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RMI Workshop - Genetic Algorithms

Genetic Algorithms and Related Optimization

Techniques Introduction and Applications

Kelly D. Crawford ARCO Crawford Software, Inc.

Other Optimization Colleagues

Donald J. MacAllister ARCO Michael D.

McCormack Richard F. Stoisits Optimization

Associates, Inc.

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!

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...

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

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.

Convergent and Divergent Behaviors

Need a balanced combination of both convergent (

) and divergent ( ) behaviors to find

solutions in complicated search spaces.

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?

Lift Gas Optimization

Lift Gas Curve

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

Total Oil Produced

Total lift gas

Genetic Algorithms - Representing a Solution

Chromosome

Genotype

...

...

Genes

...

...

Phenotype

Well 1

Well 12

Well 24

Genetic Algorithms - Crossover and Mutation

- Genetic Operations on Chromosomes - Crossover

Parents

Children

00 01010011

10 11011010

- Genetic Operations on Chromosomes - Mutation

Genetic Algorithms - Evaluating a Solutions

Fitness

So just how good are you, kid?

Total Daily Oil Production for the Field

Genetic Algorithms - The Process

Parents

Children

A

B

Crossover and Mutation

X

Y

Z

No

Yes

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)

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).

Earth Model Showing Primary Reflections

Seismic Trace

Source

Receiver

Earth Model with Surface Multiple Reflections

Seismic Trace

Source

Receiver

Multiples

What appears as reality, but isnt!

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

Seismic Surface Multiple Attenuation Using a GA

Input Data

After Multiple Removal

Another Example - Kuparuk Material Balance

Production Well

Injection Well

Injection Well

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.

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

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

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)

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 ...

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.

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?

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

Easier to see the impact graphically...

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

Gradient Slope Derivative

Continuous, Differentiable

f(a)

f(x)

f(a)

a

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-?

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

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.

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

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.

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

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!

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)

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!

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).