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1 Preferred citation style for this presentation Vitins, B.J. (2010) Grammar-Based Network Construction, presented at the Seminar Modeling Complex Socio-Economic Systems and Crises 5, ETH Zurich, Zurich, September
2 Grammar-Based Network Construction Vitins, B.J. IVT ETH Zürich September 2010
3 Source: Google Earth (2010) Example network of San Francisco 3
4 Source: Marshall (2005) p. 226 Composition 4
5 Source: Marshall (2005) p. 226 Configuration 5
6 Source: Marshall (2005) p. 227 Constitutional approach 6
7 Source: Procedural (2010) Example: City Engine 7
8 Source: Alexander (1977) p.190, S.489 Pattern language 8
9 Abstract grammar rules Network hierarchy Destination A B C D A Origin B C D Set of necessary connections, at least one for each row Set of possible connections 9
10 Possible link grammar rules Necessary connection Link types Source: after Marshall (2005) A B C A B C Possible connection Possible additional rule Multiple level node Roundabout Light-signal system T-junction Crossing 10
11 Source: Google Earth (2010) Example network of East Chicago 11
12 Resulting network : Intersections : Demand generating points 12
13 Overview of the genetic algorithm Source: Bäck and Hoffmeister (1994) p.872 Time t mutation, selection Time t n crossover n reproduction
14 Building blocks in network generation Genome 1 + Genome 2 Genome 1+2 Genome 1: ####.#### Genome 2: ####.#### Genome 1+2: point crossover 14
15 Fitness values during an optimization process 1.4E+7 1.2E+7 Shortest path assignment without travel demand Complete assingment 1.0E+7 Fitness value 8.0E+6 6.0E+6 4.0E+6 2.0E+6 0.0E+0 0.0E+0 2.0E+6 4.0E+6 6.0E+6 8.0E+6 1.0E+7 1.2E+7 1.4E+7 1.6E+7 Number of fitness calcualtion 15
16 Calibration with the p c s control map objective function 340' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' crossover rate selectio
17 Objective function Demand-weighted travel time O D Travel time t od d od P o1 d 1 Accessibility Accessibility O I o ln D o1 d 1 A d exp( t od ) P 17
18 Building blocks in network generation Genome 1 + Genome 2 Genome 1+2 Genome 1: ####.#### Genome 2: ####.#### Genome 1+2: point crossover 18
19 Results with no grammar rules : Intersections : Demand generating points 19
20 Adjacent links to links with the same or higher hierarchy : Intersections : Demand generating points 20
21 Adjacent links to links with the same or 1 higher hierarchy : Intersections : Demand generating points 21
22 Resulting fitness values Grammar rule Weighted travel time: Accessibility: No grammar rule applied during optimization Links joined to links with the same or any higher hierarchy Links joined to links with the same or 1 higher hierarchy
23 Force-based algorithm Potential energy: Source: Kamada and Kawai (1989) p.8 E tot n 1 i1 ji1 1 2 with l: Length between i and j in a relaxed state k: Spring constant v i, v j : Distance between u and v Iterative approach n k ij v i v j l ij 2 23
24 Outlook Variances of the results More grammar rules and fitness functions Larger networks with variable node positions 24
25 References Alexander, C. (1977) The Timeless Way of Building, Oxford University Press, New York. Axhausen, K.W., P. Fröhlich und M. Tschopp (2006) Changes in Swiss accessibility since 1850, Arbeitsberichte Verkehrs- und Raumplanung, 344, IVT, ETH Zürich, Zürich. Bäck, T. and F. Hoffmeister (1994) Basic aspects of evolution strategies, Statistics and Computing, 4 (2) Goldberg, D.E. (2002) The Design of Innovation, Kluwer, Norwell. Google Earth (2010) September Holland, J. (1975) Adaption in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Systems, The University Press of Michigan Press, Ann Arbor. 25
26 References Kamanda, T. and S. Kawai (1989) An algorithm for drawing general undirected graphs, Information Processing Letters, 31 (1) Kronfeld, M., H. Planatscher and A. Zell (2010) The EvA2 Optimization Framework, Proceedings of the Learning and Intelligent Optimization Conference, Venice, January Marshall, S. (2005) Streets & Patterns, Spon Press, London. Nexus (2009) Song System of Network Growth, University of Minnesota, Minneapolis, August Procedural (2010) September Vanegas, C.A., D.G. Aliaga, B. Benes, P.A. Waddell (2009) Interactive design of urban spaces using geometrical and behavioral modeling, ACM Transactions on Graphics, 28 (5)
Stability and innovation of human activity spaces
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