Differential Evolution (DE) "Biologically-inspired computing", T. Krink, EVALife Group, Univ. of Aarhus, Denmark

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1 Differential Evolution (DE)

2 Differential Evolution (DE) (Storn and Price, 199) Step 1 - Initialize and evaluate Generate a random start population and evaluate the individuals x 2 search space x 1

3 Differential Evolution (DE) (Storn and Price, 199) Step 2 - Evolve (repeat until termination) For each individual i, select three other individuals j, k and l with (i j k l) randomly x 2 j i l k search space x 1

4 Differential Evolution (DE) (Storn and Price, 199) Step 3 Calculate the difference vector between j and k x 2 j i l k search space x 1

5 Differential Evolution (DE) (Storn and Price, 199) Step 4 Add the scaled difference vector to l to create a candidate c as a crossover of this result and individual i c x 2 j i l k search space x 1

6 Differential Evolution (DE) (Storn and Price, 199) Step Replace i with c if it has a better fitness and continue with step 2 (for all individuals; repeat until termination) c x 2 j i l k search space x 1

7 Differential Evolution (DE) Approach rather far away from real biology, but... highly efficient and robust in obtaining results Performance best search heuristic for continuous numerical problems outperforms other heuristics in benchmark problems and real world problems (engineering, bioinformatics, datamining, finance)

8

9 (Bonabeau et al., 1999) What is Swarm Intelligence? The emergent collective intelligence of groups of simple agents. Examples group foraging cooperative transportation nest-building collective sorting and clustering

10 (Bonabeau et al., 1999) Two key mechanisms Self-organization Stigmergy (stimulation by work)

11 (Bonabeau et al., 1999) Self-organization Self-organization is a set of dynamic mechanisms whereby structures appear at the global level of a system from interactions of its lower-level components.

12 (Bonabeau et al., 1999) Self-organization Self-organization is a set of dynamic mechanisms whereby structures appear at the global level of a system from interactions of its lower-level components. How it works... multiple interactions of agents fluctuations (randomness, errors, e.g. random walk) positive feedback (amplification) negative feedback (for counter-balance and stabilization)

13 Ant foraging by co-operative search Nest Food

14 Ant foraging by co-operative search Nest Food

15 Ant foraging by co-operative search Nest Food

16 Ant foraging by co-operative search Nest Food

17 Ant foraging by co-operative search Nest Food

18 Ant foraging by co-operative search Nest Food

19 Ant foraging by co-operative search Nest Food

20 Ant foraging by co-operative search Nest Food

21 Ant foraging by co-operative search Nest Food

22 Ant foraging by co-operative search Nest Food

23 Ant foraging by co-operative search Nest Food

24 Ant foraging by co-operative search Nest Food

25 Ant foraging by co-operative search Nest Food

26 Ant foraging by co-operative search Nest Food

27 Ant foraging by co-operative search Nest Food

28 Ant foraging by co-operative search Nest Food

29 Tackling the Travelling Salesman Problem Task: Minimize COST(i 1,...,i n ) = n 1 d(c i j, C i j +1 ) + d(c in,c i1 ) j =1 d(c x,c y ) distance between cities x and y Find a path i between n cities (including an edge from the last city to the home city), such that the costs for travelling are minimal and each city is visited once.

30 Ant Colony Optimization Ålborg 9 Århus 10 6 Odense 4 Sandbjerg København (Dorigo et al., 1991)

31 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg

32 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg

33 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg

34 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg

35 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg

36 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34

37 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34

38 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34

39 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34

40 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34

41 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34

42 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus København Odense 4 Sandbjerg L 1 = = 34 L 2 = = 31

43 Ant Colony Optimization (Dorigo et al., 1991) time: t=1 ant: k=2 Ålborg Århus Odense Sandbjerg København

44 Ant Colony Optimization (Dorigo et al., 1991) time: t=2 ant: k=1 Ålborg p=0.47 Århus p= p= p= Odense 4 København Sandbjerg

45 Ant Colony Optimization (Dorigo et al., 1991) time: t=2 ant: k=1 p=0.0 Ålborg Århus p= Sandbjerg 10 p= Odense p=0.72 København

46 Ant Colony Optimization (Dorigo et al., 1991) time: t=2 ant: k=1 Ålborg 9 Århus Odense 4 p= København 6 p=0.6 p=0.32 Sandbjerg

47 Ant Colony Optimization (Dorigo et al., 1991) time: t=2 ant: k=1 Ålborg 9 Århus 10 6 p=0.0 4 p=1.0 Sandbjerg Odense p=0.0 København

48 Ant Colony Optimization (Dorigo et al., 1991) time: t=2 ant: k=1 Ålborg Århus 9 p=0.0 Sandbjerg 6 Odense 4 p= p=0.0 København

49 Ant Colony Optimization (Dorigo et al., 1991) time: t=2 ant: k=1 Ålborg Århus København Odense 4 Sandbjerg

50 Ant colony optimization Applications NP-hard graph problems job-shop scheduling string matching Performance original version only as good as general purpose heuristics modified version (ACS) with best-path-only pheromone marking and local search can compete with other state-ofthe-art heuristics

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