Amsterdam, The Netherlands
July 06-10, 2013
Ant Colony Optimization
and Swarm Intelligence
Migration Study on a
Pareto-bas...
• Ant Colony Optimization
• Multi-objective Optimization
• Island Model
• Pareto-based Island Model
– Model Factors
– Topo...
• Inspired in the behaviour of natural ants when searching for food.
• They cooperate to get the fastest paths between the...
• Optimize several (independent)
objectives at a time.
• There is a set of optimal solutions. Those
which are the best con...
• If you search in Google (images):
Island Model
• Classical distribution model in EAs:
– Divide or replicate the population in
different subpopulations (islands)
– They e...
• Just a few works in distributing MOACOs.
• No island model in this type of algorithms, just island model
for ACOs.
• Not...
• The colony is divided into several subcolonies or islands.
• Every island searches in a different area of the space of s...
• Migrants move to the closest
neighbour island in the
direction of the prioritary
objective in the colony (sense
of the P...
Pareto-based
Island Model
• Migrants move to the two
closest neighbour islands in
both directions.
• Aims for a better spr...
Pareto-based
Island Model
• Every migrant moves from
one island to the rest.
• Aims for a better spread of
solutions along...
• Proposed by Barán et al. in 2003 for solving the VRPTW.
• Proved to be competitive in solving the bicriteria TSP (our te...
• 16 islands, everyone in a different processor of a cluster.
• Bicriteria TSP problem: kroAB100, kroAB150 and kroAB200.
•...
• Unidirectional
Experiments and Results
• Bidirectional
Experiments and Results
• Broadcast
Experiments and Results
• Best of every
topology
Experiments and Results
• Hypervolume: it calculates the volume, in the objective space, covered by a set of non-
dominated solutions (PS). A high...
• Spread: it measures the extent of spread of a PS. It considers the Euclidean distance between
consecutive solutions on a...
• Epsilon: it is a measure of the smallest distance it would be necessary to translate every
solution in a PS so that it d...
• Cardinality: number of non-dominated solutions in the obtained PS.
Experiments and Results
• Time: the worst time among all the processors in one execution has been chosen as the
running time of that execution.
Ex...
• A novel island model for MOACOs has been tested with different
topologies and migration rates.
• Bidirectional approach ...
Questions?
----------------------------------------
Those interested in a partnership with us…
http://geneura.org
THANKYOU...
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Migration study on a Pareto-based island model for MOACOs

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This is the presentation of the paper of the same title at the Genetic and Evolutionary Computation Comference (GECCO) 2013.

The work describes an analysis of a proposed island (distribution) model for Multi-Objective Ant Coloy Optimization algorithms.
It presents the results of some different neighbourhood topologies and migration rates.

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Migration study on a Pareto-based island model for MOACOs

  1. 1. Amsterdam, The Netherlands July 06-10, 2013 Ant Colony Optimization and Swarm Intelligence Migration Study on a Pareto-based Island Model for MOACOs Antonio M. Mora, P. García-Sánchez, J.J. Merelo, P.A. Castillo Depto. de Arquitectura y Tecnología de Computadores UNIVERSIDAD DE GRANADA
  2. 2. • Ant Colony Optimization • Multi-objective Optimization • Island Model • Pareto-based Island Model – Model Factors – Topologies • MOACS Algorithm • Experiments and Results – Attainment Surfaces – Metrics and Indicators – Statistics • Conclusions and Future Work
  3. 3. • Inspired in the behaviour of natural ants when searching for food. • They cooperate to get the fastest paths between the nest and the source of food. • They use a chemical substance named pheromone. In ACO algorithms • There are a set of agents called (artificial) ants. – All of them move in a graph following and depositing (artificial) pheromone. – They cooperate to find a solution (usually every ant yields a complete solution). • There are some formulae applied in the run: – state transition rule  decides the next step for each ant – pheromone updating  contribution and evaporation – evaluation function  assigns the cost to every solution Ant Colony Optimization
  4. 4. • Optimize several (independent) objectives at a time. • There is a set of optimal solutions. Those which are the best considering all the objectives than the rest are named non- dominated solutions. • The ideal set of non-dominated solutions is called the Pareto Set (PS). • Its graphical representation is the Pareto Front (PF). Multi-Objective Optimization Example of PF for two objective functions.
  5. 5. • If you search in Google (images): Island Model
  6. 6. • Classical distribution model in EAs: – Divide or replicate the population in different subpopulations (islands) – They evolve independently – After some generations, some individuals are chosen in every island – They migrate to a neighbour island, following a specific neighbourhood topology – They replace other individuals in the receiver islands. • It Improves the algorithm performance, not just the running time Island Model Island model. Ring neighbourhood topology. Image by Pablo García-Sánchez
  7. 7. • Just a few works in distributing MOACOs. • No island model in this type of algorithms, just island model for ACOs. • Not take advantage of the multi-colony division both: – From the algorithmic point of view: very important in Multi-objective optimization. – From the computational cost point of view: due to parallelization. • Previous works by us in this line comparing multi-colony, sub-colony and island models for different MOACOs. • Island model with a fixed topology and migration rate. MOACOs
  8. 8. • The colony is divided into several subcolonies or islands. • Every island searches in a different area of the space of solutions (PF). • A l parameter is used for splitting the space in this way. Model Factors • Migration policy  the best ants (solutions in fact) are migrated. In this case, the best regarding the prioritary objective in every island. • Migrants influence  every migrant contributes to the pheromone matrix of the receiver island, in order to guide the search to its own area. • Replacement policy  the migrant is included in the island’s PS, removing those dominated solutions (by itself) in that set. • Migration rate  some different values (number of iterations) are tested. Pareto-based Island Model
  9. 9. • Migrants move to the closest neighbour island in the direction of the prioritary objective in the colony (sense of the PF). • Tries to cover the gaps between colonies. Pareto-based Island Model
  10. 10. Pareto-based Island Model • Migrants move to the two closest neighbour islands in both directions. • Aims for a better spread of solutions in the inter-colony gaps.
  11. 11. Pareto-based Island Model • Every migrant moves from one island to the rest. • Aims for a better spread of solutions along the whole PF. >>>>>>>>>>>>>>>>>>> This is a simplified example showing just the migrations from one island to the rest. >>>>>>>>>>>>>>>>>>>
  12. 12. • Proposed by Barán et al. in 2003 for solving the VRPTW. • Proved to be competitive in solving the bicriteria TSP (our test problem) in previous works. • It considers one colony, one pheromone matrix and two heuristic functions (one per objective). • The state transition rule considers l parameter for weighting the importance of the heuristic and memoristic (pheromone) information. • Initially l took a different value per ant in the colony, in order to explore the whole space of solutions (PF). • It applies a pheromone reinitialization mechanism, in order to avoid being stagnated. MOACS
  13. 13. • 16 islands, everyone in a different processor of a cluster. • Bicriteria TSP problem: kroAB100, kroAB150 and kroAB200. • Implemented with MPI (Message Passing Interface). • 20 runs per experiment. • q0 and r take values for promoting the exploration more than usual. • Global PS of all the executions for computing the metrics. Experiments and Results
  14. 14. • Unidirectional Experiments and Results
  15. 15. • Bidirectional Experiments and Results
  16. 16. • Broadcast Experiments and Results
  17. 17. • Best of every topology Experiments and Results
  18. 18. • Hypervolume: it calculates the volume, in the objective space, covered by a set of non- dominated solutions (PS). A higher value means a better result. Experiments and Results
  19. 19. • Spread: it measures the extent of spread of a PS. It considers the Euclidean distance between consecutive solutions on average and extreme distances. A value 0 means an ideal spread. Experiments and Results
  20. 20. • Epsilon: it is a measure of the smallest distance it would be necessary to translate every solution in a PS so that it dominates the optimal PF of the problem. Smaller values are better. Experiments and Results
  21. 21. • Cardinality: number of non-dominated solutions in the obtained PS. Experiments and Results
  22. 22. • Time: the worst time among all the processors in one execution has been chosen as the running time of that execution. Experiments and Results
  23. 23. • A novel island model for MOACOs has been tested with different topologies and migration rates. • Bidirectional approach yields a very good balance between quality and spread in the set of non-dominated solutions (PS). • It has a flaw concerning the computational time. If it is relevant for the user, then unidirectional approach would be a better option. • Regarding the migration rate, high values perform better. Future Work • Study some other parameters in the island model. • Implement and test in other MOACO approaches. • Compare with state-of-the-art distributed algorithms (EAs, island models) Conclusions
  24. 24. Questions? ---------------------------------------- Those interested in a partnership with us… http://geneura.org THANKYOU!!!!
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