2014 International Conference on Computational Science and Computational Intelligence
A Visual Decision-Guided Tool: Integrating Optimization Programming into Geo-data Visualization for Finding the Viable Shortest Path Chun-Kit Ngan Division of Information Science Great Valley School of Graduate Professional Studies The Pennsylvania State University Malvern, PA, USA
[email protected] Currently, a number of data analytics approaches has been proposed and developed to analyze geo-data objects to accomplish the above objective. Data mining techniques [2, 3] are computational algorithms to analyze raw data over a terrain to extract valuable information. Some algorithms include rule mining (e.g., the Apriori algorithm) [4], dimensionality reduction methods (e.g., principal components analysis) [5], supervised learning (e.g., decision trees, support vector machines, neural networks, etc.) [6], and unsupervised learning (e.g., cluster analysis) [7]. However, these mining techniques often require expert human interpretation and supervision on data to deliver the results, which are not suitable for quick decision-making during operations. To support military troops to effectively make a better decision, i.e., the shortest path determination for rescue and recovery missions, researchers proposed and developed data visualization tools that expressively display the learned results from the mined geodata objects to support the analysis. This technique is called visual analytics or visual data mining [3, 8] that combines the advantages of both visualization and data mining methodology.
Abstract—We propose a Visual Decision-Guided Tool that integrates optimization programming into geo-data visualization to determine the best path for rescue and recovery missions. First, we will develop the Top-k Objected-oriented Smoothest Paths model which captures the object dynamics of geospatial temporal network in a terrain over a time horizon. These objects include stationary entities, mobile objects, and route segments. Second, we will extend the Smoothest Path Algorithm (SPA) to be a dynamic learning algorithm, i.e., the Time-varying Smoothest Path Algorithm, which integrates the object dynamics to learn the top-k smoothest routes at each instance of time. The main advantage offered by the SPA extension is its lower logarithmic time complexity, i.e., O(NlogN), where N is the number of nodes in a terrain. Finally, we will develop a new design of visual displays that enable military operators to analyze other crucial factors, such as vehicle types, weather severity, and soldiers’ specialty levels, which are required to be interpreted by human perception, cognition, and knowledge to select the best path among the top-k smoothest routes at each instance of time for rescue and recovery missions. Keywords—data analytic; data visualization; decision support; decision optimization; query language; shortest path problems
I.
However, due to the high volume and the large size of the available data, the visual analytics approach is still very cumbersome to be used and can even overwhelm military operators during their decision-making. To solve this heavy data problem, a number of operation research methods, i.e., Mathematical Programming, e.g., Mixed Integer Linear Programming, Mixed Integer Nonlinear Programming, etc., are revised and streamlined to play a key role in this endeavor. The operation research methods help military units formulate precise objectives, e.g., minimize the cost of traveling time, as well as the constraints, e.g., the vehicles’ speed limitations, imposed on the solution [9]. Once optimal values of decision parameters (e.g., select or unselect a node and/or a route segment along a path) are learned by optimization algorithms, such as Dijkstra’s, Simplex, and Branch-and-bound, military decision makers can use the learned parameters to determine the shortest path.
INTRODUCTION
In the past decade, several military units successfully analyzed integrated geo-data objects to perform decisionmaking operations. Consider a range of peace-keeping operations [1] that a nation military force needs to accomplish in order to maintain peace in its country. One critical operation that the military troops need to determine is to find the viable shortest route to reach a target location for rescue and recovery missions so that medical and health services can efficiently be delivered to victims who can receive supports and supplies in the aftermath of natural disasters. To support such a decisionmaking operation, it is important for military researchers to develop a geo-data analytical methodology that is reliable and useful for the operation. The main challenge in such a methodology is how to expressively and efficiently represent, manipulate, and analyze those unified geo-data objects in such a way that domain experts, e.g., military units, can analytically make a concerted action together. This is exactly the focus of this paper. 978-1-4799-3010-4/14 $31.00 © 2014 IEEE DOI 10.1109/CSCI.2014.124
Recently, a number of more advanced shortest path learning algorithms has been proposed and developed. The Smoothest Path Algorithm (SPA) [10] is to find the shortest surface path over a terrain in terms of distance and slope rather 710 226
than the Euclidean distance only. The Shortest Path Algorithm for a Fixed Start Time [11] is to compute the shortest path either for a given start time or to search the start time and the path that results in the least travelling time. However, these approaches do not consider taking advantages of one another to determine the shortest route based upon the distance, slope, time schedule, and other possible terrain obstacles together.
query construct to the TOSP compiler, the compiler transforms the DOV query to be the TOSP construct, which is then sent to the TSP solver with the TSP algorithm to learn the top-k smoothest routes at each instance of time. After the compiler receives the top-k route segments and objectives, the output formatter renders the results as the optimized answers to the DOV query. In order to provide the future insight, domain experts can also construct the SV query to simulate and predict the top-k smoothest routes in the next instance of time. The answers from the both DOV and SV query, as well as the visual form from the VV query are then integrated by the Ͱ aggregator, which delivers the aggregated results to the data visualizer. The data visualizer displays analytical diagrams and figures, e.g., 2D pie charts and maps, 3D bar graphs and maps, etc., to the domain experts. The domain experts, e.g., the ground soldiers, can use the pull or push services provided by the mobile network and devices to receive the latest visual information about the routes. The Army command center can base upon the visual information to guide the soldiers’ next movements via the communication network. Collaboratively, both units are able to make a final decision on the best path based upon the optimal and simulated results of the top-k smoothest routes, as well as the other considerable factors, e.g., vehicle types, weather severity, and soldiers’ specialty, using our designed VDGT tool.
More importantly, the learned shortest paths computed from those algorithms only reflect an optimal reality under some environmental constraints rather than address the entire phenomenon, especially after natural disasters. For instance, the travelling time delivered by those models and algorithms are not considered other crucial factors, such as vehicle types, weather severity, moving entities, and soldiers’ specialty levels. Those neglected factors may impact the traveling time that still requires human perception, cognition, and knowledge for formulating a final decision. To solve the above problems, we propose a Visual Decision-Guided Tool (VDGT) that integrates optimization programming into geo-data visualization to determine the best path for rescue and recovery missions. The conceptual idea is to enable military units to make a visual decision on routes based upon the route distance optimality among all the possible paths. Specifically, we will first develop the Top-k Objectedoriented Smoothest Paths (TOSP) model which captures the object dynamics of geospatial temporal network in a terrain over a time horizon. These objects include stationary entities (e.g., houses, buildings, roads, trees, etc.), mobile objects (e.g., vehicles, people, etc.), and route segments (e.g., steep slopes, mud roads, etc.). Second, we will extend the SPA to be a dynamic learning algorithm, i.e., the Time-varying Smoothest Path (TSP) algorithm, which integrates the object dynamics to learn the top-k smoothest routes at each instance of time. The main advantage offered by the SPA extension is its lower logarithmic time complexity, i.e., O(NlogN), where N is the number of nodes in a terrain. Finally, we will develop a new design of visual displays that enable military operators to analyze other crucial factors, such as vehicle types, weather severity, and soldiers’ specialty levels, which are required to be interpreted by human perception, cognition, and knowledge to select the best path among the top-k smoothest routes at each instance of time for rescue and recovery missions.
III.
The rest of the paper is organized as follows. In Section II, we use the above military force’s example, i.e., the rescue and recovery mission, to provide an overview on our Visual Decision-Guided Tool. In Section III, we explain the initial design of our high-level 3D visual display for finding the viable shortest path among the top-k smoothest routes. Section IV concludes the paper and briefly outlines our future work. II.
INITIAL DESIGN OF 3D VISUAL DISPLAY
The initial design of our high-level 3D visual display for optimized and simulated top-k routes is shown in Fig. 2.1 and 2.2 respectively. These visual displays will be updated and refreshed for every instance of time. The display (see Fig 2.1) is divided into two portions. The right-hand portion shows the top-k optimal routes on the map, where the red line is the first optimal path, and the blue line is the second at the current time point t. Both of the routes are learned by our TSP algorithm. The left-hand portion displays the road characteristics, such as grades (e.g., HILL), conditions (e.g., BUMP), and speeds (e.g., 35 MPH), using the standard road signs, as well as show the current weather (e.g., Sunny), solders’ specialty levels (e.g., Corporal), and their vehicle types (e.g., a Four-wheel Truck). Fig 2.2, which has the same visual layout as Fig 2.1, shows the top-k simulated routes at the future time point t + t. Due to the dynamics of geospatial temporal network in a terrain over a time horizon, the simulated results render different top-k routes learned by our TSP algorithm. Using the both optimal and simulated results of the routes with other considerations shown on the visuals, the Army command center and soldiers can determine the best route for their rescue and recovery missions.
A VISUAL DECISION-GUIDED TOOL
Technically, this VDGT tool is composed of a number of operational units shown in Fig 1. The Geo-Query Language (GQL) is the Object-Relational Query (ORQ) [12] that enables domain experts to (1) retrieve data from geospatial temporal database and (2) construct decision optimization (DOV), visualization (VV), and simulation (SV) views based upon the unified geo-data objects to support the rescue and recovery missions. Once the domain users initiate the data and DOV
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Time-varying Smoothest Path (TSP) Solver
TOSP Construct
Top-k Sequences of Route Segments and Objectives
A Visual Decision-Guided Tool for the Top-k Smoothest Paths TOSP Compiler Query Translator
Output Formatter
Data and DOV Query Construct
Optimized Answer
Ground Soldiers
Mobile Network
Geo-Query Language
Geospatial Temporal Database
Decision Optimization View (DOV)
Optimized Answer
Visualization View (VV)
Visual Form
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Army Communication Network
ْ Simulation View (SV)
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Fig. 1. A Visual Decision-Guided Tool for the Top-k Smoothest Paths
Fig. 2.1. Mobile Device Example of the Top-k Optimal Routes Display
IV.
Fig. 2.2. Mobile Device Example of the Top-k Simulated Routes Display [1]
US Forest Service. (2000). http://www.fs.fed.us/fire/doctrine/genesis_and_evolution/source_materi als/joint_vision_2020.pdf [2] Maimon, O.Z. & Rokach, L. (2005). Data Mining and Knowledge Discovery Handbook. Springer New York, Inc. [3] Bertini, E. & Lalanne, D. (2009). Investigating and Reflecting on the Integration of Automatic Data Analysis and Visualization in Knowledge Discovery. ACM SIGKDD Explorations Newsletter. NY, USA. [4] Agrawal, R. & Srikant, R. (1994). Fast Algorithms for Mining Association Rules in Large Databases. Proceedings of the 20th International Conference on Very Large Data Bases. CA, USA. [5] Jolliffe, I.T. (2002). Principal Component Analysis. Springer-Verlag. [6] Mohri, M, Rostamizadeh, A, & Talwalkar, A. (2012). Foundations of Machine Learning. The MIT Press. [7] Duda, R, Hart, P, & Stork, D. (2001). Unsupervised Learning and Clustering. John Wiley & Sons, Inc. [8] Keim, D.A., Kohlhammer, J., Ellis, G., & Mansmann, F. (2010). Mastering the Information Age - Solving Problems with Visual Analytics. http://www.vismaster.eu/wpcontent/uploads/2010/11/VisMaster-book-lowres.pdf [9] Pardalos, P.M. & Hansen, P. (2008). Data Mining and Mathematical Programming. American Mathematical Society. [10] Roles, J.A. & ElAarag, H. (2013). A Smoothest Path Algorithm and its Visualization Tool. Proceedings of the IEEE SoutheastCon Conference. Florida, U.S.A. [11] George, B. & Kim, S. (2013). Shortest Path Algorithms for a Fixed Start Time. SpringerBriefs in Computer Science. Springer New York. [12] Stonebraker, M, Brown, P, & Moore, D. (1998). Object-Relational DBMSs: The Next Great Wave. Morgan Kaufmann Publishers.
CONCLUSIONS AND FUTURE WORK
In this paper, we propose a VDGT tool that is a unified decision-making application that combines both advantages of quantitative analyses (i.e., optimization programming in operation research) and qualitative methodologies (i.e., geodata visualization in data analytics) to determine the viable shortest path for rescue and recovery missions. First, we will develop the TOSP model which captures the object dynamics of geospatial temporal network in a terrain over a time horizon. These objects include stationary entities, mobile objects, and route segments. Second, we will extend the SPA to be a dynamic learning algorithm, i.e., the TSP algorithm, which integrates the object dynamics to learn the top-k smoothest routes at each instance of time. The main advantage offered by the SPA extension is its lower logarithmic time complexity, i.e., O(NlogN), where N is the number of nodes in a terrain. Finally, we will develop a new design of visual displays that enable military operators to analyze other crucial factors, such as vehicle types, weather severity, and soldiers’ specialty levels, which are required to be interpreted by human perception, cognition, and knowledge to select the best path among the top-k smoothest routes at each instance of time for rescue and recovery missions. REFERENCES
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