Dvouúrovňová evoluční optimalizace regulátorů

|Bio-inspirované metody a jejich využití

Two level Evolutionary Optimization of |Controllers

Basic Principles of Transplant evolution

Pave l Ošmera

Institute of Automation and Computer Science

Brno University of Technology, Technická 2,

616 69 Brno, Czech Republic

osmera @fme.vutbr.cz,

 

IntroductionWe are trying to piece together the knowledge of evolution with the help of biology, informatics and physics to create a complex evolutionary structure. It can speed up the creation of optimization algorithms with high quality features. The emergent properties of complex adaptive systems are presented.

One of the most highly developed skills in contemporary Western civilization is the capability to split up problems into their smallest possible components.

But we often forget to put the pieces together again. In this way we can ignore the complex interaction between our problems and the rest of the universe.

family mother & father & wife/husband & sexual partner & children & ....

social environment laws & morale & society & friends & enemy & terrorism & ..

culture books & school & television & newspaper & Internet & religions & ..

influence of memes influence of genes direction of influence

ecosystems

memory III (memes of mankind )

Dawkins theory of memes

Fig. 1 Complex evolutionary structure

&

body carrier of genes brain memory II

carrier of memes

Lamarckian imitation of memes memes memů

individual (descendant)

central nervous system

behavior (instincts) instinctive behavior

learning (rules) conscious behavior

Baldwin effect

mitochondrial genes (epigenetic information), order of cells (epigenetic structure)

genes for structure of the body genes for structure of the brain and instincts

memory Ia memory Ib

diploidy chromosomes & sexual reproduction

integrated fitness

Mendelian genetics

immune system

Darwinian selection process

parasites

prey-predator interaction (living part of nature) environment (energy of sun and earth....)

Kauffman’s enzyme nets

memory IVa memory IVb

imunitní systém hormones

chemical messenger

DNA

Computational Intelligence Game Theory and Collective Behavior Intelligence

memory III (genome & memes)

Fig. 2 Soft Computing

culture Culture Algorithms

social environment Particle Swarm Optimization, Multi-Agent EA Agent-based Multiobjective Optimalization Ant Colony Optimization, Dynamical Systems Modeling Niches, Team Optimization

family Evolutionary Computation: Evolution Strategies Genetic Programming Genetic Algorithms, Parallel GAs

body brain memory II Fuzzy Systems Neural Networks Fuzzy-rough Sets Fuzzy-neural Modeling Hybrid Learning Intelligent Control

individual (descendant)

Mitochondrial Systems

genes for structure of the body genes for structure of the brain and instincts

memory Ia memory Ib

Diploid GA with Sexual Reproduction

DNA Computing , Messy GA

Artificial Immune Algorithms

Cooperative co-evolutionary Algorithms Parasitic Optimization, Bacterial EA Artificial Life Systems, Differential EA Parallel Hierarchical EA, Meta-Heuristics Evolutionary Multi-objective Optimization

memory IVa memory IVb

Hormone Systems Clonal Selection Enzyme Behavior

Evolutionary Design , Robotics Evolvable Hardware, Embryonic Hardware Human-Computer Interaction Molecular-Quantum Computing Data Mining, Chaotic Systems, Scheduling

 Basic strategy of the evolutionary optimization 

old state of evolution

new state of evolution

negative mutation

negative cross-over

negative selection

positive mutation

positive selection

positive crossover

order (ordered structure)

chaos (chaotic structure)

edge of chaos phase transition (complex structure)

neutral mutation

sexual selection

Classical and evolutionary design

Example:antenna designs

NASA Ames (http://ic.arc.nasa.gov/projects/esg/research/antenna.htm)

Classical method Evolutionary approach

all solutions

Grammatical evolution

 The PGE is based on the grammatical evolution GE [1], where BNF grammars consist of terminals and non-terminals. Terminals are items, which can appear in the language. Non-terminals can be expanded into one or more terminals and non-terminals. Grammar is represented by the tuple {N,T,P,S}, where N is the set of non-terminals, T the set of terminals, P a set of production rules which map the elements of N to T, and S is a start symbol which is a member of N. For example, below is the BNF used for our problem:

N = {expr, fnc}

T = {sin, cos, +, -, /, *, X, 1, 2, 3, 4, 5, 6, 7, 8, 9}

S = <expr>

and P can be represented as 4 production rules:

1. <expr> := <fnc><expr>

<fnc><expr><expr>

<fnc><num><expr>

<var>

2. <fnc> := sin

cos

+

*

-

U-

3. <var> := X

4. <num> := 0,1,2,3,4,5,6,7,8,9

Forward processing (classical approach)

0 IN   0 ZD

0 N(NON)   1 ZZZ

1 NR   0 D0

2 NZ   1 D1

0 Rx   2 D2

1 RZ   3 D3

2 RZ.Z   4 D4

3 RN^N   5 D5

0 O+   6 D6

1 O-   7 D7

2 O*   8 D8

3 O/   9 D9

phenotype tree:

translation table

DNA sequence (genotype):

• The symbol "I" is always root.

• The rules are processed from the left to the right.

• The rules are applied on the leftmost non-terminal symbol.

• The rule chosen is determined by the result of the modulo operation:

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

13 mod 1 = 06 mod 3 = 0

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

2 mod 3 = 2

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

5 mod 2 = 1

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

8 mod 2 = 0

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

17 mod 10 = 7

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

2 mod 2 = 0

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

4 mod 10 = 4

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

12 mod 4 = 0

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

4 mod 3 = 1

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

4 mod 4 = 0

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

I

N

NON

ZON

ZZON

DZON

7ZON

7DON

74ON

74+N

74+R

74+x

Crossover   When using grammatical evolution the resulting phenotype coded by one gene depends on the value of

the gene and on its context. If a chromosome is crossed at random point, it is very probable that the context of the genes in second part will change. This way crossover causes destruction of the phenotype, because the newly added parts code different phenotype than in the original individual.

This behavior can be eliminated using a block marking system. Crossover is then performed as an exchange of blocks. The crossover is made always in an even number of genes, where the odd gene must be BB gene and even must be EB gene. Starting BB gene is presently chosen randomly; the first gene is excluded because it encapsulates (together with the last used gene) the whole individual.

The operation takes two parent chromosomes and the result is always two child chromosomes. It is also possible to combine the same individuals, while the resulting child chromosomes can be entirely different.

Given the parents:

1) cos( x + 2 ) + sin( x * 3 )

2) cos( x + 2 ) + sin( x * 3 )

The operation can produce children:

3) cos( sin( x * 3 ) + 2 ) + sin( x * 3 )

4) cos( x + 2 ) + x

This crossover method works similar to direct combining of phenotype trees, however this method works purely on the chromosome. Therefore phenotype and genotype are still separated. The result is a chromosome, which will generate an individual with a structure combined from its parents. This way we receive the encoding of an individual without backward analysis of his phenotype. To perform a crossover the phenotype has to be evaluated (to mark the genes), but it is neither used nor know in the crossover operation (also it doesn’t have to exist).

 

 

 

The PGE algorithm was tested with the group of 6 computers in the computer network. Five computers calculated in the structure of five subsystems MR1, MR2, MR3, MR4, and MR5 and one master MR. The male subpopulation M of MR in the higher level follows the convergence of the subsystem. Every figure presents 10 runs of the PGE- program. The shortest time of computation is only 10 generation. All calculation were finished before 40 generation. This is better to compare with backward processing on one computer. The forward processing on one computer was the slowest.

0

0,2

0,4

0,6

0,8

1

1 25 50 75 100

Generation

Fitness

0

0,2

0,4

0,6

0,8

1

1 25 50 75 100

Generation

Fitness

0

0,2

0,4

0,6

0,8

1

0 50 100

Generation

Fitness

Results:(a) forward and (b) backward processing, (c) the PGE with 5 PC using backward processing (average in bold)

Logical function XORInput values are two integer numbers a and b; a, b 2< 0, 1 >. Output number c is the value of logical function

XOR. Training data is a set of triples (a, b, c):P = {(0, 0, 0); (0, 1, 1); (1, 0, 1); (1, 1, 0)}.Thus the training set represents the truth table of the XOR function. The function can be expressed using _,

^, ¬ functions:a + b = (a ^ ¬b) _ (¬a ^ b) = (a _ b) ^ (¬a _ ¬b) = (a _ b) ^ ¬(a ^ b)The grammar was simplified so that it does not contain conditional statement and numeric constants, on the

other hand three new terminals were added to generate functions _, ^, ¬. Thus the grammar generates representations of the XOR functions using other logical functions.

1a)function xxor($a,$b) {$result = "no_value";$result = ($result) |((((~(~(~(~(~($result)))))) | (($a) & (($a) & (~($b))))) & ($a))| ((~($a)) & ($b)));return $result;}Number of generations: 321b)function xxor($a,$b) {$result = "no_value";$result = ($result) | (((~$result | ($a & ($a & ~$b))) & $a) | (~$a & $b));return $result;}

 

Logical function XOR

2a)function xxor($a,$b) {$result = "no_value";$result = ($result) | ((((~(~(~(~(~($b)))))) & (($a) & (($a) &(~($b))))) & ($a)) | ((~($a)) & ($b)));return $result;}Number of generations: 532b)function xxor($a,$b) {$result = "no_value";$result = ($result) | (((~$b & ($a & ($a & ~$b))) & $a) |(~$a & $b));return $result;

 

This paper describes the application of Two-Level Transplant Evolution (TE) that can evolve control programs using a variable length linear genome to govern the mapping of a Backus Naur Form grammar definition. TE combines Grammatical Evolution (on the genotype level) with Genetic Programming (tree structures on the phenotype level). To increase the efficiency of Transplant Evolution (TE) the parallel Diferential Evolution was added. The adaptive significance of Parallel Transplant Evolution (PTE) with male and female populations has been studied.

 .. Fitness criterions of control process 

 

 

If an individual of grammatical's evolution has some abstract parameters, differential evolution will be

run for solve them, otherwise simulation of regulation will

be run directly.

Has the grammatical individual some abstract

parameters?

MutationCrossover

Compute fitness

For all individual in population

Is stopping conditionsatisfied?

The best solution is result

Selection

Yes

Initialise of population

For all individual in new population

No

Join populations

Compute fitness

Yes

CrossoverIs stopping conditionSatisfied?

Compute fitness

The best solution is result for grammatical

evolution

Yes

No Selection

Initialise of population

Yes

Compute regulator error

and system response

Calculate regulation criteria of statility

Initialise of regulatorValue of criteria

stability is result of fitness

Is count of actual

population >= condition

No

For all individual in population

For entered regulation interval

No

Layer of Grammatical evolution

Layer of Differential evolution

Layer of Regulator

Flow chart

 . Step response for integration system with time delay

 

• Each of these systems is a network of many ”agents” acting in parallel .

• There is Complex adaptive systems share certain crucial properties (a nonlinearity, a complex mixture of positive and negative feedback, nonlinear dynamics, emergence, collective behavior, spontaneous organization, and so on).

• There is not the master agent.

• A complex adaptive system has many levels of organization (the hierarchical structure).

COMPLEX ADAPTIVE SYSTEMS

• the traditional science in the Age of the Machine tended to emphasize stability, order, uniformity, and equilibrium.

• today’s science: disorder, instability, diversity, disequilibrium, nonlinear relationships (in which small inputs can trigger massive consequences), and temporality ( a sensitivity to the flow of time).

Conclusions

• The Parallel Transplant Evolution can be used for the automatic generation of programs. We are far from supposing that all difficulties are removed but first results with TPEs are very promising.

MENDEL 2012

Call for Papers

18th International Conference

on Soft Computing

Evolutionary Computation, Genetic Programming, Bayesian

Method, Fuzzy Logic, Neural Networks, Rough Sets, Fractals

June 27 - 29, 2012

Brno, CZECH REPUBLIC

http://www.mendel-conference.org/