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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