a self-organized criticality online adjustment of genetic algorithms’ mutation rate
DESCRIPTION
Fernandes, Merelo, Ramos, Rosa, presented at the Self-* workshop within the PPSN conference, Kraków 2010TRANSCRIPT
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
A Self-Organized Criticality Online Adjustment of Genetic Algorithms’
Mutation Rate
Carlos M. Fernandes1,2
J.L.J. Laredo1
J.J. Merelo1
Agostinho C. Rosa2
1Department of Architecture and Computer Technology, University of Granada, Spain2 LaSEEB-ISR-IST, Technical Univ. of Lisbon (IST), Portugal
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Motivation and Objectives
• Develop a diversity maintenance scheme for Genetic Algorithms to deal with Dynamic Optimization Problems
(DOPs).
DOPs require diversity (when using population-based heuristics).
In DOPs, the fitness function and the constraints of the problem are not constant. When changes occur, the solutions already found may be no longer valuable and the process must engage in a new search effort.
Genetic Algorithms, dues to its characteristics are good candidate to solve some Dynamic Optimization Problems. But they tend to converge its population towards a specific region.
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Motivation and Objectives
Keep it simple! Avoid new parameters or complex parameter control.
Hypothesis: self-organized criticality
Sand pile Mutation Operator
Possible solution: online variation of the parameter values
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Summary
GAs parameter controlEvolutionary approaches to dynamic optimizationSelf-organized criticalitySand Pile Mutation OperatorTest Set and ResultsMutation Rates and distributionConclusion
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Parameter Control
Deterministic: parameter values change according to deterministic rules
Adaptive: the values change variation depends indirectly on the problem and the search stage
Self- adaptive: the values to evolve together with the solutions to the problem
PPSN’10 - KrakowFernandes, Merelo, Ramos and Rosa – “Sandpile Mutation GA”
Evolutionary Dynamic Optimization
Reaction to ChangesMemoryMulti-PopulationDiversity Maintenance
PPSN’10 - KrakowFernandes, Merelo, Ramos and Rosa – “Sandpile Mutation GA”
Self-Organized Criticality
SOC is a state of criticality formed by self-organization in a long transient
period at the border of order and chaos.
Unlike many physical systems, SOC systems are able to self-tune to the
critical point.
SOC has been used in EC, but there are few studies
Krink et al.: power-law is computed offline
SORIGA: uses a SOC model to introduce random immigrants in the
population
Our proposal: Sand Pile Mutation
PPSN’10 - KrakowFernandes, Merelo, Ramos and Rosa – “Sandpile Mutation GA”
The Sand Pile Model
8
Power law relationship between the size of the events and their frequency
PPSN’10 - KrakowFernandes, Merelo, Ramos and Rosa – “Sandpile Mutation GA”
The Sand Pile Mutation
l1
l2
l3
…
0
1
2
3
4
n1
n2
n3
…
Z
0
1
2
3
4Z
Mutates if a random value (0,1.0) is above the normalized fitness
Grains are dropped at a rate g
PPSN’10 - KrakowFernandes, Merelo and Rosa – “Dissortative Mating GA”
Test Set
Severity of change: This criterion establishes how strongly the problem is changing
Frequency of change: This criterion establishes how often the environment changes
• Yang and Yao’s dynamic problems generator
• By using a binary mask, dynamic environments are created by applying the mask to each solution before its evaluation.
• Severity of change is controlled by setting the number of 1’s in the mask.
• Speed of change is controlled by defining the number of generations between the application of a different mask.
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Test Set
Performance is measured by the mean best-of-generation values, i.e.,
best fitness averaged over all generations, and then over all runs
4-trap, knapsack and royal road
Compared a generational GA with Sand Pile Mutation (GGASM ) with:
Standard Generational GA (GGA)
Self-Organized Criticality Random Immigrants GA (SORIGA).
Elitism-based Immigrants GA (EIGA)
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Results
30 runs each configuration
Uniform crossover
pc = 1.0
Binary tournament
Speed was set to 1200, 2400, 24000, 48000 evaluations
Population size n = 30, 60, 120
pm : 1/(16×l), 1/(8×l), 1/(4×l), 1/(2×l), 1/l, 2/l, 4/l
Severity was set to ρ = 0.05, 0.3, 0.6 and 0.95
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Results
ρ →
ε = 1200 ε = 2400 ε = 24000 ε = 48000.05 .3 .6 .95 .05 .3 .6 .95 .05 .3 .6 .95 .05 .3 .6 .95order-4
GGA − − ≈ ≈ ≈ ≈ ≈ ≈ + + + + + + + +
SORIGA ≈ + + + ≈ + + + + + + + + + + +
EIGA − − ≈ − − ≈ ≈ − + + + + + + + +
R. Road
GGA + ≈ ≈ ≈ ≈ + ≈ ≈ ≈ + + + + + + +
SORIGA + + + ≈ + + + ≈ + + + + + + + +
EIGA ≈ ≈ + ≈ + + + ≈ + + + + + + + +
Knapsack
GGA − − + + − ≈ + + + + ≈ − + + + ≈
SORIGA − ≈ + + ≈ ≈ + + + + ≈ ≈ + + + ≈
EIGA − − + + − − + + + + − − + + + −
Kolmogorov-Smirnov tests with 0.05 level of significance. + signs when GGASM is significantly better than the specified GA, − signs when GGASM is significantly worst, and ≈ signs when the
differences are not statistically significant (i.e., the null hypothesis is not rejected)
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Mutation rates and distribution
Mutation rate:
m(i,j) = 1if the gene of the chromosome has mutated, and 0 otherwise n is the population size and l is the chromosome length
ρ↓ ε = 2400
ε = 24000
0.05 0.0011 0.00070.3 0.0021 0.00110.6 0.0023 0.00140.95 0.0010 0.0009
.
Order-4 traps. Mutation rate median values.
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Mutation rates and distribution
0.001 0.01 0.1 1
0.1
1
10
100
1000
10000
ρ = 0.05
size
quan
tity
0.001 0.01 0.1 1
0.1
1
10
100
1000
10000
ρ = 0.6
size
3 372 741 11101479184822172586295533243693
0
0.1
0.2
0.3
0.4
0.5ρ = 0.05
generations
onli
ne m
utat
ion
rate
3 318 633 948 126315781893220825232838315334683783
0
0.1
0.2
0.3
0.4
0.5ρ = 0.95
generations
Order- dynamic trap problems. GGASM online mutation rate.
Logarithm of the mutation rates abundance plotted against their values.
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Conclusions
The Sand Pile GA improves Standard GA’s performance on many dynamic scenarios (namelly those with low frequency)
It clearly outperforms SORIGA, and it at least competitive with EIGA.
There hints of a dependence of the mutation rate and mutation distribution on the type of dynamics.
PPSN’10 - KrakowFernandes, Laredo, Merelo and Rosa
Future Work
The Sand Pile mutation may be hybridized with any kind of Evolutionary Algorithm, and maybe with other bio-inspired paradigms.
Study the mutation rates and mutation distribution.
Constrained dynamic optimization.
Stationary Optimization.