Ting L. Lei

Mapping transit-based access: integrating GIS, routes and schedules

Accessibility is a concept that is not entirely easy to define. Gould (1969) once stated that it is a ‘slippery notion … one of those common terms that everyone uses until faced with the problem of defining and measuring it’. Considerable research over the last 40 years has been devoted to defining and measuring accessibility, ranging from access to jobs within an hours travel time to the ease at which given places can be reached. This article is concerned with the measurement of access provided by transit. It includes a review of past work on measuring accessibility in general and with respect to transit services in particular. From this overview of the literature, it can be seen that current methods fall short in measuring transit service access in several meaningful aspects. Based on this review and critique, we propose new refinements that can be used to help overcome some of these shortcomings. As a part of this, we define an extended GIS data structure to handle temporal elements of transit service. To demonstrate the value of these new measures, examples are presented with respect to mapping accessibility of transit services in Santa Barbara, California. Finally, we show how these measures can be used to develop a framework for supporting transit service analysis and planning.

Development of Indicators of Opportunity-Based Accessibility

“Accessibility,” defined as the ease (or difficulty) with which opportunities for activity can be reached from a given location, can be measured with the cumulative amount of opportunities from an origin within a given amount of travel time. These indicators can be used in regional planning and modeling efforts to integrate land use and travel demand, and an attempt should be made to calculate these indicators for the smallest geographic area. The primary objective of this paper is to illustrate the creation of realistic space-sensitive and time-sensitive block-level accessibility indicators to track the availability of opportunities. These indicators support the development of an activity-based travel demand model by Southern California Association of Governments to provide second-by-second and parcel-by-parcel modeling and simulation. The indicators also provided the base information for mapping opportunities of access to 15 types of industries at different times during a day. The indicators and their maps were defined for the entire region of Southern California through largely available data that included the Census Transportation Planning Package, Dun & Brad-street postprocessed data, detailed highway networks and travel times from the four-step regional models, and arrival and departure times of workers by industry.

Constructs for Multilevel Closest Assignment in Location Modeling

In the classic p-median problem, it is assumed that each point of demand will be served by his or her closest located facility. The p-median problem can be thought of as a ‘‘single-level’’ allocation and location problem, as all demand at a specific location is assigned as a whole unit to the closest facility. In some service protocols, demand assignment has been defined as ‘‘multilevel’’ where each point of demand may be served a certain percentage of the time by the closest facility, a certain percentage of the time by the second closest facility, and so on. This article deals with the case in which there is a need for ‘‘explicit’’ closest assignment (ECA) constraints. The authors review past location modeling work that involves single-level ECA constraints as well as specific constraint constructs that have been proposed to ensure single-level closest assignment. They then show how each of the earlier proposed ECA constructs can be generalized for the ‘‘multilevel’’ case. Finally, the authors provide computational experience using these generalized ECA constructs for a novel multilevel facility interdiction problem introduced in this article. Altogether, this article proposes both a new set of constraint structures that can be used in location models involving multilevel assignment as well as a new facility interdiction model that can be used to optimize worst case levels of facility disruption.

Vector Assignment Ordered Median Problem

The vector assignment p-median problem (VAPMP) and the ordered p-median problem (OMP) are important extensions of the classic p-median problem. The VAPMP extends the p-median problem by allowing assignment of a demand to multiple facilities, and a wide variety of multi-assignment and backup location problems are special cases of this problem. The OMP optimizes a weighted sum of service distances according to their relative ranks among all demands. The OMP is well known as it represents a generalization of both the p-median and the p-center problems. In this article, a new model is developed which extends both the VAPMP and OMP problems. In addition, beyond median, center, and vector assignment, this new model can resolve problems where the system objective involves maximizing distance. The new model also gives rise to meaningful special-case problems, such as a “reliable p-center” problem. Different integer linear programming (ILP) formulations of the new problem are presented and tested. It is demonstrated that an efficient formulation for a special case of the VAOMP problem can solve medium sized problems optimally in a reasonable amount of time.

Hedging against service disruptions: an expected median location problem with site-dependent failure probabilities

The vector assignment p-median problem (VAPMP) (Weaver and Church in Transp Sci 19(1):58–74, 1985) was one of the first location-allocation models developed to handle split assignment of a demand to multiple facilities. The underlying construct of the VAPMP has been subsequently used in a number of reliable facility location and backup location models. Although in many applications the chance that a facility fails may vary substantially with locations, many existing models have assumed a uniform failure probability across all sites. As an improvement, this paper proposes a new model, the expected p-median problem as a generalization of existing approaches by explicitly considering site-dependent failure probabilities. Multi-level closest assignment constraints and two efficient integer linear programming (ILP) formulations are introduced. While prior research generally concludes that similar problems are not integer-friendly and cannot be solved by ILP software, computational results show that our model can be used to solve medium-sized location problems optimally using existing ILP software. Moreover, the new model can be used to formulate other reliable or expected location problems with consideration of site-dependent failure probabilities.

Identifying functionally connected habitat compartments with a novel regionalization technique

Landscape ecologists have increasingly turned to the use of landscape graphs in which a landscape is represented as a set of nodes (habitat patches) connected by links representing inter-patch-dispersal. This study explores the use of a graph-based regionalization method, Graph-based REgionalization with Clustering And Partitioning (GraphRECAP), to detect structural groups of habitat patches (compartments) in a landscape graph such that the connections (i.e. the movement of individual organisms) within the groups are greater than those across groups. Specifically, we mapped compartments using habitat and dispersal data for ring-tailed lemurs (Lemur catta) in an agricultural landscape in southern Madagascar using both GraphRECAP and the widely-used Girvan and Newman method. Model performance was evaluated by comparing compartment characteristics and three measures of network connectivity and traversability: the connection strength of habitat patches in the compartments (modularity), the potential ease of individual organism movements (Harary index), and the degree of alternative route presence (Alpha index). Compartments identified by GraphRECAP had stronger within-compartment connections, greater traversability, more alternative routes, and a larger minimum number of habitat patches within compartments, all of which are more desirable traits for ecological networks. Our method could thus facilitate the study of ecosystem resilience and the design of nature reserves and landscape networks to promote the landscape-scale dispersal of species in the fragmented habitats.

A unified approach for location-allocation analysis: integrating GIS, distributed computing and spatial optimization

Location-allocation modeling is an important area of research in spatial optimization and GIScience. A large number of analytical models for location-allocation analysis have been developed in the past 50 years to meet the requirements of different planning and spatial-analytic applications, ranging from the location of emergency response units (EMS) to warehouses and transportation hubs. Despite their great number, many location-allocation models are intrinsically linked to one another. A well-known example is the theoretical link between the classic p-median problem and coverage location problems. Recently, Lei and Church showed that a large number of classic and new location models can be posed as special case problems of a new modeling construct called the vector assignment ordered median problem (VAOMP). Lei and Church also reported extremely high computational complexity in optimally solving the best integer linear programming (ILP) formulation developed for the VAOMP even for medium-sized problems in certain cases. In this article, we develop an efficient unified solver for location-allocation analysis based on the VAOMP model without using ILP solvers. Our aim is to develop a fast heuristic algorithm based on the Tabu Search (TS) meta-heuristic, and message passing interface (MPI) suitable for obtaining optimal or near-optimal solutions for the VAOMP in a real-time environment. The unified approach is particularly interesting from the perspective of GIScience and spatial decision support systems (DSS) as it makes it possible to solve a wide variety of location models in a unified manner in a GIS environment. Computational results show that the TS method can often obtain in seconds, solutions that are better than those obtained using the ILP-based approach in hours or a day.

On the unified dispersion problem: Efficient formulations and exact algorithms

Facility dispersion problems involve placing a number of facilities as far apart from each other as possible. Four different criteria of facility dispersal have been proposed in the literature (Erkut & Neuman, 1991). Despite their formal differences, these four classic dispersion objectives can be expressed in a unified model called the partial-sum dispersion model (Lei & Church, 2013). In this paper, we focus on the unweighted partial sum dispersion problem and introduce an efficient formulation for this generalized dispersion problem based on a construct by Ogryczak and Tamir (2003). We also present a fast branch-and-bound based exact algorithm.

Designing Robust Coverage Systems: A Maximal Covering Model with Geographically Varying Failure Probabilities

Covering models have been used in a wide range of modeling and geospatial analysis applications ranging from planning emergency services to natural reserve design. One topic in coverage modeling that has received considerable research attention is addressing uncertainty due to facility unavailability and service disruptions. In this article, we propose a covering model that maximizes the expected coverage of demand by considering the possibility of facility failures. Unlike existing models that assume a uniform failure probability across all sites in an area, the proposed model can account for spatially varying failure probabilities and describes better the underlying geographic processes that cause facility failures. The model is posed as a spatial optimization problem using integer linear programming. We compare two different formulations of the covering model and discuss their properties. The proposed model formulations have been tested computationally using a warning sirens data set that has been widely used in assessing covering models. We conclude with a summary of findings as well as possible directions of future research.

Sub-Pixel Location of Motion Blurred Weak Celestial Objects in Optical Sensor Image Based on Elliptical 2D Gaussian Surface Fitting

Fast moving objects are important objects of concern for deep space exploration or astronomical missions. Challenges in accurately locating these objects (especially at the sub-pixel level) include motion blur caused by the fast movement and the defocusing of optical sensors. In this letter, we explore a new method for removing these effects. Instead of estimating each of the effects individually e.g. via image restoration, the proposed method estimates the combined effect of defocusing and blurring in one step. Based on the observed similarity between the appearance of fast moving objects (such as asteroids) and 2D Gaussian surfaces, we use the Gaussian surface as model for fitting and locating the objects. Experimental results demonstrate that the proposed algorithm can locate the centroids of LAGEOS satellite in real optical sensor images and achieve 0.15 pixel in accuracy when blurring length is below 15 pixels in simulated data, and still achieve sub-pixel accuracy when 0dB Gaussian white noise is superimposed. The results suggest the proposed method has potential applications in navigation or orbital debris surveillance.