1. Genetic algorithms: A Stochastic Approach for Improving the Current Cadastre Accuracies Anna Shnaidman Uri Shoshani Yerach Doytsher Mapping and Geo-Information Engineering Technion – Israel Institute of Technology

2. 2  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work Outline

3. 3  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

4. 4  Cadastral measurement is a continuous process of recording the redefinition and updates of boundaries  The cadastre in Israel is of an analogical nature  Different measurements of inconsistent accuracy stored mostly on paper  One of the main objectives on the SOI agenda is transition to a coordinate based (digital) cadastre Introduction

5. 5  Digital cadastre is one of the concrete topics being discussed and researched in many countries: Digital cadastre accuracies Transformation of graphical data into digital Improvement of dataset points accuracy using GNNS technology Global adjustment model  Most customary solutions are based mainly on the deterministic Least Square (LS) method Introduction cont.

6. 6  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

7. 7  Due to population growth an automated and reliable land management system is urgently required  The current cadastre precludes: efficient and computerized management of real estate faster planning of development projects minimizing border conflicts keeping up with modern customary high work standards  The transition to an analytical cadastre is both crucial and inevitable The problem at hand

8. 8  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

9. 9 The proposed algorithm  The conventional methods are mainly analytical and straightforward  The proposed method is based on biological optimizations and is known as Genetic Algorithms (GAs)  Characteristics: stochastic method founded on evolutionary ideas and Darwin's principles of selection and survival of the fittest a natural selection which operates on a population of solutions – chromosomes (individuals)

10. 10 The proposed algorithm cont.  The generic framework of GAs:  Create the initial population of n vectors  Evaluate (grade) the individuals by assigning a fitness value  Create the new population by applying variation- inducing operators: selection, crossover and mutation

11. 11 The proposed algorithm cont.  Genetic operators - selection:  Two parent chromosomes are selected from a population according to their fitness  Guiding principle – selection of the fittest Superior individuals are of higher probability to be selected (survive)  Selection method – roulette wheel selection Roulette slots’ size is determined by the fitness value

12. 12 The proposed algorithm cont.  example

13. 13 The proposed algorithm cont.  Genetic operators - crossover:  Two offspring are created using single point crossover Parents chromosomes children chromosomes  Genetic operators - mutation:  The new offspring are changed randomly to ensure diversity

14. 14  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

15. 15 Implementation of GAs – cadastral analogy  A generation of individuals - vectors of turning points coordinates of parcels  Each individual - a set of block coordinates stored in an array (vector) structure  Parcel areas and lines - provide the cadastral and geometrical constraints  An objective function - minimizes the differences between the legal (registered) coordinates and those provided by the solution under the specified conditions

16. 16 Implementation of GAs – cadastral analogy cont.  With each generation the vectors are altered according to the best solution provided  Every individual may assumed to be a set of coordinates, representing acceptable observations received from different sources  The GAs method was evaluated using synthetic data

17. 17 Implementation of GAs – cadastral analogy cont.  Definitions:  The preliminary population of n vectors is produced by randomly altering an "ideal" cadastral block  A registered area criteria, straight, parallel and perpendicular lines were chosen for analyzing the GAs' competence and effectiveness in the cadastral domain

18. 18  Cadastral conditions :  Objective function employs Cartesian area calculation and a desirable MSE of parcel coordinates  Fitness function considers parcel size to determine its weight  Geometrical conditions :  Objective function uses turning point angles, line segment lengths and the perpendicular distances  Fitness function computes line weight using the number of points in both lines and the total line lengths  Total grade Implementation of GAs – cadastral analogy cont.

19. 19 Implementation of GAs – cadastral analogy cont. – Objective function  Areas  Lines

20. 20 Implementation of GAs – cadastral analogy cont. – Fitness function  Areas  Lines  Total grade

21. 21 Implementation of GAs – cadastral analogy cont.  Iterations – creation of successive generation :  Parent selection - for each parcel and line/lines in the block two parents are selected according to the tournament method  Crossover - a single point crossover is performed  Process repetition - until the original population size (N) is reached  Averaging - mean coordinates are calculated  Mutation

22. 22 The proposed algorithm - graphical illustration … … Set 1 … Set 2 … Set N Parcel 1 Lines 1 Parents selection Single point crossover Offspring 1 Offspring 2 next generation –Averaging coordinates, adding mutation, creation of new sets … … New set 1 … New set 2 … New set N Parent 1

23. 23  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

24. 24 Simulation results  The proposed method's quality and accuracy were examined by performing simulations on the synthetic data  The main purpose of these simulations is to test the ability of the GAs to converge to the initial theoretical state - an ideal, errorless solution  For comparison a Least Square iterative adjustment was applied as well

25. 25 Simulation results cont. A characteristic set of synthetic data

26. 26 Simulation results cont.  A characteristic example of the solution accuracy (meters) Param - eters Min dX Min dY Max dX Max dY Mean X Mean Y  X  Y Initial -0.619-0.7040.6300.497-0.0120.0100.2160.224 GAs -0.168-0.1900.1540.134-0.0030.0030.0440.043 LS -0.619-0.7040.5690.456-0.0120.0100.1840.173  The f ollowing parameters have been used:  Standard deviation error - 0.25 meter  An expected MSE of the coordinates - 0.05 meter  Maximum generations (iterations) - < 100

27. 27 Simulation results cont.  Solution improvement throughout the generations

28. 28 Simulation results cont. Param- eters  min  max  STD XX 0.0390.0490.004 YY 0.0370.0450.002  Solution stability examination results (meters)

29. 29  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

30. 30 Summary  The proposed method presents a new approach for achieving homogeneous coordinates by using evolutionary algorithms - GAs  GAs imitate the natural process of evolving solutions  Applying the GAs to synthetic data yields satisfactory results  Repeated simulation executions showed similar results  The GAs method is more accurate and provides better results than those of the traditional LS approach

31. 31  Introduction  The problem at hand  The proposed algorithm  Implementation of GAs – cadastral analogy  Results  Summary  Future work

32. 32 Future work  The simplicity of the algorithm enables considering additional cadastral and geometric conditions without altering its fundamental mechanism  Objectives:  more detailed analysis of single blocks  expansion of the dimensions of the problem  implementation of the algorithm on "real" data

33. 33 Thank you