1. Stochastic Traffic Signal Timing Optimization using GAby
Sam Pearce
Jeremy Moreau
Hassan Salamy
Santosh Verma
Krishnendu Roy
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2. References
B. Park, N. M. Rouphail and J. Sacks, “Assessment of a Stochastic Signal Optimization Method Using Microsimulation”, 80th TRB Annual Meeting, November 2000
A. Kamarajugadda and B. Park, “Stochastic Traffic Signal Timing Optimization”, Centre for Transportation Studies, University of Virginia.
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3. Outline Introduction Methodology Comparisons of Algorithms
Changes in System Demand
Conclusion
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4. Background Road Transportation extremely important
Signaling System – one of the key constituents
Causes vehicular delay
Increases total travel time
Reduces system’s speed and cost-effectiveness
Secondary effect such as increased air/sound pollution and energy consumption
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5. Traffic Engineer’s Goal
Quantify Delay
Optimize the Signal System for minimum delay
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6. Delay Estimate Equation
Highway Capacity Manual (HCM)
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7. Shortcomings of the Delay Equation
Traffic volumes usually collected for a day or two
So, delay based on average demand
Demand follows stochastic variability
Variables like green-time, saturation rate are also stochastic
Additional factors - % of trucks, driver characteristics
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8. Contributions of this research
Variability of HCM delay
Optimize the signaling intersection using GA stochastic variability and evaluate the scheme using traffic simulation programs like CORSIM and show its superiority over TRANSYT-7F (T7F)
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9. Test Network And Evaluation
The test network in Chicago had 9 signalized intersections
Coded into CORSIM using 59 links and 31 internal nodes
Traffic volume data was collected during AM and PM hours by manual means
Maximum Queue Lengths (MQL’s) were collected for evaluation
Was coded in both TRANSYT-7F and CORSIM
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10. Test Network
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11. TRANSYT-7F (T7F)
Widely used urban traffic signal optimization package (macroscopic)
Features: modeling of saturated and queue spillback conditions, step-wise simulation, horizontal queuing, multiple cycles and multiple periods, optimization under congested conditions
Can optimize: delay, fuel consumption, stops, throughput, progression opportunities, and combinations of these
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12. CORSIM
Stochastic and periodic-scan based urban traffic program (microscopic)
Generates the delay and queue time for a link
Average link delay is the total delay time divided by the number of vehicle through the link
Queue time is the time in a queue due to link control
CORSIM at times may underestimate the link delay of congested networks
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13. Genetic Algorithms
Genetic algorithms are probabilistic optimization techniques based on the model of natural evolution and solve problems of high complexity.
Genetic algorithms use a group of randomly initialized points, a population, in order to non-deterministically search the decision space.
The population is characterized by the fact that each individual encodes all necessary problem parameters (genes).
Genetic algorithms work with a coding of the parameter set and not the parameters themselves.
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14. Genetic Algorithm
Therefore, one requirement when employing GAs in order to solve a combinatorial optimization problem is to find an efficient representation of the solution in the form of a chromosome.
The population is modified according to the natural evolution process following a parody of Darwinian principle of the survival of the fittest.
Individuals are selected according to their quality to produce offspring and to propagate their genetic material into the next generation.
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15. Genetic Algorithm
Genetic algorithms employs an iterative process of selection and recombination that are executed in a loop for a fixed number of iterations where each iteration is called a generation.
The selection process is intended to improve the average quality of the population by giving individuals of higher quality a higher probability of survival.
Selection thereby focuses on the search of promising regions in the decision space.
The quality of an individual is measured by a fitness function.
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16. Genetic Algorithm
Each offspring undergoes a sequence of probabilistic recombination that changes the genetic material in the population either by inversion, crossover, mutation or possibly other user defined operators.
The process exploits new points in the decision space by providing a diversity of the population and avoiding premature convergence to a single local optimum.
The iterative process of selection and combination of “good” individuals should yield even better ones, until a solution is found or a certain stopping criterion is met.
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17. Genetic Algorithms
The three basic operators found in every genetic algorithm.
Reproduction
Crossover
Mutation
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18. Genetic Algorithm 1- Reproduction: What?
It is the selection of chromosomes from the population
to the mating pool, which is used as the basis of the
next generation.
How?
There are different ways such as:
Always select the fittest and discards the worst.
Roulette Wheel Method:
Chooses the Chromosomes in a statistical fashion based on the
fitness values
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19. Genetic algorithm 2- Crossover:
Two chromosomes are chosen from the mating pool
and then crossover is applied to them based on a
probability p.
If crossover does take place, then a random splicing point is
chosen in a chromosome.
The two chromosomes are spliced and the spliced regions are mixed
to create two (potentially) new chromosomes.
These child chromosomes are then placed in the new population.
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20. Genetic Algorithm - Example1 1
Crossover 1 1
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21. Genetic Algorithm 3- Mutation:
Based on the initial population, there might not be enough variety of
Chromosome solutions.
The mutation operator can overcome this problem.
Mutation is usually applied with small probability m.
Mutation Randomly changes an element in the chromosome.
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22. Genetic Algorithm
Example: 1
Mutation 1
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23. GA-SOM
Initial signal timing plans in binary representation form are randomly
generated.
REXX code is used to convert the timing plans into integer values.
Those integer values will be inserted into CORISM input file.
A single CORISM run for each tested signal plan is executed.
This process continues until all signal plans proposed by the GA optimizer
are run
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24. GA-SOM plan from the corresponding CORSIM text output file.
A second REXX code extracts the performance measures for each signal
plan from the corresponding CORSIM text output file.
These performance measures are then fed to the GA.
the GA evaluates the performance measure.
The GA then generates a new set of signal timing plans.
This whole routine will continue until a pre-specified number of iterations is
reached.
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25. GA-SOM The author’s objective function is:
The objective function can be any combination of outputs from CORSIM.
The author’s objective function is:
Where:
SQT = system queue time,
QT(i) = queue time on link I, i=1,…,L, and
L = number of one-way links on the network.
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26. GA-SOM
GA-SOM can simultaneously optimize cycle length, green splits and
offsets.
The number of generations is 25.
Population size is 25.
Crossover probability = 0.4
Mutation probability = 0.03
Elitism is used.
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27. GA-SOM
Convergence Analysis:
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28. GA-SOM
A Detailed Example:
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29. GA-SOM A chromosome is a 36 bit binary string.
For this example a population of size n = 20 is used.
A chromosome is a 36 bit binary string.
The bits are used to code one cycle length and eight green times
for the eight possible movements.
The coding procedure has to generate a set of feasible green times.
The 36 bit string is broken down into 6 strings of 6 bits each.
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30. GA-SOM a decimal number and dividing by 63.
Six fractions are then generated by converting the binary string into
a decimal number and dividing by 63.
The six fractions are used to code the green times and cycle length
as:
Cycle = cycle length,
MIN = minimum allowed cycle length,
MAX = maximum allowed cycle length, and
f(0) = random number generated/ fraction generated
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31. GA-SOM The left turn green times are encoded as follows:
Green(1) = 10 +Int((Cycle – 50)*f(1)*f(2)) – 4
Green(3) = 10 +Int((Cycle – 50)*(1 - f(1))*f(4)) – 4
Green(5) = 10 +Int((Cycle – 50)*f(1)*f(3)) – 4
Green(7) = 10 +Int((Cycle – 50)*(1 – f(1))*f(5)) – 4
where,
Green(i) = effective green time for the NEMA phase i,
Cycle = cycle length generated in the cycle Equation, and
f() = random numbers/fractions generated.
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32. GA-SOM The through green times are encoded as follows:
Green(2) = 15 +Int((Cycle – 50)*f(1)*(1-f(2))) – 4
Green(4) = 15 +Int((Cycle – 50)*(1 - f(1))*(1-f(4))) – 4
Green(6) = 15 +Int((Cycle – 50)*f(1)*(1-f(3))) – 4
Green(8) = 15 +Int((Cycle – 50)*(1 – f(1))*(1-f(5))) – 4
The green times along with the volumes and the cycle length are used to calculate the intersection delay and variance.
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33. GA-SOM
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34. GA-SOM
Step I: Computation of average and variance of the degree of saturation (X)
Capacity (c) = s*(g/s)
Average X = Average volume / Capacity
Standard deviation of Volume
Variance X = Variance volume / Capacity2
Standard deviation X
STEP II: Approximate the HCM delay equation
The generalized Taylor Series expansion of any function F(x):
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35. GA-SOM
STEP III: Compute the expectation values of X based on the distribution
Given that X follows a normal distribution, and using the mean and variance (or COV)
from step I and Equation below following values are obtained.
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36. GA-SOM
STEP IV: Apply the expectation values onto delay and delay squared
STEP V: Compute delay average and its variance from the expectation values
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37. Comparison of Signal Timing Plans
GA-SOM and the best T7F timing plans are evaluated on the basis of both CORSIM and T7F.
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38. Results of 100 CORSIM simulations using the GA-SOM and the best T7F timing plans
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39. Not only does the histogram of the GA-SOM plan lie substantially to the left of the T7F plan, but it is far less variable.
The long tail in the distribution of the T7F timing plan is alarming considering high system queue time is indicative of or serious spill-back or gridlock.
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40. During the AM period approximately 5/100 simulations resulted in System queue time of 300 or greater. During the PM period approximately 30/100 had the same result. Over the course of 20 week days a driver will run into major problems seven times.
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41. The T7F timing plan was customized for a specific traffic flow pattern with a few optimization features based on traffic indicators. It is not capable of learning or making adjustments outside of the limited built-in options.
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42. Random Changes in Traffic Demand
Until this point, mean arrivals at external nodes assumed constant
Mean arrivals are also based on manual count and subject to considerable error
Changes of ±(15) from base demand are considered
(31)8 total combinations of demand patterns
Use sampling method called Latin Hypercube Design to generate 204 demand combinations
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43. Random Changes in Traffic Demand – AM period
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44. Random Changes in Traffic Demand – AM period
GA-SOM produces lower queue time than T7F in 95% of the cases
The queue time of GA-SOM is compared to for T7F
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45. Random Changes In Demand – PM period
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46. Systematic Changes in Demand
How robust is the present system if traffic demand increases over time?
When is it necessary to update the system?
Following are evaluated:
Base demand, base optimal GA-SOM plan
Base demand, updated GA-SOM plan
Updated demand, base optimal GA-SOM plan
Updated demand, updated GA-SOM plan
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47. Systematic Changes in Demand
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48. Systematic Changes in Demand
Do nothing approach is costly for updated demand(4 is better than 3)
With updated plan and base demand(1 vs 2), there is a performance drop but it is less variable
The sets 1 and 3 represent performance for base signal plan
The sets 2 and 4 represent performance for updated signal plan
It is good strategy to develop signal strategies with assumption of increased demand rates
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49. Conclusion and Discussion
Results are promising, but computational burden is non-trivial
T7F takes minutes, GA-SOM 7-8 hours on Pentium 2(450 Mhz) processor
Unlike T7F, GA-SOM explicitly accounts for stochastic nature of traffic flow
The computations are suitable for parallel computation
Another network, three times the size was tested
Initial results prove it is much more effective with much less variation than T7F under varying demand.
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