Title: PPT%20Primer%20on%20Evolutionary%20Algorithms%20(also%20known%20as%20Genetic%20Algorithms)
1PPT Primer on Evolutionary Algorithms (also
known as Genetic Algorithms)
2Introduction to Evolutionary Computation
- Natural Evolution
- Search and Optimisation
- Hillclimbing / Gradient descent
- Local Search
- Population-Based Algorithms (i.e. Evolutionary
Algorithms) - Advantages and Disadvantages of EAs
- Applications of EAs
- Reading Material and Resources
3Natural Evolution as a Problem Solving Method
- We seem to have evolved from tiny stuff in the
sea. How??? - The theory is given
- a population of organisms which have a lifetime
and which can reproduce in a challenging/changing
environment - a way of continually generating diversity in
new child organisms - A survival of the fittest principle will
naturally emerge organisms which tend to have
healthy, fertile children will dominate (I.e.
their descendents will).
4Evolution/Survival of the Fittest
-
- In particular, any new mutation that appears in
a child (e.g. longer neck, longer legs, thicker
skin, longer gestation period, bigger brain,
light-sensitive patch on the skin, a harmless
loose bone, etc etc) and which helps it in its
efforts to survive long enough to have children,
will become more and more widespread in future
generations. - The theory of evolution is the statement that all
species on Earth have arisen in this way by
evolution from one or more very simple
self-reproducing molecules in the primeval soup.
I.e. we have evolved via the accumulation of
countless advantageous (in context) mutations
over countless generations, and species have
diversified to occupy niches, as a result of
different environments favouring different
mutations.
5Evolution as Problem Solving
-
- Heres a problem
- Design a material for the soles of boots that
can help you walk up a smooth vertical brick wall - We havent solved this, but nature has Geckos
6Evolution as a Problem Solving Method
Can view evolution as a way of solving the
problem How can I survive in this
environment? The basic method of it is trial and
error. I.e. evolution is in the family of methods
that do something like this 1. Come up with
a new solution by randomly changing an old one.
Does it work better than previous
solutions? If yes, keep it and throw away
the old ones. Otherwise, discard it. 2. Go to
1.
But this appears to be a recipe for problem
solving algorithms which take forever, with
little or no eventual success!
7The Magic Ingredients
Not so since there are two vital things (and
one other sometimes useful thing) we learn from
natural evolution, which, with a sprinkling of
our own commonsense added, lead to generally
superb problem solving methods called
evolutionary algorithms Lesson1 Keep a
population/collection of different things on the
go. Lesson2 Select parents with a relatively
weak bias towards the fittest.
Its not really plain survival of the fittest,
what works is the fitter you are,
the more chance you have to reproduce,
and it works best if even the least fit still
have some chance. Lesson3 It can sometimes help
to use recombination of two or more
parents I.e. generate new candidate
solutions by combining bits and
pieces from different previous solutions.
8A Generic Evolutionary Algorithm
- Suppose you have to find a solution to some
problem or other, and suppose, given any
candidate solution s you have a function f(s)
which measures how good s is as a solution to
your problem. - Generate an initial population P of randomly
generated solutions (this is typically 100 or 500
or so). Evaluate the fitness of each. Then - Repeat until a termination condition is reached
- Selection Choose some of P to be parents
- Variation Apply genetic operators to the
parents to produce some children, and then
evaluate the fitness of the children. - Population update Update the population P by
retaining some of the children and removing some
of the incumbents.
9Basic Varieties of Evolutionary Algorithm
-
- Selection Choose some of P to be parents
- Variation Apply genetic operators
- Population update Update the population P by
There are many different ways to select e.g.
choose top 10 of the population choose with
probability proportionate to fitness choose
randomly from top 20, etc
There are many different ways to do this, and it
depends much on the encoding (see next slide). We
will learn certain standard ways.
There are many several ways to do this, e.g.
replace entire population with the new children
choose best P from P and the new ones, etc.
10Some of what EA-ists (theorists and
practitioners) are Most concerned with
How to select? Always select the best? Bad
results, quickly
Select almost randomly? Great results, too
slowly How to encode? Can make all the
difference, and is
intricately tied up with How to vary?
(mutation, recombination, etc)
small-step mutation preferred, recombination
seems to be a principled
way to do large steps, but large
steps are usually abysmal. What
parameters? How to adapt with time?
11What are they good for ?
- Suppose we want the best possible schedule for
a university lecture timetable. - Or the best possible pipe network design for a
ships engine room - Or the best possible design for an antenna with
given requirements - Or a formula that fits a curve better than any
others - Or the best design for a comms network in terms
of reliability for given cost - Or the best strategy for flying a fighter
aircraft - Or the best factory production schedule we can
get, - Or the most accurate neural network for a data
mining or control problem, - Or the best treatment plan (beam shapes and
angles) for radiotherapy cancer treatment - And so on and so on .!
- The applications cover all of optimisation and
machine learning.
12More like selective breeding than natural
evolution
Time
13Every Evolutionary Algorithm
- Given a problem to solve, a way to generate
candidate solutions, and a way to assign fitness
values - Generate and evaluate a population of candidate
solutions - Select a few of them
- Breed the selected ones to obtain some new
candidate solutions, and evaluate them - Throw out some of the population to make way for
some of the new children. - Go back to step 2 until finished.
14Initial population
15Select
16Crossover
17Another Crossover
18A mutation
19Another Mutation
20Old population children
21New Population Generation 2
22Generation 3
23Generation 4, etc
24Bentley.s thesis work
Fixed wheel positions, constrained bounding area,
Chromosome is a series of slices fitnesses
evaluated via a simple airflow simulation
25Buy it
26The Evolutionary Computation Fossil Record
- The first published ideas using evolution in
optimisation came in the 50s. But the lineage of
current algorthms is like this
An intellectual curiosity
Rechenberg, Berlin, Evolutionsstrategie
Holland, Michigan Classifier Systems, Genetic
plans
Fogel, San Diego Evolutionary Programming
60s 80s 90s
Goldberg, Michigan Genetic Algorithms
A gift from Heaven
Koza, Stanford Genetic Programming
Ross, Corne, logistics
Parmee, Eng. design
Fleming, control systems
Savic, Walters, Water systems
27One of the very first applications. Determine
the internal shape of a two-phase jet nozzle that
can achieve the maximum possible thrust under
given starting conditions
Ingo Rechenberg was the very first, with
pipe-bend design This is slightly later work in
the same lab, by Schwefel
Starting point
EA (ES) running
Result
A recurring theme design freedom ? entirely new
and better designs based on principles we dont
yet understand.
28Some extra slides if time, illustrating some
high-profile EAs
An innovative EC-designed Propellor from Evolgics
GmbH, Associated with Rechenbergs group.
29Evolving Top Gun strategies
30Evolving Top Gun strategies
31Credit Jason Lohn
NASA ST5 Mission had challenging requirements for
antenna of 3 small spacecraft. EA designs
outperformed human expert ones and are nearly
spacebound.
32Credit Jason Lohn
Oh no, we knew something like this would happen
33A Standard Evolutionary Algorithm
- The algorithm whose pseudocode is on the next
slide is a steady state, replace-worst EA with
tournament selection, using mutation, but no
crossover. - Parameters are popsize, tournament size,
mutation-rate. - It can be applied to any problem the details
glossed over are all problem-specific.
34A steady state, mutation-only, replace-worst EA
with tournament selection
- 0. Initialise generate a population of popsize
random solutions, evaluate their fitnesses. - Run Select to obtain a parent solution X.
- With probability mute_rate, mutate a copy of X to
obtain a mutant M (otherwise M X) - Evaluate the fitness of M.
- Let W be the current worst in the population
(BTR). If M is not less fit than W, then replace
W with M. (otherwise do nothing) - If a termination condition is met (e.g. we have
done 10,000 evals) then stop. Otherwise go to 2. - Select randomly choose tsize individuals from
the population. Let c be the one with best
fitness (BTR) return X. -
35A generational, elitist, crossovermutation EA
with Rank-Based selection
- 0. Initialise generate a population G of popsize
random solutions, evaluate their fitnesses. - Run Select 2(popsize 1) times to obtain a
collection I of 2(popsize-1) parents. - Randomly pair up the parents in I (into popsize
1 pairs) and apply Vary to produce a child from
each pair. Let the set of children be C. - Evaluate the fitness of each child.
- Keep the best in the population G (BTR) and
delete the rest. - Add all the children to G.
- If a termination condition is met (e.g. we have
done 100 or more generations (runs through steps
15) then stop. Otherwise go to 1, -
36A generational, elitist, crossovermutation EA
with Rank-Based selection, continued
-
- Select sort the contents of G from best to
worst, assigning rank popsize to the best,
popsize-1 to the next best, etc , and rank 1 to
the worst. - The ranks sum to F popsize(popsize1)/2
- Associate a probability Rank_i/F with each
individual i. - Using these probabilities, choose one
individual X, and return X. -
- Vary
- 1. With probability cross_rate, do a
crossover - I.e produce a child by applying a
crossover - operator to the two parents. Otherwise,
let the - child be a randomly chosen one of the
parents. - 2. Apply mutation to the child.
- 3. Return the mutated child.
37Back to Basics
-
- With your thirst for seeing example EAs
temporarily quenched, the story now skips to
simpler algorithms. - This will help to explain what it is about the
previous ones which make them work.
38The Travelling Salesperson Problem
An example (hard) problem, for illustration
The Travelling Salesperson Problem Find the
shortest tour through the cities.
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
The one below is length 33
B
C
E
D
A
39Hillclimbing
0. Initialise Generate a random solution c
evaluate its fitness, f(c). Call c the
current solution. 1. Mutate a copy of the
current solution call the mutant m Evaluate
fitness of m, f(m). 2. If f(m) is no worse than
f(c), then replace c with m, otherwise do
nothing (effectively discarding m). 3. If a
termination condition has been reached, stop.
Otherwise, go to 1.
Note. No population (well, population of 1).
This is a very simple version of an EA, although
it has been around for much longer.
40Why Hillclimbing?
Suppose that solutions are lined up along the x
axis, and that mutation always gives you a nearby
solutions. Fitness is on the y axis this is a
landscape
9
6
10
7
5, 8
4
3
1
2
- Initial solution 2. rejected mutant 3. new
current solution, - 4. New current solution 5. new current solution
6. new current soln - 7. Rejected mutant 8. rejected mutant 9. new
current solution, - 10. Rejected mutant,
41Example HC on the TSP
We can encode a candidate solution to the TSP as
a permutation
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Current solution
Mutant
B
B
C
C
E
D
E
A
D
A
42HC on the TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
We randomly mutate (swap randomly chosen adjacent
nodes) current to ABEDC which has fitness 33
-- so current stays the same
Current solution
Mutant
B
B
C
C
E
D
E
A
D
A
43HC on the TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
We randomly mutate (swap randomly chosen adjacent
nodes) current (ABDEC) to CBDEA which has
fitness 38 -- so current stays the same
Current solution
Mutant
B
B
C
C
E
D
E
A
D
A
44HC on the TSP
We randomly mutate (swap randomly chosen adjacent
nodes) current (ABDEC) to BADEC which has
fitness 28
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
So this becomes the new current solution
Current solution
Mutant
B
B
C
C
E
D
E
A
D
A
45HC on the TSP
We randomly mutate (swap randomly chosen adjacent
nodes) current (BADEC) to BADCE which also has
fitness 28
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
This becomes the new current solution
Current solution
Mutant
B
B
C
C
E
D
E
A
D
A
46Landscapes
- Recall S, the search space, and f(s), the
fitness of a candidate in S
f(s)
members of S lined up along here
The structure we get by imposing f(s) on S is
called a landscape What does the landscape look
like if f(s) is a random number generator? What
kinds of problems would have very smooth
landscapes? What is the importance of the
mutation operator in all this?
47Neighbourhoods
- Let s be an individual in S, f(s) is our
fitness function, and M is our mutation operator,
so that M(s1) ? s2, where s2 is a mutant of s1.
Given M, we can usually work out the
neighbourhood of an individual point s the
neighbourhood of s is the set of all possible
mutants of s E.g. Encoding permutations of
k objects (e.g. for k-city TSP)
Mutation swap any adjacent pair of objects.
Neighbourhood Each individual has k
neighbours. E.g. neighbours of EABDC
are AEBDC, EBADC, EADBC, EABCD, CABDE
Encoding binary strings of length L (e.g. for
L-item bin-packing) Mutation choose a
bit randomly and flip it. Neighbourhood
Each individual has L neighbours. E.g.
neighbours of 00110 are 10110, 01110,
00010, 00100, 00111
48Landscape Topology
- Mutation operators lead to slight changes in the
solution, which tend to lead to slight changes in
fitness. - I.e. the fitnesses in the neighbourhood of s are
often similar to the fitness of s. - Landscapes tend to be locally smooth
- What about big mutations ??
- It turns out that .
49Typical Landscapes
f(s)
members of S lined up along here
Typically, with large (realistic) problems, the
huge majority of the landscape has very poor
fitness there are tiny areas where the decent
solutions lurk. So, big random changes are very
likely to take us outside the nice areas.
50Typical Landscapes II
Plateau
Unimodal
Multimodal
Deceptive
As we home in on the good areas, we can identify
broad types of Landscape feature. Most
landscapes of interest are predominantly
multimodal. Despite being locally smooth, they
are globally rugged
51Beyond Hillclimbing
-
- HC clearly has problems with typical landscapes
- There are two broad ways to improve HC, from the
algorithm viewpoint - Allow downhill moves a family of methods called
Local Search does this in various ways. - Have a population so that different regions can
be explored inherently in parallel I.e. we keep
poor solutions around and give them a chance to
develop.
52Local Search
- Initialise Generate a random solution c
evaluate its - fitness, f(s) b call c the
current solution, - and call b the best so far.
- Repeat until termination conditon reached
- Search the neighbourhood of c, and choose one, m
- Evaluate fitness of m, call that x.
- 2. According to some policy, maybe replace c with
x, and - update c and b as appropriate.
E.g. Monte Carlo search 1. same as
hillclimbing 2. If x is better, accept it as
new current solutionif x is worse, accept it
with some probabilty (e.g. 0.1).
E.g. tabu search 1. evaluate all immediate
neighbours of c 2. choose the best from (1)
to be the next current solution, unless it
is tabu (recently visited), in which choose the
next best, etc.
53Population-Based Search
- Local search is fine, but tends to get stuck in
local optima, less so than HC, but it still gets
stuck. - In PBS, we no longer have a single current
solution, we now have a population of them. This
leads directly to the two main algorithmic
differences between PBS and LS - Which of the set of current solutions do we
mutate? We need a selection method - With more than one solution available, we
neednt just mutate, we can mate, recombine,
crossover, etc two or more current solutions. - So this is an alternative route towards
motivating our nature-inspired EAs and also
starts to explain why they turn out to be so
good.
54TSP, this time with an EA
- A steady state EA with mutation-only, running for
a few steps on the TSP example, with an
unidentified selection method.
55Running a Steady State EA -- TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Lets encode a solution as a permutation
Initial randomly generated pop of 5
ACEBD DACBE BACED CDAEB
ABCED
Evaluation 32 33
28 31 28
Mutant of selected parent CDAEB ? ADCEB
Evaluation of mutant
26
Mutant enters population, replacing worst
56Running a Steady State EA -- TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Generation 2 ACEBD ADCEB
BACED CDAEB ABCED
Evaluation 32 26
28 31 28
Mutant of selected parent BACED ? BDCEA
Evaluation of mutant
33
Mutant discarded worse than current worst
57Running a Steady State EA -- TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Generation 3 ACEBD ADCEB
BACED CDAEB ABCED
Evaluation 32 26
28 31 28
Mutant of selected parent ABCED ? ABECD
Evaluation of mutant
28
Mutant enters population, replacing worst
58Running a Steady State EA -- TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Generation 4 ABECD ADCEB
BACED CDAEB ABCED
Evaluation 28 26
28 31 28
Mutant of selected parent ADCEB ? BDCEA
Evaluation of mutant
33
Mutant is discarded
59Running a Steady State EA -- TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Generation 5 ABECD ADCEB
BACED CDAEB ABCED
Evaluation 28 26
28 31 28
Mutant of selected parent ABCED ? ABECD
Evaluation of mutant
28
Mutant enters population, replacing worst
60Running a Steady State EA -- TSP
A B C D E
A 5 7 4 15
B 5 3 4 10
C 7 3 2 7
D 4 4 2 9
E 15 10 7 9
Generation 6 ABECD ADCEB
BACED ABECD ABCED
Evaluation 28 26
28 28 28
And so on.
Note population starting to converge,
genotypically and phenotypically