RMI Workshop - Genetic Algorithms

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RMI Workshop - Genetic Algorithms
Genetic Algorithms and Related Optimization
Techniques Introduction and Applications
Kelly D. Crawford ARCO Crawford Software, Inc.
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Other Optimization Colleagues
Donald J. MacAllister ARCO Michael D.
McCormack Richard F. Stoisits Optimization
Associates, Inc.
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A no hype introduction to genetic algorithms
(GA)
What every intro to GAs talk begins with -
Biology - Evolution - Survival of the
fittest What I am not going to talk about -
Biology - Evolution - Survival of the
fittest - Exception nomenclature/jargon Its
not about biology - its about search!
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Optimization
Given a potential solution vector to some
problem x Any set of constraints on x Ax ?
b And a means to assess the relative worth of
that solution f(x) (which may be continuous
or discrete) Optimization describes the
application of a set of proven techniques
that can find the optimal or near optimal
solution to the problem. Examples of
optimization techniques Genetic algorithms,
genetic programming, simulated annealing,
evolutionary programming, evolution strategies,
classifier systems, linear programming,
nonlinear programming, integer programming,
pareto methods, discrete hill climbers, gradient
techniques, random search, brute force
(exhaustive search), backtracking, branch
and bound, greedy techniques, etc...
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Optimization Application Examples at ARCO
Gas lift optimization (Ashtart) x Amount
of gas injected into each well Ax ? b Max
total gas available, max water produced
f(x) Total oil produced Technique Learning
bit climber Free Surface Multiple Suppression
x Inverse source wavelet Ax ?
b Min/max wavelet amplitudes f(x) Total
seismic energy after wavelet is applied
Technique Genetic algorithm and learning bit
climber
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What to look for in an Optimization Technique
Convergent techniques continuous Gradient
search, linear programming discrete Integer
programming, gradient estimators Ok for search
spaces with a single peak/trough Divergent
techniques Random search, brute force
(exhaustive search) Ok for small search
spaces Hard problems (large search spaces,
multiple peaks/troughs) need both convergent
and divergent behaviors Genetic algorithms,
simulated annealing, learning hill climbers,
etc. These techniques can exploit the
peaks/troughs, as well as intelligently
explore the search space.
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Convergent and Divergent Behaviors
Need a balanced combination of both convergent (
) and divergent ( ) behaviors to find
solutions in complicated search spaces.
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Genetic Algorithms - A Sample Problem

• Ashtart gaslift optimization
• 24 wells - Offshore Tunisia
• Given A fixed amount of gas for injection
• Question What is the right amount of gas to
  inject into each well to maximize oil production?

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Lift Gas Optimization
Lift Gas Curve

• Objective
• Maximize oil production rate.
• No capital expenditures.

Total Oil Produced
Total lift gas
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Genetic Algorithms - Representing a Solution
Chromosome
Genotype
...
...
Genes
...
...
Phenotype
Well 1
Well 12
Well 24
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Genetic Algorithms - Crossover and Mutation

• Genetic Operations on Chromosomes - Crossover

Parents
Children
00 01010011
10 11011010

• Genetic Operations on Chromosomes - Mutation

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Genetic Algorithms - Evaluating a Solutions
Fitness
So just how good are you, kid?
Total Daily Oil Production for the Field
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Genetic Algorithms - The Process
Parents
Children
A
B
Crossover and Mutation
X
Y
Z
No
Yes
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What are the necessary requirements for using a
GA?
When you need ...some way to represent potential
solutions to a problem (representation bit
string, list of integers or floats,
permutation, combinations, etc). ...some way to
evaluate a potential solution resulting in a
scalar. This will be used by the GA to rank the
worth of a solution. This fitness (or
evaluation) function needs to be very
efficient, as it may need to be called thousands
- even millions - of times. But you do not
need... ...the final solution to be
optimal. ...speed (this varies)
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When should you not use a GA?
When ...you absolutely must have the optimal
solution to a problem. ...an analytical or
empirical method already exists and works
adequately (typically means the problem is
unimodal, having only a single peak). ...evalua
ting a potential solution to your problem
takes a long time to compute. ...there are so
few potential solutions that you can easily
check all of them to find the optimum (small
search spaces).
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Earth Model Showing Primary Reflections
Seismic Trace
Source
Receiver
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Earth Model with Surface Multiple Reflections
Seismic Trace
Source
Receiver
Multiples
What appears as reality, but isnt!
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Estimating the Inverse Source Wavelet
-0.0176 -0.00978 0.087976 0.213099 -0.57283
0.909091 -0.6393 0.885631 -0.88172 1.151515
1.784946 1.249267 -0.44379 -0.73705
1.644184 -1.12806 0.209189 0.26784 -0.04106 -0.1
1926 0.076246
01101100101011001010101001001010101010101001010101
01010101010101010100001011000110101101001010001100
10101001010010010101001010101101001101010101010101
01010100110101101010110101010010101010100101010101
0101001010
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Seismic Surface Multiple Attenuation Using a GA
Input Data
After Multiple Removal
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Another Example - Kuparuk Material Balance
Production Well
Injection Well
Injection Well
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The Material Balance Problem
Production Well
Injection Well
Each producer may get fluids from multiple
patterns. Each injector may put fluids into
multiple patterns.
This is a diagram of a single pattern showing 16
allocation factors. The entire field has between
3000 to 7000 allocation factors, represented
using 10 bits each.
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Normalized Solution Vectors
?
.01 .56
.22 .21
1
Several normalized groups...
?
1
.33 .41
.26
?
1
.16
.18 .32
.25 .09
.01 .56
.22 .21
.33 .41
.26
.16
.18 .32
.25 .09
combined into one chromosome
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Normalization Example
Actual Chromosome Before Normalization
.5 .8
.2 .3
.4 .3
.9
Group 1
Group 2
.33 .53
.14 .16
.21 .16
.47
Translated Chromosome After Normalization
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Initial Solution Attempt

• Simple floating-point genetic algorithm
• generational model
• 1-point crossover
• Worked ok for a 9 pattern simulated field (small)
• Estimated time required for full field 1 month
  on an SGI workstation 10 months on 167 MHz PC.
• Back to the drawing board...
• When done the traditional way (by hand), this
  problem was already taking 10 man-months (spread
  out across a number of drill-site engineers)

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Formulating the problem as a string of bits
A potential solution to this problem consists of
a list containing both allocation factors and
pressures, each of which are floating point
values Any single allocation factor or pressure,
x, has a range of 0..1. Assuming we need a
resolution of 0.01, we can represent each x
using 10 bits.
0.01 0.23 0.82
0.53 ...
0011011010 1010011011 1001101010 1010011010 ...
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Material Balance - Second Try

• Bit encoded genetic algorithm
• Steady-state model
• Uniform crossover
• Much faster on this particular problem (10x)
• Added gray coding
• Gained additional performance (20x)
• Everything we tried from this point on worked
  with varying degrees of performance.

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Some Insights

• Since we are normalizing subsets within the
  chromosome, crossover is a potentially
  destructive operation. What if we just used
  mutation instead.
• In fact, what if we only used mutations that
  probabilistically tended to result in smaller
  changes to the chromosome, resulting in less
  disruption, and perhaps better convergence?

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An Example
Before normalization
After normalization
.4 .3
.9
.21 .16
.47
.3
.16
Current state
.4 .2
.9
.22 .11
.5
.3
.17
Small change
0 -.1
0
.01 -.05
.03
0
.01
Difference
.4 .9
.9
.16 .36
.36
.3
.12
Large change
.0 .7
0
-.06 .25
-.08
0
-.05
Difference
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Easier to see the impact graphically...
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Material Balance - Third and Fourth Try

• Used a standard bit climber
• flip a bit
• evaluate
• if fitness is worse, unflip the bit
• if we get stuck, scramble some number of bits and
  restart
• Performed even better
• Perhaps the problem is not as complex as we had
  once thought...?
• Used a modified bit climber
• flip bits according to changing probabilities
• 200x speedup over the original version
• Project now feasible

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Gradient Slope Derivative
Continuous, Differentiable
f(a)
f(x)
f(a)
a
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Gradient Estimator
Noncontinuous, Nondifferentiable, but we can
estimate the gradient
g(a-?) vs g(a)
g(a)
g(a-?)
g(x)
g(a?)
g(a) vs g(a?)
?
?


a?
a
a-?
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What are bit climbers?
Essentially a hill climber, but there is no
analytical information about what direction is
up (i.e., no gradient, or derivative).
Instead, you sample neighboring points.
Bit Climber Algorithm Randomly generate a
string of bits, X Evaluate f(X) Loop (until
stopping criteria satisfied) Randomly select
a bit position, j, in X, and flip it
(i.e., if X(j) 1, set to 0, and vice versa)
Evaluate the new f(X) If fitness is worse,
unflip X(j) (put it back like it was) End Loop
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Keeping the changes to a minimum
The bit climber does not attempt to avoid large
changes to the chromosome (a single bit flip can
result in a large overall change).
10010101 10010101 01010010
1.0
0.0
A simple heuristic Assign high probabilities to
the low order bits, low probabilities to the high
order bits.
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The Modified Bit Climber

• Generate and evaluate a random bit string
• Do until stopping criteria satisfied
• Randomly select a bit position, k
• Randomly generate p from 0..1
• If p lt probability of flipping bit k
• Flip the kth bit
• Evaluate the new string
• If fitness is worse, unflip the bit
• If count exceeds a threshhold, rerandomize the
  string
• Avoids making large changes to the bit string
• Worked much better than standard bit climber for
  this particular problem

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Dont backtrack
10010101 10010101 01010010
1.0
0.0
Another simple heuristic Multiply a bits
flipping probability by .25 (give or take) when
we flip it. This decreases the likelihood of ever
flipping it again.
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Adding a bit of memory (Tabu Search?)

• Generate and evaluate a random bit string
• Do until stopping criteria satisfied
• Randomly select a bit position, k
• Randomly generate p from 0..1
• If p lt probability of flipping bit k
• Flip the kth bit
• Evaluate the new string
• If fitness is worse, unflip the bit
• Else, decrease the probability for this bit
• If count exceeds a threshhold, rerandomize the
  string
• Avoids undoing changes to the bit string
• Avoids making large changes to the bit string
• Worked better than the modified bit climber for
  this particular problem

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Problem with the memory technique

• It gets stuck when the probabilities get too low
• But, based on the probabilities, we can compute a
  mean and standard deviation for each gene
  representing the most likely change that would
  occur if we kept looking for a bit that we could
  flip.
• In other words, we can simulate the modified bit
  climber using a simple statistical analysis.
• This leads us to a much simpler, much faster
  algorithm that never gets stuck - a floating
  point, bit climber!

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A floating point Bit climber

• Randomly generate and evaluate a float string
• Compute ? and ? based on each genes
  probabilities (a gene is a group of bits, say 10)
• Until stopping criteria satisfied
• Select a single string position, i
• Generate a mutation value as N(?, ?)
• Add mutation value to string(i)
• Evaluate the new string
• If fitness is worse, undo the mutation
• Else, recompute ? and ? for that gene
• If count exceeds a threshhold, rerandomize the
  string
• 10x faster than other bit climbers tested (2000x
  faster than original solution)

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Conclusions

• ARCO has had many technical successes in the use
  of Genetic Algorithms and related technologies
• The modified bit climber with memory has worked
  well in most, but not all, of the applications
  weve tried at ARCO material balance, gaslift
  optimization (except one) and seismic multiple
  suppression.
• ARCO will no longer exist, per se, after this
  year. The new name BP Amoco
• Could these events be relatednahhhhh!

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GA/Oil-Related Publications

• McCormack, Michael D., Donald J. MacAllister,
  Kelly D. Crawford, Richard J. Stoisits,
  Maximizing Production from Hydrocarbon
  Reservoirs Using Genetic Algorithms, The Leading
  Edge (SEG, Tulsa, OK, 1999).
• Crawford, Kelly D., Michael D. McCormack, Donald
  J. MacAllister, A Probabilistic, Learning Bit
  Climber for Normalized Solution Spaces, GECCO
  1999.
• Stoisits, Richard J., Kelly D. Crawford, Donald
  J. MacAllister, Michael D. McCormack, A. S.
  Lawal, D. O. Ogbe. Production Optimization at
  the Kuparuk River Field Utilizing Neural Networks
  and Genetic Algorithms, SPE paper 52177 (OKC,
  OK, 1998).