March 23, 2003 AAAI symposium, Stanford.

Jianjun Hu, Erik D. Goodman, Kisung Seo Zhun Fan, Ronald C. Rosenberg

Genetic Algorithm Research & Applications Group (GARAGe)

Michigan State University

HFC: a Continuing EA Framework for Scalable Evolutionary Synthesis

March 23, 2003 AAAI symposium, Stanford.

Evolutionary Synthesis: the problem

Topology innovation: How many and what types of building blocks, How to connect them?

Parameter innovation: How to size the elements?

R

S

C I

R1

Input:

>Building blocks>Function Specification(Evaluation function)>EA settings (operators, parameters…)

Output:

Design solutions

Evolution

March 23, 2003 AAAI symposium, Stanford.

Sustainable & scalable evolutionary synthesis: Definition and Reality

Definition: the capability to obtain better results or solve larger scale problems when given more computing resourcesReality: not sustainable and not scalable

Bloating and aging problem (e.g.:Innovation in 50 generations in GP)Demand for huge population size (GP)Premature convergence and local optima (all EA)

But biological evolution is sustainable and scalable!

March 23, 2003 AAAI symposium, Stanford.

Sustainable & scalable evolutionary synthesis: two types of obstacles

Two types of obstacles:1. Convergent nature of current EA framework

one of major factors leading to :GP aging phenomenonpremature convergencedependence on huge population size

2. Non-scalable compositional mechanisms for topological and parametric evolution

possible solutions: modularity, hierarchical organization, biological developmental principles…

This paper: addresses the EA convergence problem

March 23, 2003 AAAI symposium, Stanford.

Comparison with biological evolution: how to achieve sustainable evolution

Biological evolutionAlmost infinite population sizeSimultaneous evolution of all levels of organisms: bacteria coexist with humans Fair competition: different levels of organism coexist in different nichesSustainable innovation possible

Artificial evolution (EA)Limited population sizeFocusing on current high-fitness individuals Unfair competition: highly-evolved individuals compete with new offspring of low fitnessInnovation capability rapidly depleted

March 23, 2003 AAAI symposium, Stanford.

Sustainable evolution: example & comparisonSustainable education system: how generations of talents are educated?

Unsustainable EA: how generations of solutions are evolved?

Academiclevel

primaryschool

middleschool

highschool

college

graduateschool

New babi es

Simultaneoustraining at alllevels

Fitness(usually also

complexity in GP)

High-fitnessindividuals

Randomindividuals

One-epochsearch

Gen1

Gen10

Gen100

Gen1000

Gen50000

March 23, 2003 AAAI symposium, Stanford.

Assembly-line structured continuing EAs

randomindividuals

individuals containingintermediate levels of

building blocks

end products: thesolution

building blocks from low order tohigh order

Lowlevel

Highlevel

Fitness from lower to higher

March 23, 2003 AAAI symposium, Stanford.

HFC-EA framework

(a) In HFC model, subpopulations are organized in ahierarchy with ascending fitness level. Each level (with oneor more subpopulations) accomodates individuals within acertain fitness range determined by the admission thresholds

fitness

fmin

fmaxsubpop9

subpop8

subpop7

subpop5,6

subpop3,4

subpop0,1,2

ADT5

AdmissionBuffers

randomindividualgenerator

ADT:Admission Threshold

ADT4

ADT3

ADT2

ADT1

(b) HFC model extends the search horizontally in searchspace and vertically in fitness dimension and kills badindividuals at appropriate times while allowing promisingyoung individuals grow up continuously

level 1

level 2

level 3

level 4

level 5

fitness

The Streamlined Structure of HFC Model (a) and HFCfrom the Perspective of Landscape (b).

level 6

March 23, 2003 AAAI symposium, Stanford.

System synthesis problem: eigenvalue placement

-2.0 -3.3 -2.0 3.3 -7.5 -4.5 -7.5 4.5 -3.5 -12.0 -3.5 12.0 -3.4 -12.0 -3.4 12.0-10.0 -8.0-10.0 8.0

-2.063 -3.005 -2.063 3.005 -7.205 -4.581 -7.205 4.581 -3.580 -11.835 -3.580 11.835 -3.334 -12.526 -3.334 12.526 -9.997 -8.040

-9.997 8.040 Max distance error 0.530

Average distance error 0.272

2 hours

Sf

1Se 1

1

0

C

R

I

1

R C

I

0

R C

C

0 RL

March 23, 2003 AAAI symposium, Stanford.

Experiment result: sustainability& robustnessDynamic system synthesis problem with simultaneous

topology and parameter search

Average Eigenvalue Location Error vs Evaluation NumberHFC-GP

Evaluation Number (thousands)

0 50 100 150 200 250 300 350

Loca

tion

Err

or

0.0

.5

1.0

1.5

2.0

STD

Average Eigenvalue Location Error vs Evaluation NumberMultiPopulation-GP

Evaluation Number (thousands)

0 50 100 150 200 250 300 350

Loca

tion

Err

or

0.0

.2

.4

.6

.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

STD

March 23, 2003 AAAI symposium, Stanford.

Experiment result: handling GP aging problem

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

generation

sta

ndard

fitness

Standardized fitness of Best Individual of run

OnePopMulPopHFC-GP

10 eigenvalue dynamic system synthesis problem

March 23, 2003 AAAI symposium, Stanford.

Experiment result: small population size works equally well

10-parity problem with function set {and, xor, or, not)

Success Rate

0%10%20%30%40%50%60%70%80%90%

100%

150 250 400 800PopSize

succ

ess

rate

OnePop

MulPop

HFC

HFC_ADM

HFCATP

March 23, 2003 AAAI symposium, Stanford.

Why HFC works: the explanation

Fitness LevelsNormal EA individualsHFC individuals

Random Individual Generator

March 23, 2003 AAAI symposium, Stanford.

Conclusion: Hierarchical Fair Competition Principle for EA

HFC is very effective in evolutionary synthesisSimultaneous evolution at all (fitness) levels, from the random population to best individualsAvoid premature convergence by allowing emergence of new optima rather than trying to jump out of local optimaAllow use of strong selection pressure without risk of premature convergenceSmall population size also works

March 23, 2003 AAAI symposium, Stanford.

Ongoing & future work

Developing single population HFC (CHFC) (with continuous level segmentations) algorithm to achieve sustainable evolutionDeveloped HFC-enhanced multi-objective EAs (GECCO2003)To develop hybrid parallel-HFC GA/GP system where each deme is implemented as a CHFC populationTo develop multi-level system synthesis: from framework evolution to complete solutions

March 23, 2003 AAAI symposium, Stanford.

Generalization of HFC-EA Framework

A generic framework for continuing sustainable evolutionary computation (GA, GP, ES, …)Especially good for Evolutionary Synthesis for Sustainable topological innovation which has extremely rugged fitness landscape.Especially effective for problems with:

High multi-modality Strong tendency of premature convergenceRequirement on robustnessRequirement on adaptation in dynamic environment

Also applicable for artificial life evolution

March 23, 2003 AAAI symposium, Stanford.

Scaling Mechanism of HFC

A natural parallel evolutionary computation model. Better than island parallel modelHybridizing with single-population HFC EAs (Each deme is a sustainable HFC subpop)Natural hybridizing with explicit hierarchical building block discovery mechanismsAllow using small population size and longer time to achieve good resultsNo restart to waste computing effort