Heuristic Optimization: Other Optimization Techniques

A review of other heuristic optimization techniques:
- Ant Colony Optimization
- Cultural Algorithms
- Memetic Algorithms

Athens 2005 Heuristic Optimization (http://laurel.datsi.fi.upm.es/docencia/cursos/heuristic_optimization)

Transcript

1. Athens: Heuristic Optimization Other optimization techniques Oscar Cubo Medina (ocubo@fi.upm.es)
2. Outline 1.  Ant Colony Optimization 2.  Cultural Algorithms 3.  Memetic Algorithms
3. ACO: Ant Colony Optimization l  Based on the behaviour of real ants l  The key concept is pheromone l  Multi-agent system l  Each agent is an artificial ant l  All ants collaborate in the generation of the solution
4. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2
5. ACO: Example E A Nest C 2 2 4 ( ) ( ) 1 1 0 i ij ij i k ij ij j N ij i d j N p d j N β α β α τ τ ∈ ⎧ ⎛ ⎞ ⎪ ×⎜ ⎟ ⎜ ⎟ ⎪ ⎝ ⎠ ∈ ⎪ ⎛ ⎞ = ⎛ ⎞ ⎨ ⎜ ⎟ ×⎜ ⎟ ⎪ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎪ ⎝ ⎠ ⎪ ∉ ⎩ ∑ Arc Prob Nest A 2/5 Nest C 1/5 Nest E 2/5
6. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2 ( ) ( ) 1 ij ij t t τ τ τ + = + Δ
7. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2
8. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2
9. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2 Ant 1: 15
10. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2 Ant 1: 15 Ant 2: 11
11. ACO: Example E A F B Nest Food C D 2 2 4 4 2 2 2 2 5 2 4 5 2 Ant 1: 15 Ant 2: 11 Ant 3: 12
12. ACO: Requirements l  Finite set of components (nodes) l  Finite set of transitions between the components (arcs) l  Assigned a cost for each transition l  Existence of neighbourhood l  Solutions are a sequence of components l  Each solution has a cost (sum of the costs of the arcs)
13. Cultural Algorithms l  Based on the learning of culture l  Two spaces: l  Population Space l  Belief Space l  Communication between spaces: l  Best individuals of population influences in belief space l  The belief space influences the generation of new individuals
14. CA: Pseudocode cultural_algorithm p = create_population(); b = create_beliefs(); for(t=0;end condition; t++) { fitness = evaluate(p); b = update(b,accept(p)); p = envolve(p, influence(b)); } // for
15. CA: Types of beliefs l  Normative: Best ranges for variables l  Situational: Set of examples l  Topographical: Best individuals of each zone l  Domain: Knowledge about the problem that guides the search l  Historical or temporal: Records the principal events
16. Memetic Algorithms l  Hybrid population based algorithms l  Local Search + Crossover operators l  Faster than Genetic Algorithms l  Also called: Parallel Genetic Algorithms, Genetic Local Search…
17. Memetic Algorithms l  Genetic algorithm but: l  Individuals (called agents) has a internal local search optimization l  Convergence of population implies a restart procedure l  New operators definitions: l Cross l Mutation l Meta-mutation: local search
18. Memetic Algorithms memetic_algorithm() p = create_population(); do { p = envolve(p); if convergence(p) { p = restart_population(p); } // if } until (convergence_ma);
19. Memetic Algorithms create_population(p) for(i=BEST+1;i<INDIVS;i++) { new[j] = local_search(); } // for restart_population(p) for(i=0;i<BEST;i++) { new[i] = best(p,i); } // for for(j=BEST+1;j<INDIVS;j++) { new[j] = local_search(); } // for