genetic algorithms: a stochastic approach for improving the current cadastre accuracies anna...
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3 Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Results Summary Future workTRANSCRIPT
Genetic algorithms: A Stochastic Approach for Improving the Current
Cadastre AccuraciesAnna ShnaidmanUri Shoshani Yerach Doytsher
Mapping and Geo-Information Engineering Technion – Israel Institute of Technology
2
Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
Outline
3
Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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
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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
Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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 projectsminimizing border conflictskeeping up with modern customary high work standards
The transition to an analytical cadastre is both crucial and inevitable
The problem at hand
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Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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 methodfounded 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)
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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
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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
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The proposed algorithm cont .
example
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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
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Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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
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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
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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
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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 .
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Implementation of GAs – cadastral analogy cont. – Objective function
1 1
( ) min( )
1 ( )2
f i i ideal calculated
calculated i i i
T u S S S S
S Y X X
1/100 2 2 2 1/100 21 1
( ) min( )
& : :
( )( ) ( )
f
ij i j i j i i i i
T u Delta
paralel perpendicular lines straight lines
Delta l l d d Delta l l d
Areas
Lines
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Implementation of GAs – cadastral analogy cont. – Fitness function
Areas
Lines
Total grade( ) ( ) ( ) ( ) ...b p l lGrade u f u f u f u
2 2 2
( )
100
[( ) ( ) ]XY
ip i i i
i
i ii
i i
i i
i i
Sf u u p pS
A SuA T
S ST mY X
1.5
1.5( ) ( )
( )( ) ( )
100
i j i ji i il
i j i j
i ii i
i
n n l lf u u w w
n n l lA Su S DeltaA
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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
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The proposed algorithm - graphical illustration
……Set 1
…Set 2
…Set N
Parcel 1 Parcel 1 Parcel 1 Lines 1 Lines 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
Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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
Simulation results cont.
A characteristic set of synthetic data
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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-0.619-0.7040.6300.497-0.0120.0100.2160.224GAs-0.168-0.1900.1540.134-0.0030.0030.0440.043LS-0.619-0.7040.5690.456-0.0120.0100.1840.173
The following parameters have been used: Standard deviation error - 0.25 meter An expected MSE of the coordinates - 0.05 meter Maximum generations (iterations) - < 100
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Simulation results cont.
Solution improvement throughout the generations
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Simulation results cont.
Param- etersminmaxSTD
X0.0390.0490.004
Y0.0370.0450.002
Solution stability examination results (meters)
29
Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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
Introduction
The problem at hand
The proposed algorithm
Implementation of GAs – cadastral analogy
Results
Summary
Future work
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
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Thank you