial optimization for regionalization problems with spatial interaction: a heuristic approach

Spatial optimization techniques are commonly used for regionalization problems, often represented as p-regions problems. Although various spatial optimization approaches have been proposed for finding exact solutions to p-regions problems, these approaches are not practical when applied to large-size problems. Alternatively, various heuristics provide effective ways to find near-optimal solutions for p-regions problem. However, most heuristic approaches are specifically designed for particular geographic settings. This paper proposes a new heuristic approach named Automated Zoning Procedure-Center Interchange (AZP-CI) to solve the p-functional regions problem (PFRP), which constructs regions by combining small areas that share common characteristics with predefined functional centers and have tight connections among themselves through spatial interaction. The AZP-CI consists of two subprocesses. First, the dissolving/splitting process enhances diversification and thereby produces an extensive exploration of the solution space. Second, the standard AZP locally improves the objective value. The AZP-CI was tested using randomly simulated datasets and two empirical datasets with different sizes. These evaluations indicate that AZP-CI outperforms two established heuristic algorithms: the AZP and simulated annealing, in terms of both solution quality and consistency of producing reliable solutions regardless of initial conditions. It is also noted that AZP-CI, as a general heuristic method, can be easily extended to other regionalization problems. Furthermore, the AZP-CI could be a more scalable algorithm to solve computational intensive spatial optimization problems when it is combined with cyberinfrastructure.     

Optimal spatial allocation of water resources based on Pareto ant colony algorithm

The spatial allocation of water resources is optimised using the multi-objective functions and multi-constrained conditions of the Pareto ant colony algorithm (PACA). The objective function is the highest benefit to the economy, society and the environment, while the constraints include water supply, demand and quality. The PACA is improved by limiting local pheromone scope and dynamically updating global pheromone levels. Since both strategies guide the ant towards borders of high-pheromone concentration, the new approach enhances the global search capability and convergence speed. Programming, database management and interface tools are then integrated into geographic information systems (GIS) software. The study area is located in Zhenping County, Henan Province, China, and water resource data are obtained using remote sensing (RS) and GIS technology. The improved PACA is solved in the GIS environment. Optimal spatial allocation schemes are obtained for surface, ground and transferred water and the model yields optimal spatial benefit schemes of water resources, embracing economic, social and ecological benefits. The results of improved PACA are superior to those of other intelligent optimisation algorithms, including the ant colony algorithm, multi-objective genetic algorithm and back-propagation artificial neural network. Therefore, the integration of RS, GIS and PACA can effectively optimise the large-scale, multi-objective allocation of water resources. The model also enhances the global search capability, convergence speed and result precision, and can potentially solve other optimal spatial problems with multi-objective functions.     

基于GIS的任意发生元Voronoi图逼近方法

许多地理问题的空间分析中需要采用Voronoi图,但是目前我们尚缺乏一些简单的易于实现的构建任意发生元Voronoi图的方法,也缺乏一个能直接生成任意发生元Voronoi图的软件,为此我们提出了一种基于GIS的构建任意发生元的未加权Voronoi图的逼近方法。首先用有限点来逼近原始发生元,然后构建这些点发生元Voronoi图,最后消除那些属于同一发生元的顶点和边,即得到原始发生元的逼近的Voronoi图。在该算法的具体实现过程中,充分利用了现有GIS软件可以生成点发生元Voronoi图的特性和处理空间数据的能力。试验结果表明,这种方法可以生成未加权的任意形状发生元的逼近Voronoi图,能满足地理问题空间分析的需要。如地理客体可以是点状地理客体(城市、县城、交通枢纽、商业中心和金融中心等)、线状地理客体(交通运输线、经济地带和河系等)、面状地理客体(经济区、公园和绿地等)或者它们的组合,它们的空间影响范围或空间服务范围都可以采用Voronoi图来界定。     

Development of Voronoi-based cellular automata -an integrated dynamic model for Geographical Information Systems

This paper presents a development of the extended Cellular Automata (CA), a Voronoi-based CA, to model dynamic interactions among spatial objects. Cellular automata are efficient models for representing dynamic spatial interactions. A complex global spatial pattern is generated by a set of simple local transition rules. However, its original definition for a two-dimensional array limits its application to raster spatial data only. This paper presents a newly developed Voronoi-based CA in which the CA is extended by using the Voronoi spatial model as its spatial framework. The Voronoi spatial model offers a ready solution to handling neighbourhood relations among spatial objects dynamically. By implementing this model, we have demonstrated that the Voronoi-based CA can model local interactions among spatial objects to generate complex global patterns. The Voronoi-based CA can further model interactions among point, line and polygon objects with irregular shapes and sizes in a dynamic system. Each of these objects possesses its own set of attributes, transition rules and neighbourhood relationships. The Voronoi-based CA models spatial interactions among real entities, such as shops, residential areas, industries and cities. Compared to the original CA, the Voronoi-based CA is a more natural and efficient representation of human knowledge over space.     

遗传算法和GIS结合进行空间优化决策

资源的有效利用和管理往往涉及到空间的优化配置问题。例如需要在空间上确定n个设施的最佳位置。当选址问题涉及多个目标和不同的约束性条件时,就会变得十分复杂。利用一般的brute-force搜索方法无法对涉及高维数据的问题进行求解。利用遗传算法和GIS结合来解决复杂的空间优化配置问题,具有智能的搜索方法可以大大提高空间的搜索能力。在基于进化的优化过程中,根据GIS的空间数据来计算不同解决方案 (染色体) 的适应度。针对不同的应用目的,GIS可以给出不同的适应度函数。实验表明,所提出的方法比简单的搜索方法和退火算法有更大的优越性。该方法在处理复杂的空间优化问题有更好的表现。     

Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space

This paper presents a new derivative-free search method for finding models of acceptable data fit in a multidimensional parameter space. It falls into the same class of method as simulated annealing and genetic algorithms, which are commonly used for global optimization problems. The objective here is to find an ensemble of models that preferentially sample the good data-fitting regions of parameter space, rather than seeking a single optimal model. (A related paper deals with the quantitative appraisal of the ensemble.)
  The new search algorithm makes use of the geometrical constructs known as Voronoi cells to derive the search in parameter space. These are nearest neighbour regions defined under a suitable distance norm. The algorithm is conceptually simple, requires just two 'tuning parameters', and makes use of only the rank of a data fit criterion rather than the numerical value. In this way all difficulties associated with the scaling of a data misfit function are avoided, and any combination of data fit criteria can be used. It is also shown how Voronoi cells can be used to enhance any existing direct search algorithm, by intermittently replacing the forward modelling calculations with nearest neighbour calculations.
  The new direct search algorithm is illustrated with an application to a synthetic problem involving the inversion of receiver functions for crustal seismic structure. This is known to be a non-linear problem, where linearized inversion techniques suffer from a strong dependence on the starting solution. It is shown that the new algorithm produces a sophisticated type of 'self-adaptive' search behaviour, which to our knowledge has not been demonstrated in any previous technique of this kind.     

Spatial analysis weighting algorithm using Voronoi diagrams

Data layers that represent geographical constraints in a multidimensional GIS model must be appropriately weighted to effectively account for the diversity as well as the functional and spatial interrelationships between the constraints. This paper presents a spatial analysis weighting algorithm (SAWA) using Voronoi diagrams. The basic functions of the SAWA are defined so that the spatialization of weights is done according to two approaches: a global spatialization method based on the statistical distribution of the original data and a contextual approach where neighbourhood defined by Voronoi diagrams is integrated into the weighting functions. Different simulations on artificial and real maps applied to the problem of shortest path optimisation are analysed. The results show that the effective integration of the spatial dimension in a weighting process is not only possible but also improves the optimisation of shortest paths. Research is continuing to improve the contextual phase of the algorithm.     

A modified particle swarm optimization algorithm for optimal allocation of earthquake emergency shelters

Allocation for earthquake emergency shelters is a complicated geographic optimization problem because it involves multiple sites, strict constraints, and discrete feasible domain. Huge solution space makes the problem computationally intractable. Traditional brute-force methods can obtain exact optimal solutions. However, it is not sophisticated enough to solve the complex optimization problem with reasonable time especially in high-dimensional solution space. Artificial intelligent algorithms hold the promise of improving the effectiveness of location search. This article proposes a modified particle swarm optimization (PSO) algorithm to deal with the allocation problem of earthquake emergency shelter. A new discrete PSO and the feasibility-based rule are incorporated according to the discrete solution space and strict constraints. In addition, for enhancing search capability, simulated annealing (SA) algorithm is employed to escape from local optima. The modified algorithm has been applied to the allocation of earthquake emergency shelters in the Zhuguang Block of Guangzhou City, China. The experiments have shown that the algorithm can identify the number and locations of emergency shelters. The modified PSO algorithm shows a better performance than other hybrid algorithms presented in the article, and is an effective approach for the allocation problem of earthquake emergency shelters.     

Parallelization of a regionalization heuristic in distributed computing platforms – a case study of parallel-p-compact-regions problem

In this paper, we report efforts to develop a parallel implementation of the p-compact regionalization problem suitable for multi-core desktop and high-performance computing environments. Regionalization for data aggregation is a key component of many spatial analytical workflows that are known to be NP-Hard. We utilize a low communication cost parallel implementation technique that provides a benchmark for more complex implementations of this algorithm. Both the initialization phase, utilizing a Memory-based Randomized Greedy and Edge Reassignment (MERGE) algorithm, and the local search phase, utilizing Simulated Annealing, are distributed over available compute cores. Our results suggest that the proposed parallelization strategy is capable of solving the compactness-driven regionalization problem both efficiently and effectively. We expect this work to advance CyberGIS research by extending its application areas into the regionalization world and to make a contribution to the spatial analysis community by proposing this parallelization strategy to solve large regionalization problems efficiently.     

基于局部聚类的网络Voronoi图生成方法研究

提出一种将网络约束下的Voronoi和空间聚类相结合的方法,通过构造局部的聚类分析方法对网络边进行加权,根据实际的点过程性质可以把权重定义为加权或者乘权,进行标准化后与道路段本身长度融合进行计算,依此生成网络Voronoi图,以期理解城市街道的空间特性。以武汉市江汉区为例,对城市网格管理系统产生的城市事件进行算法验证,结果表明,该方法提供了一种灵活的网络约束下的服务区域划分工具,可用于基于网络空间点过程影响下的服务区划分,也可用于系统性地定量刻画城市管理的动态特性。     

基于Voronoi图剖分的区域旅游中心城市体系——以苏浙沪地区为例

在区域范围的城市旅游体系中,引入"中心地的中心性"概念,可以在这种旅游性的空间网络中考察城市地位的相对重要性,划分出城市的等级层次,判断出不同级别的中心城市,更可以进一步得到区域空间的城市旅游构成关系.Voronoi图在地理学中是一种利用中心地的中心性广泛用于空间分割、空间邻域查找的空间剖分方法.引入这种方法,以苏浙沪地区为例,在25个地级以上城市中,利用Voronoi图的空间分割原理,找出不仅具有规模性,而且具有空间组织功能的旅游中心城市.     

蒙古国植被自然恢复潜力

植被自然恢复能力评估是生态恢复实践的重要内容。基于蒙古国的MODIS EVI植被指数产品、气象数据及土壤数据,依据相似生境原则,构建了植被恢复潜力计算模式,计算得到蒙古国植被恢复潜力值（VRP,可代表在自然条件下区域植被能够恢复到的最佳状况）及植被恢复潜力指数（VRPI,代表植被生长现状与最大潜力之间的差距）,并用蒙古国纵贯铁路沿线长期围封区的采样分析数据进行了验证。结果表明：（1）蒙古国整体上具有较高的植被恢复潜力,植被自然恢复潜力值0.6—0.9;（2）受降水、气温、土壤等自然要素组配的空间分异影响,蒙古国植被自然恢复潜力具有较大的空间差异性,其中北部及东部地区为VRP高值区和VRPI低值区,植被轻度退化,且较容易恢复;南部及西部地区为VRP中低值区和VRPI高值区,植被退化程度较重,恢复难度相对较大。     

Area aggregation in map generalisation by mixed-integer programming

Topographic databases normally contain areas of different land cover classes, commonly defining a planar partition, that is, gaps and overlaps are not allowed. When reducing the scale of such a database, some areas become too small for representation and need to be aggregated. This unintentionally but unavoidably results in changes of classes. In this article we present an optimisation method for the aggregation problem. This method aims to minimise changes of classes and to create compact shapes, subject to hard constraints ensuring aggregates of sufficient size for the target scale. To quantify class changes we apply a semantic distance measure. We give a graph theoretical problem formulation and prove that the problem is NP-hard, meaning that we cannot hope to find an efficient algorithm. Instead, we present a solution by mixed-integer programming that can be used to optimally solve small instances with existing optimisation software. In order to process large datasets, we introduce specialised heuristics that allow certain variables to be eliminated in advance and a problem instance to be decomposed into independent sub-instances. We tested our method for a dataset of the official German topographic database ATKIS with input scale 1:50,000 and output scale 1:250,000. For small instances, we compare results of this approach with optimal solutions that were obtained without heuristics. We compare results for large instances with those of an existing iterative algorithm and an alternative optimisation approach by simulated annealing. These tests allow us to conclude that, with the defined heuristics, our optimisation method yields high-quality results for large datasets in modest time.     

Voronoi tessellation on the ellipsoidal earth for vector data

Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm.     

Integration of genetic algorithms and GIS for optimal location search

Optimal location search is frequently required in many urban applications for siting one or more facilities. However, the search may become very complex when it involves multiple sites, various constraints and multiple‐objectives. The exhaustive blind (brute‐force) search with high‐dimensional spatial data is infeasible in solving optimization problems because of a huge combinatorial solution space. Intelligent search algorithms can help to improve the performance of spatial search. This study will demonstrate that genetic algorithms can be used with Geographical Information systems (GIS) to effectively solve the spatial decision problems for optimally sitting n sites of a facility. Detailed population and transportation data from GIS are used to facilitate the calculation of fitness functions. Multiple planning objectives are also incorporated in the GA program. Experiments indicate that the proposed method has much better performance than simulated annealing and GIS neighborhood search methods. The GA method is very convenient in finding the solution with the highest utility value.     

Accuracy of quantized Voronoi diagrams

Quantization of spatial objects, which usually means vector‐to‐raster conversion in GIS and remote sensing, is a basic operation used for handling spatial data from data creation to visualization. Since quantization is an approximation of spatial objects, it inevitably yields errors in measuring their properties such as area, perimeter, diameter, and so forth. This paper discusses the accuracy of a quantized Voronoi diagram, a spatial tessellation generated from a set of points. A measure is proposed to evaluate the accuracy of the area of Voronoi regions calculated after quantization. In one‐dimensional space the measure is expressed as an explicit function of the expected number of generators in a cell. In two‐dimensional space, on the other hand, the measure is defined by an implicit function, whose approximation is derived in an explicit form. These functions permit us to evaluate the accuracy of quantization in relation to the size of lattice cells and the density of Voronoi generators. This leads to an appropriate choice of a lattice to keep the quality of a quantized Voronoi diagram at a desirable level.