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Heuristic Optimization: Other Optimization Techniques

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)

Oscar Cubo Medina

November 18, 2005
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  1. 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
  2. ACO: Example E A F B Nest Food C D

    2 2 4 4 2 2 2 2 5 2 4 5 2
  3. 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
  4. 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
  5. ACO: Example E A F B Nest Food C D

    2 2 4 4 2 2 2 2 5 2 4 5 2
  6. ACO: Example E A F B Nest Food C D

    2 2 4 4 2 2 2 2 5 2 4 5 2
  7. 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
  8. 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
  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 Ant 2: 11 Ant 3: 12
  10. 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)
  11. 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
  12. 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
  13. 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
  14. 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…
  15. 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
  16. Memetic Algorithms memetic_algorithm() p = create_population(); do { p =

    envolve(p); if convergence(p) { p = restart_population(p); } // if } until (convergence_ma);
  17. 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