genetic.ppt

 A class of probabilistic optimization

algorithms

 Inspired by the biological evolution process

 Uses concepts of “Natural Selection” and

“Genetic Inheritance” (Darwin 1859)

 Originally developed by John Holland

 Particularly well suited for hard problems

where little is known about the underlying search space

 Widely-used in business, science and

Search Techniqes

Calculus Base

Techniqes Guided random search _techniqes

Enumerative Techniqes

BFS

DFS Dynamic

Programming

 Selection replicates the most successful

solutions found in a population at a rate

proportional to their relative quality

 Recombination decomposes two distinct

solutions and then randomly mixes their parts to form novel solutions

 Mutation randomly perturbs a candidate

Genetic Algorithm Nature

Optimization problem Environment

Feasible solutions Individuals living in that

environment

Solutions quality (fitness function)

Individual’s degree of adaptation to its

Genetic Algorithm Nature

A set of feasible solutions A population of organisms

(species)

Stochastic operators Selection, recombination

and mutation in nature’s evolutionary process

Iteratively applying a set of stochastic operators on a set of feasible solutions Evolution of populations to

The computer model introduces simplifications (relative to the real biological mechanisms),

BUT

produce an initial population of individuals

evaluate the fitness of all individuals

while termination condition not met do

select fitter individuals for reproduction

recombine between individuals

mutate individuals

evaluate the fitness of the modified individuals

selection

population evaluation

modification

discard

deleted members parents

modified offspring

evaluated offspring initiate

&

Suppose we want to maximize the number of ones in a string of l binary digits

Is it a trivial problem?

It may seem so because we know the answer in advance

 An individual is encoded (naturally) as a

string of l binary digits

 The fitness f of a candidate solution to the

MAXONE problem is the number of ones in its genetic code

 We start with a population of n random

We toss a fair coin 60 times and get the following initial population:

s₁ = 1111010101 f (s₁) = 7

s₂ = 0111000101 f (s₂) = 5

s₃ = 1110110101 f (s₃) = 7

s₄ = 0100010011 f (s₄) = 4

s₅ = 1110111101 f (s₅) = 8

Next we apply fitness proportionate selection with the roulette wheel method:

2 1 n 3 Area is Proportional to fitness value

Individual i will have a

probability to be chosen

 i i f i f ) ( ) ( 4

We repeat the extraction as many times as the

Suppose that, after performing selection, we get the following population:

s₁` = 1111010101 (s₁)

s₂` = 1110110101 (s₃)

s₃` = 1110111101 (s₅)

s₄` = 0111000101 (s₂)

s₅` = 0100010011 (s₄)

Next we mate strings for crossover. For each couple we decide according to crossover

probability (for instance 0.6) whether to actually perform crossover or not

Suppose that we decide to actually perform crossover only for couples (s₁`, s<sub>2</sub>`) and (s₅`, s<sub>6</sub>`).

For each couple, we randomly extract a

Type of Crossover

:

Single site

Two Points

Multi points

Uniform

s₁` = 1111010101

s₂` = 1110110101

s₅` = 0100010011

s₆` = 1110111101

Before crossover:

After crossover:

s₁`` = 1110110101

s₂`` = 1111010101

s₅`` = 0100011101

s₁` = 1111010101 s<sub>2</sub>` = 1110110101

s₅` = 0100010011 s<sub>6</sub>` = 1110111101

Before crossover:

After crossover:

s₁`` = 1110110101 s<sub>2</sub>`` = 1111010101

s₁` = 1111010101

s₂` = 1110110101

s₅` = 0100010011 s<sub>6</sub>` = 1110111101

Before crossover:

After crossover:

s₁`` = 1110110101 s<sub>2</sub>`` = 1111010101

s₁` = 1111010101

s₂` = 1110110101

s₅` = 0100010011 s<sub>6</sub>` = 1110111101

Before crossover:

After crossover:

s₁`` = 1110110101 s<sub>2</sub>`` = 1111010101

The final step is to apply random mutation: for each bit that we are to copy to the new population we allow a small

probability of error (for instance 0.1)

Before applying mutation:

s₁`` = 1110110101

s₂`` = 1111010101

s₃`` = 1110111101

s₄`` = 0111000101

After applying mutation:

s₁``` = 1110100101 f (s<sub>1</sub>``` ) = 6

s₂``` = 1111110100 f (s<sub>2</sub>``` ) = 7

s₃``` = 1110101111 f (s<sub>3</sub>``` ) = 8

s₄``` = 0111000101 f (s<sub>4</sub>``` ) = 5

s₅``` = 0100011101 f (s<sub>5</sub>``` ) = 5

Before: (1 0 1 1 0 1 1 0)

After: (0 1 1 0 0 1 1 0)

Before: (1.38 -69.4 326.44 0.1)

After: (1.38 -67.5 326.44 0.1)

 Causes movement in the search space

(local or global)

The traveling salesman must visit every city in his territory exactly once and then return to the starting point; given the cost of travel between all cities, how should he plan his itinerary for minimum total cost of the entire tour?

TSP  NP-Complete

The Traveling Salesman Problem:

Find a tour of a given set of cities so

that

• _{each city is visited only once}

Representation is an ordered list of city

numbers known as an

order-based

GA.

1) London 3) Dunedin 5) Beijing 7) Tokyo 2) Venice 4) Singapore 6) Phoenix 8) Victoria

Crossover combines inversion and recombination:

* *

Parent1 (3 5 7 2 1 6 4 8) Parent2 (2 5 7 6 8 1 3 4)

Child (5 8 7 2 1 6 3 4)

Mutation involves reordering of the list:

* *

Before: (5 8 7 2 1 6 3 4)

The sub-string between two randomly selected points in the path is reversed

Example:

(1 2 3 4 5 6 7 8 9) is changed into (1 2 7 6 5 4 3 8 9)

0 20 40 60 80 100 120

0 10 20 30 40 50 60 70 80 90 100

y

0 20 40 60 80 100 120

0 10 20 30 40 50 60 70 80 90 100

y

x

44 62 69 67 78 64 62 54 42 50 40 40 38 21 35 67 60 60 40 42 50 99 0 20 40 60 80 100 120

0 10 20 30 40 50 60 70 80 90 100

y

x

0 20 40 60 80 100 120

0 10 20 30 40 50 60 70 80 90 100

y

x

42 38 35 26 21 35 32 7 38 46 44 58 60 69 76 78 71 69 67 62 84 94 0 20 40 60 80 100 120

0 10 20 30 40 50 60 70 80 90 100

y

x

0 200 400 600 800 1000 1200 1400 1600 1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

D is ta n ce Generations (1000)

TSP30 - Overview of Performance

Best

Worst

“ Almost eight years ago ...

people at Microsoft wrote a program [that] uses some

genetic things for finding short code sequences. Windows 2.0 and 3.2, NT,

and almost all Microsoft applications products have

shipped with pieces of code created by that

system ”.

 Decade long debate: which one is better /

necessary / main-background

 Answer (at least, rather wide agreement):

• _{it depends on the problem, but} • _{in general, it is good to have both} • _{both have another role}

• _{mutation-only-EA is possible, Xover-only-EA would not}

Exploration: Discovering promising areas in the search space, i.e. gaining information on the problem

Exploitation: Optimising within a promising area, i.e. using information

There is co-operation AND competition between them

 Crossover is explorative, it makes a big jump to an

area somewhere “in between” two (parent) areas

 Mutation is exploitative, it creates random small

 Only crossover can combine information from two

parents

 Only mutation can introduce new information

(alleles)

 Crossover does not change the allele frequencies of

the population (thought experiment: 50% 0’s on first bit in the population, ?% after performing n

crossovers)

A problem definition as input, and

Each cell of a living thing contains chromosomes - strings of DNA

Each chromosome contains a set of genes - blocks of DNA

Each gene determines some aspect of the organism (like eye colour)

A collection of genes is sometimes called a

genotype

A collection of aspects (like eye colour) is sometimes called a phenotype

Reproduction involves recombination of genes from parents and then small amounts of mutation

(errors) in copying

Possible individual’s encoding

 Use a data structure as close as possible to

the natural representation

 Write appropriate genetic operators as

needed

 If possible, ensure that all genotypes

correspond to feasible solutions

 If possible, ensure that genetic operators

preserve feasibility

Start with a population of randomly generated individuals, or use

- A previously saved population - A set of solutions provided by

a human expert

 Purpose: to focus the search in promising

regions of the space

 Inspiration: Darwin’s “survival of the fittest”  Trade-off between exploration and exploitation

of the search space

 Derived by Holland as the optimal

trade-off between exploration and exploitation

Drawbacks

 Different selection for f₁(x) and f₂(x) = f₁(x) + c

 Superindividuals cause convergence (that

Extracts k individuals from the population

with uniform probability (without re-insertion) and makes them play a “tournament”,

where the probability for an individual to win is generally proportional to its fitness

Purpose: to simulate the effect of errors that happen with low probability during

duplication

Results:

- Movement in the search space

 Solution is only as good as the

evaluation function; choosing a good one is often the hardest part

 Similar-encoded solutions should have a

Examples:

 A pre-determined number of generations or

time has elapsed

 A satisfactory solution has been achieved

 No improvement in solution quality has

 Two or more species evolve and interact

through the fitness function

 Closer to real biological systems

 Competitive (prey-predator) or Cooperative

 Examples: Hillis (competitive), my work



Choosing basic implementation issues:

♦representation

♦population size, mutation rate, ...

♦selection, deletion policies

♦crossover, mutation operators



Termination Criteria



Performance, scalability

Solution is only as good as the



Concept is easy to understand



Modular, separate from application



Supports multi-objective optimization



Good for “noisy "environments



Always gives answer; answer gets

better with time



Multiple ways to speed up and

improve a GA-based application as

knowledge about problem domain is

gained



Easy to exploit previous or alternate

solutions



Flexible building blocks for hybrid

applications

Alternate solutions are too slow or much

complicated

Need an exploratory tool to examine new

approaches

Problem is similar to one that has already

been successfully solved.

Want to hybridize with an existing

solution

Benefits of the GA technology meet key



Domain

Application

Types

Control gas pipeline, pole balancing, _{missile evasion, pursuit}

Design semiconductor layout, aircraft

design, keyboard configuration, communication networks

Scheduling _{manufacturing, facility scheduling,}

resource allocation

Robotics _{trajectory planning}

Signal Processing _{filter design}

Game Playing poker, checkers, prisoner’s

dilemma

Combinatorial Optimization

set covering, travelling salesman, routing, bin packing, graph

 Essentials of Darwinian

evolution:

 Organisms reproduce in

proportion to their fitness in the environment

 Offspring inherit all traits from

parents

 Traits are inherited with some

variation, via mutation and sexual recombination

Essentials of evolutionary algorithms:

 Computer “organisms”(e.g.,

programs) reproduce in proportion to

their fitness of problem environment

(e.g., how well they perform a desired task)

 Offspring (outcome) inherit only

strong traits (fitness)from their parent.

 ♦Traits are inherited, with some

C. Darwin. On the Origin of Species by Means of Natural Selection; or, the Preservation of flavored Races in the Struggle for Life. John Murray, London, 1859.

W. D. Hillis. Co-Evolving Parasites Improve Simulated

Evolution as an Optimization Procedure. Artificial Life 2, vol 10, Addison-Wesley, 1991.

J. H. Holland. Adaptation in Natural and Artificial Systems. The

University of Michigan Press, Ann Arbor, Michigan, 1975.

Z. Michalewicz. Genetic Algorithms + Data Structures =

Evolution Programs. Springer-Verlag, Berlin, third edition, 1996.

M. Sipper. Machine Nature: The Coming Age of Bio-Inspired Computing. McGraw-Hill, New-York, first edition, 2002.

M. Tomassini. Evolutionary algorithms. In E. Sanchez and

M. Tomassini, editors, Towards Evolvable Hardware, volume