1. Genetic Algorithm with Real-coded Binary Rep. 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. Genetic Algorithm with Real-coded Binary Rep. 2 Real-coded Binary Representation Pseudo-binary representation – binary gene values coded by real numbers from the interval  0.0, 1.0  interpretation(r)=1, if r > 0.5 =0, if r < 0.5 Example: ch 1 = [0.92 0.07 0.23 0.62] ch 2 = [0.65 0.19 0.41 0.86] interpretation(ch 1 )=interpretation(ch 2 )=[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. Genetic Algorithm with Real-coded Binary Rep. 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. Genetic Algorithm with Real-coded Binary Rep. 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. Genetic Algorithm with Real-coded Binary Rep. 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) Genes survive through more generations not being changed due to the gene-strength adjustment mechanism

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

7. Genetic Algorithm with Real-coded Binary Rep. 7 Deceptive function DF3 Test Problems F101 function Hierarchical IF and only IF Oscillating Knapsack Problem 14 objects, w i =2 i, i=0,...,13 f(x)=1/(1+target -  w i x i ) Target oscillates between two values 12643 and 2837, which differ in 9 bits

8. Genetic Algorithm with Real-coded Binary Rep. 8 Results on Static Problems DF3 H-IFF F101

9. Genetic Algorithm with Real-coded Binary Rep. 9 Single Gene Diversity Monitoring DF3

10. Genetic Algorithm with Real-coded Binary Rep. 10 Single Gene Diversity Monitoring (Cnd.) F101 H-IFF

11. Genetic Algorithm with Real-coded Binary Rep. 11 Results on Knapsack Problem Oscillating knapsack problem

12. Genetic Algorithm with Real-coded Binary Rep. 12 Results on Knapsack Problem Oscillation period Algorithm 1 2345678910 GARB C=0.025 46 07017600119 GARB C=0.075 45 195119167101210 GARB C=0.125 41 353137383236354132 GARB C=0.175 32 282528293335212831 GARB C=0.025 47 101063214 GARB C=0.075 50 463442284329402543 GARB C=0.125 49 4749 50 48 GARB C=0.175 46 4244 483946444342 Haploid-Recover 45 443345334429433747 Extended-Additive 43 294442394045373940 Ng-Wong 32 214125342732263227 Osc. period10 gener. Osc. period20 gener.

13. Genetic Algorithm with Real-coded Binary Rep. 13 Recovering from Homogen. State DF3Knapsack problem

14. Genetic Algorithm with Real-coded Binary Rep. 14Conclusions 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