Ningchuan Xiao

Using evolutionary algorithms to generate alternatives for multiobjective site-search problems

Multiobjective site-search problems are a class of decision problems that have geographical components and multiple, often conflicting, objectives; this kind of problem is often encountered and is technically difficult to solve. In this paper we describe an evolutionary algorithm (EA) based approach that can be used to address such problems. We first describe the general design of EAs that can be used to generate alternatives that are optimal or close to optimal with respect to multiple criteria. Then we define the problem addressed in this research and discuss how the EA was designed to solve it. In this procedure, called MOEA/Site, a solution (that is, a site) is encoded by using a graph representation that is operated on by a set of specifically designed evolutionary operations. This approach is applied to five different types of cost surfaces and the results are compared with 10 000 randomly generated solutions. The results demonstrate the robustness and effectiveness of this EA-based approach to geographical analysis and multiobjective decisionmaking. Critical issues regarding the representation of spatial solutions and associated evolutionary operations are also discussed.

Using Genetic Algorithms to Create Multicriteria Class Intervals for Choropleth Maps

Abstract During the past three decades a large body of research has investigated the problem of specifying class intervals for choropleth maps. This work, however, has focused almost exclusively on placing observations in quasi-continuous data distributions into ordinal bins along the number line. All enumeration units that fall into each bin are then assigned an areal symbol that is used to create the choropleth map. The geographical characteristics of the data are only indirectly considered by such approaches to classification. In this article, we design, implement, and evaluate a new approach to classification that places class-interval selection into a multicriteria framework. In this framework, we consider not only number–line relationships, but also the area covered by each class, the fragmentation of the resulting classifications, and the degree to which they are spatially autocorrelated. This task is accomplished through the use of a genetic algorithm that creates optimal classifications with respect to multiple criteria. These results can be evaluated and a selection of one or more classifications can be made based on the goals of the cartographer. An interactive software tool to support classification decisions is also designed and described.

A Unified Conceptual Framework for Geographical Optimization Using Evolutionary Algorithms

During the last two decades, evolutionary algorithms (EAs) have been applied to a wide range of optimization and decision-making problems. Work on EAs for geographical analysis, however, has been conducted in a problem-specific manner, which prevents an EA designed for one type of problem from being used on others. In this article, a formal, conceptual framework is developed to unify the design and implementation of EAs for many geographical optimization problems. The key element in this framework is a graph representation that defines the spatial structure of a broad range of geographical problems. Based on this representation, four types of geographical optimization problems are discussed and a set of algorithms is developed for problems in each type. These algorithms can be used to support the design and implementation of EAs for geographical optimization. Knowledge specific to geographical optimization problems can also be incorporated into the framework. An example of solving political redistricting problems is used to demonstrate the application of this framework.

Interactive evolutionary approaches to multiobjective spatial decision making: A synthetic review

Abstract This paper reviews recent developments in evolutionary algorithms and visualization in the context of multiobjective spatial decision making. A synthetic perspective is employed to bridge these two areas and to create a unified conceptual framework that can be used to address a broad range of multiobjective spatial decision problems. In this framework, evolutionary algorithms are employed to generate optimal, or near-optimal, solutions to a problem being addressed. Alternatives created are then displayed in an interactive visual support system that can be used by decision makers to discover the competing nature of multiple objectives and to gain knowledge about the tradeoffs among alternatives.

Exploring the Geographic Consequences of Public Policies Using Evolutionary Algorithms

Abstract Public policies with geographical consequences are often difficult to analyze because they affect multiple stakeholders with competing objectives. While such problems fall conceptually into the domain of multiobjective evaluation, associated analytical techniques often search for a single optimum solution. Within the context of geographical problems, optimality often means different things to different stakeholders and, thus, an optimum optimorum may not exist. In this article, we present a new technique based on an evolutionary algorithm (EA) that produces a large number of optimal and near-optimal solutions to a large class of land management problems. As implemented for this article, solutions represent landscape patterns that produce services that meet stakeholder needs to varying degrees. The construction of curves that illustrate the trade-offs among various services given limited resources is central to this approach. Decision makers can use these curves to help find solutions that strike a balance among conflicting objectives and, thus, meet stakeholder needs. To provide context to this work we consider the impact of the U.S. Department of Agricultures (USDA) Conservation Reserve Program on rural landscapes. Three objectives are assumed: (1) maximize farm income, (2) maximize environmental quality, (3) minimize public investment in conservation programs; the first two are viewed as services desired by stakeholders. Analytical and visualization tools are developed to reduce the burden associated with exploring the large number of solutions that are produced by this technique. The results illustrate that the EA-based approach can produce results equal to and significantly more diverse than conventional integer programming techniques.

Heuristics in Spatial Analysis: A Genetic Algorithm for Coverage Maximization

Many government agencies and corporations face locational decisions, such as where to locate fire stations, postal facilities, nature reserves, computer centers, bank branches, and so on. To reach such location-related decisions, geographical information systems (GIS) are essential for providing access to spatial data and analysis tools. Moreover, geographic insights can be gained from GIS as they enable capabilities for better reflecting problems of interest in location modeling. The resulting models can be complex, however, and hence computationally challenging to solve. This article examines an important model for regional service coverage maximization. This model is solved heuristically using a genetic algorithm. The new heuristic innovatively incorporates problem-specific knowledge by exploring the geographical structure of the problem under study. Comparative application results demonstrate important nuances of the new genetic algorithm, enhancing overall performance.

A specialized island model and its application in multiobjective optimization

This paper discusses a new model of parallel evolutionary algorithms (EAs) called the specialized island model (SIM) that can be used to generate a set of diverse non-dominated solutions to multiobjective optimization problems. This model is derived from the island model, in which an EA is divided into several subEAs that exchange individuals among them. In SIM, each subEA is responsible (i.e., specialized) for optimizing a subset of the objective functions in the original problem. The efficacy of SIM is demonstrated using a three-objective optimization problem. Seven scenarios of the model with a different number of subEAs, communication topology, and specialization are tested, and their results are compared. The results suggest that SIM effectively finds non-dominated solutions to multiobjective optimization problems.

A Multiobjective Evolutionary Algorithm for Surveillance Sensor Placement

Automated or semiautomated surveillance monitoring involves movement tracking and sensor handoff. In order to track moving objects over a large area, sensor coverage needs to overlap significantly. Overlapping coverage can be modeled using the concept of backup coverage, a location modeling approach that seeks to maximize primary and backup coverage simultaneously. This kind of sensor placement problem belongs to the class of NP-hard combinatorial optimization problems, so computational difficulty is expected when solving large problem instances, not to mention the need for dealing with multiple objectives. Beyond this, backup coverage for supporting sensor placement actually brings about confounding problem instances for branch-and-bound approaches because of the trade-off between primary and backup coverage. To address these difficulties, this paper develops a multiobjective evolutionary algorithm for the backup coverage problem to support sensor placement. The solutions of this algorithm are evaluated in terms of computational requirements and solution quality.

Assessing the effect of attribute uncertainty on the robustness of choropleth map classification

Choropleth maps are often used to visualize the spatial distribution of information collected for enumeration units. Such maps, however, are normally produced without considering the effect of uncertainty associated with data, which can contribute to incorrect interpretation. The purpose of this paper is to develop a method that can be used to evaluate the classification robustness of choropleth maps when the attribute uncertainty associated with the data is known or can be estimated. We first develop a measure to indicate the robustness of classification schemes. We then design a set of experiments to examine the robustness of different choropleth map classifications under various levels and types of uncertainty. Our experiments suggest that the robustness of a choropleth classification scheme is a function of uncertainty and the number of classes used. Increases in data uncertainty will decrease map robustness. However, it is possible to increase map robustness by choosing a smaller number of classes. We also discuss a visualization approach that can be used to display the classification robustness of each enumeration unit within a choropleth map.

A multiobjective evolutionary algorithm for optimizing spatial contiguity in reserve network design

Landscape fragmentation is a well-recognized threat to the long-term survivability of many plant and animal species. As a complex concept, fragmentation has multiple spatial and functional components, of which spatial contiguity is of great importance. A contiguous landscape provides physical condition and increases the opportunities for species dispersal and migration. However, in real planning situations, contiguity is either too expensive to achieve or impractical because of barriers of urban landscapes. As such, the traditional yes/no function of contiguity has been extended into a notion of relative contiguity which has the value range between zero and one. Relative contiguity measures levels of interconnectivity of landscapes based on graph theory and spatial interaction. It takes into account both inner-reserve relationship (i.e. reserve sizes) and inter-reserve spatial proximity. This paper presents a multiobjective evolutionary algorithm approach to maximizing relative contiguity in reserve network design. This approach obtains solutions that maximize the measure of relative contiguity, minimize the total acquisition area, and satisfy constraints on the coverage of individual species. Application results show the developed algorithm has significant advantages in optimizing relative contiguity and generating a variety of alternative solutions.