report deliverable 2

7/30/2019 Report Deliverable 2

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Deliverable 2Use Genetic Algorithm to optimize the sectorization ofthe Barcelona FIR

20/05/2013

Yanik Lacroix

Joaquim Villn


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ContenidoExecutive summary ................................................................................................................. 3

Introduction ............................................................................................................................ 4

Methodology ........................................................................................................................... 5

Optimizing sectorization with GA considering aircraft counts ........................................... 5

Finding intersections ........................................................................................................... 8

Results & Conclusions ............................................................................................................. 9

Optimizing sectorization with GA considering aircraft counts ........................................... 9

Morning Traffic................................................................................................................ 9

Mid-day Traffic .............................................................................................................. 12

Night Traffic ................................................................................................................... 13

Conclusions about Sectorization ................................................................................... 14

Finding intersections ......................................................................................................... 15

Bibliography .......................................................................................................................... 17


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Executive summary

This whole project aims to optimize of the airspace using Genetic Algorithm and Voronoi

diagrams. The airspace chosen for optimizing has been Barcelonas FIR. This task is really

interesting and important because in this way the air services providers companies will be

able to save a lot of money having less controllers and controllers will have a more regulated

work and egalitarian.

This complex work has been divided in several parts. The first part was about defining

Barcelonas FIR and evaluating the workload and variance given of one sectorization so in the

next parts it was possible to get better sectorizations and optimizing the airspace.

This part of the project, the second, aims to use Genetic Algorithm to optimise

sectorization considering aircraft counts. This part is really important and because Genetic

Algorithm will help to get a low variance sectorization which is really interesting thing because

it means that the controllers will have similar workload in terms of number of aircrafts in

charge of them.

This is a big step forward on the whole project because from this it will be possible to get a

really good sectorization with only making changes on the computing of the workload, and

making the optimization considering workload and not only aircraft counts.


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Introduction

This part of the work is a previous work so in the future it will be possible to optimize the

sectorization considering more important factors like for example the workload.

The first factors that will be considered in this deliverable are the number of aircraft in

each sector using Voronoi diagrams and optimization with Genetic Algorithms. At the end the

program will be able to find the best sectorization with lower variance though a process of

natural selection with Genetic Algorithms.

It will also calculate the intersection between the airways, a factor that will be important in

the future to use Genetic Algorithms with Workload instead of Aircraft Counts.

Workload is the quantity of work that a controller has in one sector. This factor depends on

a lot of different issues, but one that is really important is the intersections between airways.

This intersection can be conflictive points where aircraft from different aircrafts could crash

because they are in the same point. These conflictive points will take time to the controller

solving possible crashes so this will make the workload increase.


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Methodology

Optimizing sectorization with GA considering aircraft counts

In the computer science field of artificial intelligence, a genetic algorithm (GA) is

a search heuristic that mimics the process of natural evolution. This heuristic (also sometimes

called ametaheuristic) is routinely used to generate useful solutions

to optimization and search problems.[1]

Genetic algorithms belong to the larger class

of evolutionary algorithms (EA), which generate solutions to optimization problems using

techniques inspired by natural evolution, such as inheritance, mutation, selection,

and crossover.

Genetic Algorithms were implemented in the program with the aim of find the best

sectorization of the Barcelona FIR keeping in mind the number of aircrafts in each sector. Each

sector should contain no more than 15 aircrafts, if this is not possible, the minimum of aircraft

on each sector will change to 20. The FIR must be divided in minimum two sectors. The

program will minimize the sectors needed to find the best sectorization (the sectorization with

lower variance).

First of all a brief explanation about the operation of the algorithm:

The program creates a chromosomes matrix, the size of the matrix is [Number of

individuals, Number of Variables x Precision] in our case the number of individuals will be a

number large enough to evaluate all area of the FIR and small enough to dont affect the time

of execution. The program will need two variables for each sector, so the number of variables

will change depending on how many sectors we are looking for (Number Variables = 2*

Number of Sectors). The Precision is the number of binary numbers used to represent a

variable.

When the programs had this chromosomes matrix, a decodification matrix is needed to

evaluate the binary combinations and decodificate it in decimals values, keeping in mindthe

limits imposed and the precision of each variable. In our case we need to make two FieldD

matrix and put it together because the limits of X and Y variables are not the same. As it can be

seen in Picture 1, this is the format of and individual after the decodification from binary to

decimal numbers, the first part of the matrix was decodificated with FieldDX and the second

part with FieldDY due to the difference of limits.


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Picture 1: Individual format after decodification with decodification needed in each part

With this randomly obtained matrix of X and Y points in the domain that is being studied

the next step is to evaluate it to look which individuals are the bests. The evaluation is

conducted by Objective Function. The Objective Function will compute the variance for each

combination of points. First it calculates the aircraft inside each sector of this voronoi

combination using the workload function and after that it calculates its variance, the objective

function returns a vector with all variance of all combination of points, which can be looked as

the degree of goodness of this combination of points. This vector with the variance values is

called ObjV.

When the programs had this initial population and this initial evaluation of our randomly

marked population it can begin to make iterations to follow a way to find the best points

combination.

The number of iterations we will make has to be enough to find the best variance but cant

be so high because it will take a lot of time to be executed. The iterations will follow always the

same process. First fitness is calculated and program makes a selection of best individuals with

a probability of Gap (if Gap is 0.9 and we have 100 individuals, it will save 10% of 100, so it will

save the 10 bests). After that with the rest of individuals that are not saved the crossover

function makes crossover between chromosomes of the different individuals, not all

individuals are crossed, there is also a crossover probability. With the results of crossovers, the

individuals are mutated with a probability mutation, to try to obtain best individuals.

After all this process we evaluate the new individuals and we add the individuals saved

before, calculating the best of the entire result.

Doing a lot of iterations of this process only the best individuals will survive so at the end it

will be best variance related with voronoi points, and the Genetic Algorithm function will

return the best sectorization for a determined number of sectors. As it can be seen in Picture


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2, the Algorithm will always find a best variance until it gets the minimum and only the best

variances will survive.

Picture 2 Example of application of Genetic Algorithm for a determinate number of sectors

After this explanation of the process that Genetic Algorithm takes to find the best

sectorization, its needed to find the best sectorization, with n sectors (more than 2). Thats

why the program have to make Genetic algorithm for 2 sectors to n sectors, where n is the

maximum number of sectors. There is no maximum number of sectors but its known that in

reality a lot of sectors will make a lot of transfers between sectors so it has to be maximum, in

this case the maximum will be 25 sectors.

When the algorithm with all numeration of sectors is done a vector with variance and

another one with voronoi points corresponding to each variance is obtained. There is the

restriction that no more than 15 aircraft can be in one sector, so the programs look if all the

variance comply the restriction and delete which dont comply it. At the end it is only the best

variances that accomplish the restriction, the program choose the best and thats the one that

have the best sectorization.

In the case where no sectorization have less than 15 aircraft in each sector, the program

try to find which ones have less than 20 aircraft in each sector.


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Finding intersections

To find the intersection between airways it has been used the matlab function

IntersectSegments which has been developed particularly for this part of the work.

This function can obtain the intersection point between two 2D vectors given. To do this

first the program obtains the lines which contain each vector. Once the lines have been

obtained the program solves an equations system of two equations and two variables to find

the intersection between the two lines.

However the result obtained is the intersection between the two vectors and not between

the two lines so after finding the intersection point between the two lines the program looks if

this intersection point belongs to both vectors. If affirmative the program has found the

intersection point between both vectors, and if negative there is no intersection point

between both vectors. The results are all rounded because this is wanted to get the

intersections between airways and if two segments are really close (less than 1 unit, in

airways, 1 km) its considered that the airways intersect because the controller would have to

separate the traffic despite the aircrafts are not going to collapse.

Using this function with all the airways its possible to find the intersection points between

all the airways. To find all the intersection points all the airways are compared with the other

only once. Despite this fact some points will be found more than once because there might be

more than two airways than intersect in the same point. To know how many airways intersect

on one point another function will be developed called numSegInters.

This function with the results obtained comparing all the airways once will count how

many times there is the same element in the list. This number is how many times the airways

intersect in one point and this is called the total occurrence. But to know how many airways

intersect in that point, what its called real occurrence, the next equation must be solved:

022

= tnn where n is the number of airways intersecting (real occurrence) and t is

the number of times the intersection has been found (total occurrence). This equation is only

valid for values of n bigger or equal to 2. If not this means that there are only two airways

intersecting and this means that total occurrence and real occurrence are one.

Finally the program has obtained the number of different intersections between all the

airways in the Barcelonas FIR .


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Results & Conclusions

Optimizing sectorization with GA considering aircraft counts

Following the method of Genetic Algorithm searching the best sectorization with voronoi

points inside the limits of our FIR, considering a maxim number of sectors of 25 and knowing

that no more than 15 aircraft can be in one sector. Its needed to make the process with the

three files of traffic, so the result will be 3 sectorization for 3 periods of the day.

The chromosomes matrix Genetic Algorithm is created randomly, then its normal that the

program obtain a different result every time, in the results there are examples of possible

results.

Morning Traffic

The morning traffic is the one that have more aircrafts and in this one there is the problem

that no sectorization is founded with no more than 15 aircrafts in each sector, so we had to

consider that the restriction is no more than 20 aircraft in each sector.

In this case the program has worked with 200 iteration for each number of sectors, this

process has been long but the results are more accurate.

The program has obtained: The best sectorization is with 7 Sectors and it has a Variance of

17.904762, the number of aircraft in each Sector are: 18 11 11 20 9 14 10

Picture 3 Different variances with different number of sectors


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As it can be seen in Picture 3 the best variance is with 7 sectors and the other variances are

higher, the number of sectors can be increased but it wont get a better variance.

With this variance obtained there the Sectorization of the airspace obtained is shown in

Picture 4.

Picture 4: Best sectorization of Morning Traffic (7 Sectors) with high precision, high execution time.

Due to the long time that it takes to arrive to that result another test is made and tried to

find the best sectorization with 50 iterations (not 200) and with lower number of individuals.

The maximum number of sectors is reduced also to initial number of sectors+9 (in the case of

Morning Traffic is 15).

With that changes to increase the speed of execution the results obtained in less time than

before are:

The best sectorization is with 9 Sectors and it has a Variance of 22.500000, the number of

aircraft in each Sector is: 7 15 9 18 9 2 8 13 12


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As it can be seen in Picture 4 and comparing it with Picture 6 it can be assumed that the

different results obtained are due to the randomly made matrix and concluded that with a

lower time of execution and regulating the parameters of execution the results can be good in

lower time.

Picture 3: Different variances with different number of sectors Morning Traffic

The Voronoi sectorization related to the best variance in lower execution time is shown in

Picture 6.

Picture 4: sectorization of Morning Traffic with low execution time.


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Mid-day Traffic

Due to long time of execution to get a non-high precision compared with the precision

reached with the second try of parameters in Morning Traffic test. The parameters for Mid-day

Traffic and Nigh Traffic will be the second ones taken in Morning traffic test.


aircraft in each Sector is: 5 5 8 5 5 6

The variance obtained is very good result, so the assumption did before worked good.

In Picture 7 it can be seen the different variances for each number of Sectors evaluated

and in Picture 8 the Voronoi diagram related with the best variance sectorization.

Picture 5 Variances for each sectorization of Mid-day Traffic


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Picture 6: Sectorization obtained for Mid-day Traffic

Night Traffic

With the Night Traffic the same process is done and the results obtained are:


aircraft in each Sector is: 8 7

As it can be seen in Picture 10, there are 2 sectorization with 0.5 variance but the program

takes the one with lower number of sectors. In picture 11 it can be seen the Voronoi diagram

related with best variance in Morning Traffic file.

Picture 7: Variance for each Sectorization in Night Traffic


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Picture 8: Sectorization for Night Traffic

Conclusions about Sectorization

The best sectorization found in the three cases of air traffic is with a determinate number

of sectors, in the following table it can be seen the difference between variance of having

more or less aircraft in our FIR. With a lot of aircraft is more difficult to get a lower variance

and with little amount of aircraft it's easier to make good sectors. It means that in different

periods of the day the Barcelona FIR will need different configurations of Sectors to absorb the

whole demand of aircraft, and to maximize efficiency of controllers without having an excess

of workload.

Period of Day Total Aircrafts Variance

Morning Traffic 93 22.5

Mid-day Traffic 34 1.466667

Night Traffic 15 0.5


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Finding intersections

Doing all the procedure explained above finally the number of different intersections

found has been 96. Most of the intersections are of just 2 airways but there are also points

with intersection of 3 or more airways.

With this results the conclusion is that as a future work the genetic algorithm will have to be

done considering Workload of the controller because there are intersections with a really big

real occurrence so a controller in charge of these waypoints will have a huge increase of work

as for example in BCN (real occurrence 13).

Real occurrence Quantity

1 76

3 4

4 5

5 5

6 1

7 2

8 1

10 1

13 1

Picture 12: Real occurrence of all intersections


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All the intersections can be seen in the Picture 13.

Picture 13: Intersection points


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Bibliography

Mitchell, Melanie (1996).An Introduction to Genetic Algorithms. Cambridge

Delgado L., (2013),GEAIO project Deliverable 2[Power Points slides].

report deliverable 2

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