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.

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. • 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. • 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. • 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. • If you search in Google (images):
Island Model

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. • 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. • 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. • 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. 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. 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. • 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. • 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. • Unidirectional
Experiments and Results

15. • Bidirectional
Experiments and Results

16. • Broadcast
Experiments and Results

17. • Best of every
topology
Experiments and Results

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. • 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. • 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. • Cardinality: number of non-dominated solutions in the obtained PS.
Experiments and Results

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. • 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. Questions?
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