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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
1111111111111111
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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