GAs and Premature Convergence

1. GAs and Premature Convergence • Premature convergence - GAs converge too early to suboptimal solution • as the population gets homogeneous, only a little new can be evolved • Reasons for premature convergence: • improper selection pressure • insufficient population size • deception • improper representation and genetic operators

2. Real-coded Binary Representation • Pseudo-binaryrepresentation – binary gene values coded by real numbers from the interval0.0, 1.0 interpretation(r)=1, ifr> 0.5 = 0, if r < 0.5 Example: ch1 = [0.92 0.07 0.23 0.62] ch2 = [0.65 0.19 0.41 0.86] interpretation(ch1)=interpretation(ch2)=[1001] • Gene strength – gene’s stability measure • The closer the real value is to 0.5 the weaker the gene is • „one-valued genes“:0.92 > 0.86 > 0.65 > 0.62 • „zero-valued genes“: 0.07 > 0.19 > 0.23 > 0.41

3. Gene-strength Adjustment • Every offspring gene is adjusted depending on • its interpretation • the relative frequency of ones at given position in the population • Vector P[] stores the population statistic Ex.: P[0.82 0.17 0.35 0.68]  82% of ones at the first position, 17% of ones at the second position, 35% of ones at the third position, 68% of ones at the fourth position.

4. Gene Strengthening/Weakening • Zero-valued gene: gene’ =gene+c*(1.0-P[i])weakening gene’ = gene – c*P[i]strengthening • One-valued gene gene’ =gene+c*(1.0-P[i])strengthening gene’ = gene – c*P[i]weakening • C stands for a maximal gene-adaptation step: c (0.0,0.2 • Gene value interpreted with above-average frequency at given position in the chromosome is weakened, the other one is strengthened.

5. Boosting-up the Exploitation • Genotype of promising solutions should be stabilized for subsequent generations • newly generated solutions that are better than their parents • disable rapid changes in their genotype interpretation • All genes of such individuals are strengthened • zero-valued genes are set to be close to 0.0 • one-valued genes are rescaled to be close to 1.0 Ex.: ch = (0.71, 0.45, 0.18, 0.57)  ch’= (0.97,0.03, 0.02, 0.99) • Genessurvive through more generations not being changed due to the gene-strength adjustment mechanism

6. GARB Algorithm 1 begin 2 initialize(OldPop) 3 repeat 4 calculate P[] from OldPop 5 repeat 6 select Parents from OldPop 7 generate Children 8 adjust Children genes 9 evaluate Children 10 if Child is better than Parents 11 then rescale Child 12 insert Children to NewPop 13 until NewPop is completed 14 switch OldPop and NewPop 15 until termination condition 16 end

7. Test Problems • Hierarchical IF and only IF • F101 function • Oscillating Knapsack Problem 14 objects, wi=2i, i=0,...,13 f(x)=1/(1+target-wixi) Target oscillates between two values12643 and2837, which differ in 9 bits • Deceptive function DF3

8. DF3 H-IFF F101 Results on Static Problems F101

9. Single Gene Diversity Monitoring DF3

10. Single Gene Diversity Monitoring(Cnd.) F101 H-IFF

11. Results onKnapsackProblem Oscillating knapsack problem

12. Results onKnapsackProblem Osc. period 10 gener. Osc. period 20 gener.

13. Recovering from Homogen. State DF3 Knapsack problem

14. Conclusions • A novel approach for preventing the premature convergence • based on pseudo-binary representation • preserves the diversity of the evolved population during the whole run • enables to escape even from the homogeneous state • enhances exploration capabilities of the genetic algorithm • Steady-state evolutionary model • might be faster in responding to the convergence trend observed in the population • Does not deal with the linkage problem • not another competent genetic algorithm • might be combined with some chromosome reordering techniques