An Ant Colony Optimization Algorithm for Multi-objective Clustering in Mobile Ad Hoc Networks

1. An Ant Colony Optimization Algorithm for Multi-objective Clustering in Mobile Ad Hoc Networks Chung-Wei Wu, Tsung-Che Chiang, and Li-Chen Fu IEEE Congress on Evolutionary Computation (CEC) Beijing, July 11, 2014,

2. Outline • Introduction • Proposed algorithm • Experimental results • Conclusions

3. Introduction • Mobile Ad Hoc Networks (MANETs) • MANET is a wireless network constructed by mobile devices. • The mobile devices communicate without infrastructures (base stations). • It has great applications in a variety of areas such as disaster relief, mobile conferences, and battle fields.

4. Clustering in MANET • Clustering constructs a hierarchical structure to reduce the routing scale of MANETs. • It divides nodes in a MANET into several groups (clusters). • For each cluster, a cluster headwill be chosen for communication. • Each node is either a cluster head or a cluster member. • Cluster members are chosen from the neighbor set.

5. Objective functions • Number of clusters • denotes the set of cluster heads. • Load imbalance •  is defined by (), where is the number of nodes in the whole network. • denotes the number of members of cluster head . • Total power consumption • denotes the Euclidean distance of .

6. Multi-objective optimization • Minimize • denotes the solution space. • denotes the objective function. • Pareto dominance • We say solution A dominates solution B if and only if • A is not worse than B for all objective functions. • A is better than B for at least one objective. • Pareto optimal solution • a solution that cannot be dominated by any other solution • Goal • find or approximate the set of Pareto optimal solutions

7. ACO-based approach for multi-objective clustering problem • Cluster construction Repair function Initialization Repair solutions Bit string encoding Removal redundant heads No Evaluation Fitness function Yes Pheromone update end Adjust cluster head tendency

8. Permutation encoding (literature) • It encodes a solution into a sequence of integers. • It decodes a solution by picking up heads and then assigning members. : number of nodes 5 5 1 4 3 3 2 6 6

9. Permutation encoding (literature) • Multiple encoded sequence generate the same solution. • Some solutions cannot be generated. 5 5 5 5 1 1 4 4 3 3 3 3 2 2 6 6 6 6 5 5 1 4 3 3 2 6 6

10. Bit string encoding (proposed) • It encodes a solution into a bit string. • A 1-bit denotes that the node is chosen as a cluster head. 1 5 3 3 4 4 2 6

11. Bit string encoding : number of nodes

12. Repair function • Repair the invalid solutions • Invalidsolutions : the solutions which can’t cover the whole networks • Some nodes are neither cluster heads nor cluster members

13. Repair function • Repair the invalid solutions • We calculate a score of each uncovered node and then choose the node with the lowest score as a cluster head until the network is completely covered.

14. Repair function • Remove the redundant cluster heads • A cluster head is redundantif its members and itself can be covered by other cluster heads. • We calculate the score of each redundant head, then delete the head with the highest score until there are no redundant heads. Redundant head

15. Fitness evaluation • We do non-dominated sorting to rank solutions. • Fitness function of solution • denotes the set of solutions f2 rank 1 rank 2 rank 3 rank 4 f1 0 0.25 0.25 0.5 fitness = (3-1)/(2+1+1+0) = 0.5

16. Pheromone structure pheromone Node 3 is selected as a head in probability 0.5. bit sequence 1 5 3 3 4 4 2 6 clusters

17. Pheromone update • Pheromone update function • Update the pheromone based on the difference in average fitness • An example of calculating denotes the pheromone of node atgeneration t is a constant, called pheromone evaporation factor population fitness pheromone 0.5 0.25 0.25 0 (0.5+0.25)/2  (0.25+0)/2= +0.25

18. Experimental settings • Problem instances • gird size (M): 100100 and 200200 • number of nodes: 100, 200, and 300 • Parameters:

19. Experimental settings • Benchmark algorithms: • weighted clustering algorithm (WCA) • a greedy heuristic based on weighted sum of objectives • genetic algorithm (GA) • permutation encoding + weighted sum of objectives • weighted sum ACO (WSACO) • bit string encoding + weighted sum of objectives • multiobjective ACO (MOACO) • bit string encoding + Pareto ranking • Each algorithm was applied 10 times to each scenario.

20. grid instances • WCA : Greedy heuristic • GA : Permutation encoding+ aggregated objective clustering • WSACO : Bit string encoding + aggregated objective clustering • MOACO : Bit string encoding + multi-objective clustering • : Number of clusters • : Degree of load balance • : Power consumption • : Number of nodes The best value is marked in bold

21. grid instances • WCA : Greedy heuristic • GA : Permutation encoding+ aggregated objective clustering • WSACO : Bit string encoding + aggregated objective clustering • MOACO : Bit string encoding + multi-objective clustering • : Number of clusters • : Degree of load balance • : Power consumption • : Number of nodes The best value is marked in bold

22. Conclusions • We proposed an MOACO algorithm for the clustering problem in MANET. • The proposed bit-string encoding/decoding scheme avoids duplicate solutions and the position dependency in the traditional permutation scheme. • We proposed a repair algorithm to make solutions feasible and better. • MOACO performs better than several benchmark algorithms. • Future work is to extend our work with the dynamic situations, and we will investigate the impact of parameter values on the algorithm performance.

23. Thank you for your attention

24. Repair function • Remove the redundant cluster heads • A cluster head is redundant if its members and itself can be covered by other cluster heads. • We calculate the score of each redundant head, then delete the head with the highest score until there are no redundant heads. Random choosing the heads Redundant head Black: heads Gray: members