INVESTIGATING REPLACEMENT STRATEGIES

FOR THE

ADAPTIVE DISSORTATIVE MATING GENETIC

ALGORITHMCarlos Fernandes1,2

J.J. Merelo1

Agostinho C. Rosa2

1Department of Architecture and Computer Technology, University of Granada, Spain 2 L aSEEB-ISR-IST, Technical Univ. of Lisbon (IST), Portugal

SUMMARY

ADMGA

Non-Stationary Fitness Landscapes

Motivation

Replacement Strategies

Results

Conclusions and Future Work

Dissortative MatingDissortative Mating

Mating between dissimilar individuals. Higher diversity.

Disruptive effect

High selective pressure + high disruption effectparent

parent

Chromosomes are alowed to crossover if and only their Hamming Distance is above the threshold value.

The threshold self-adapts its initial value, and varies during the run according to the population diversity

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Hamming dist.: 4selection

ADMGA differs from the SGA at the recombination stage

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the number of positions at which the corresponding symbols are different

Adaptive Dissortative Mating Adaptive Dissortative Mating GA (ADMGA)GA (ADMGA)

ADMGAADMGAPopulation

New population = Offspring population + best parents

Selects two and computes h.d.

if h. d. > ts

if h. d. ≤ ts

Crossover and mutate

after n/2 (n is the population size)

Updates threshold

if (failed matings > successful matings) ts← ts−1else ts ← ts+1

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diversity is controlling the threshold

population-wide elitism (or steady-state)

Stationary Fitness Functions:Stationary Fitness Functions:Scalability with Trap FunctionsScalability with Trap Functions

order-2 (k = 2) order-3 order-4

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non-deceptive nearly-deceptive fully deceptive

Scalability with problem size

Alternative Replacement StrategiesThreshold ValueThreshold Value

Initial threshold value

n = 10,000; l = 10

n = 10; l = 10,000n = 100

order-2

Dynamic Optimization Dynamic Optimization ProblemsProblems

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ADMGA: Dynamic ADMGA: Dynamic Optimization ProblemsOptimization Problems

Better performance on “slower” dynamic problems

The performance degrades as the optimum moves faster

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MotivationMotivation

Improve ADMGA’s performance on faster problems

Is population-wide elitism a good or bad strategy for fast dynamic problems?

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Replacement StrategiesReplacement Strategies

RS 1: Original

RS 2: Mutated copies of the old solutions

RS 3: Mutated copies of the best solution

RS 4: Random Immigrants (random solutions)

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ADMGA: Dynamic ADMGA: Dynamic Optimization ProblemsOptimization Problems

Yang’s (2003) dynamic problem generator:• frequency of change (1/ε)• severity (ρ)

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ε : 600, 1200, 2400, 4800, 9600, 19200, 38400 ρ : random

Offline performance: average of the best fitness throughout the run

Statistical tests

TestsTests

Several mutation probability and population size values.• mutation: dissortative mating affects optimal

probability• population size: avoid extra computational effort

binary tournament 2-elitism uniform crossover (p=1.0)

• Balance disruptive effect and selective pressure

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Results TestsTestsRS 1 vs GGA

RS 2 vs GGA

ε→ 600 1200 2400 4800 9600 19200 38400

onemax − − ≈ ≈ ≈ ≈ ≈trap ≈ ≈ + + + + +

knapsack − − ≈ ≈ ≈ + +

ε→ 600 1200 2400 4800 9600 19200 38400

onemax − − − − ≈ ≈ ≈trap − − − ≈ + + +

knapsack − − − − − ≈ +

Results TestsTests

RS 2 vs EIGA

ε→ 600 1200 2400 4800 9600 19200 38400

onemax − − − ≈ ≈ ≈ ≈trap ≈ ≈ + + + + +

knapsack − − ≈ ≈ ≈ ≈ ≈

Genetic Diverstiy

Conclusions and Future Work

Mutating old solutions speeds up AMDGA on dynamic problems

Only two parameters need to be adjusted: population size and mutation rate

ADMGA is at least competitive with EIGA

Performance according to severity

Constrained Dynamic Problems