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 2010. 1
Grammar-Based Network Construction Vitins, B.J. IVT ETH Zürich September 2010
Source: Google Earth (2010) Example network of San Francisco 3
Source: Marshall (2005) p. 226 Composition 4
Source: Marshall (2005) p. 226 Configuration 5
Source: Marshall (2005) p. 227 Constitutional approach 6
Source: Procedural (2010) Example: City Engine 7
Source: Alexander (1977) p.190, S.489 Pattern language 8
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
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
Source: Google Earth (2010) Example network of East Chicago 11
Resulting network : Intersections : Demand generating points 12
Overview of the genetic algorithm Source: Bäck and Hoffmeister (1994) p.872 Time t mutation, selection Time t n crossover n+1 00111 11100 01010 11100 11100 01010 reproduction 01100 11010 01100 13
Building blocks in network generation Genome 1 + Genome 2 Genome 1+2 Genome 1: 01001 0001####.#### Genome 2: ####.####01000 0000 Genome 1+2: 01001 000101000 0000 1-point crossover 14
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
Calibration with the p c s control map 330000-340000 objective function 340'000 330'000 320'000 310'000 300'000 290'000 280'000 270'000 260'000 250'000 240'000 230'000 220'000 210'000 200'000 190'000 180'000 170'000 160'000 150'000 0.2 0.3 0.4 0.5 crossover rate 0.6 0.7 0.8 2 5 20 selectio... 320000-330000 310000-320000 300000-310000 290000-300000 280000-290000 270000-280000 260000-270000 250000-260000 240000-250000 230000-240000 220000-230000 210000-220000 200000-210000 190000-200000 180000-190000 170000-180000 160000-170000 150000-160000 16
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
Building blocks in network generation Genome 1 + Genome 2 Genome 1+2 Genome 1: 01001 0001####.#### Genome 2: ####.####01000 0000 Genome 1+2: 01001 000101000 0000 1-point crossover 18
Results with no grammar rules : Intersections : Demand generating points 19
Adjacent links to links with the same or higher hierarchy : Intersections : Demand generating points 20
Adjacent links to links with the same or 1 higher hierarchy : Intersections : Demand generating points 21
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 78 003 34.7 78 682 35.9 79 174 35.9 22
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
Outlook Variances of the results More grammar rules and fitness functions Larger networks with variable node positions 24
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) 51-63. Goldberg, D.E. (2002) The Design of Innovation, Kluwer, Norwell. Google Earth (2010) http://earth.google.com/, September 2010. 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
References Kamanda, T. and S. Kawai (1989) An algorithm for drawing general undirected graphs, Information Processing Letters, 31 (1) 7-15. Kronfeld, M., H. Planatscher and A. Zell (2010) The EvA2 Optimization Framework, Proceedings of the Learning and Intelligent Optimization Conference, Venice, January 2010. Marshall, S. (2005) Streets & Patterns, Spon Press, London. Nexus (2009) Song System of Network Growth, www.nexus.umn.edu, University of Minnesota, Minneapolis, August 2009. Procedural (2010) www.procedural.com, September 2010. 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) 1-10. 26