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

Networks

Chung-Wei Wu, Tsung-Che Chiang, and Li-Chen FuIEEE Congress on Evolutionary Computation (CEC)

Beijing, July 11, 2014,

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Outline• Introduction• Proposed algorithm• Experimental results• Conclusions

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.

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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 head will be chosen for

communication.– Each node is either a cluster head or a cluster member. – Cluster members are chosen from the neighbor set.

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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 .

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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

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ACO-based approach for multi-objective clustering problem

Initialization

No

end

Yes 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑒 ?

Cluster constructionBit string encoding

Repair functionRepair solutions

Removal redundant heads

Evaluation

Fitness function

Pheromone update

Adjust cluster head tendency

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Permutation encoding• It encodes a solution into a sequence of integers.

–

• It decodes a solution by picking up heads and then assigning members.3 2 1 4 5 6

3

1 5

2

4

6

5

6

3

: number of nodes3 2 1 4 5 6

(literature)

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Permutation encoding• Multiple encoded sequence generate the same

solution.

• Some solutions cannot be generated.

3 2 1 4 5 6 3 4 5 6 1 2

31 5

24

6

5

6

31 5

6

42

5

3

6

3

(literature)

3

1 5

24

6

5

6

3

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Bit string encoding• It encodes a solution into a bit string.

– – A 1-bit denotes that the node is chosen as a cluster head.

node1 node2 node3 node4 node5 node6

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1

2

5

0 0 1 1 0 0

64

3

(proposed)

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Bit string encoding

Permutation encoding Bit string encoding

Search spaceMapping Many to one One to one cluster head selection Depends on the position

in the sequenceIndependent

: number of nodes

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Repair function• Repair the invalid solutions

– Invalid solutions : the solutions which can’t cover the whole networks• Some nodes are neither cluster heads nor cluster

members0 0 1 1 0 0 0 0 0 0 0 0

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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.

𝑠𝑐𝑜𝑟𝑒𝑣=𝑤 ∙𝑝𝑜𝑤𝑒𝑟 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛𝑜𝑓 𝑣+ (1−𝑤 ) ∙ 𝑙𝑜𝑎𝑑𝑖𝑚𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑜𝑓 𝑣

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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.

Redundant head

𝑠𝑐𝑜𝑟𝑒𝑣=𝑤 ∙𝑝𝑜𝑤𝑒𝑟 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛𝑜𝑓 𝑣+ (1−𝑤 ) ∙ 𝑙𝑜𝑎𝑑𝑖𝑚𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑜𝑓 𝑣

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Fitness evaluation• We do non-dominated sorting to rank solutions.

• Fitness function of solution

– denotes the set of solutions

f1

f2

rank 1rank 2rank 3rank 4

fitness = (3-1)/(2+1+1+0) = 0.5

0.25

0.25

0

0.5

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Pheromone structure

node1 node2 node3 node4 node5 node60.2 0.3 0.5 0.5 0.4 0.4

0 0 1 1 0 0pheromone

bit sequence

3 4

1

2

5

643

clusters

Node 3 is selected as a head in probability 0.5.

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Pheromone update• Pheromone update function

– Update the pheromone based on the difference in average fitness• An example of calculating

denotes the pheromone of node at generation tis a constant, called pheromone evaporation factor

0 0 1 1 0 00 0 1 1 0 01 0 1 0 0 0

population fitness

0.25

0.5

0.25

(0.5+0.25)/2 (0.25+0)/2= +0.25

1 0 1 1 0 0

0

0.4 0.3 0.8 0.7 0.2 0.1pheromone

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Experimental settings• Problem instances

• gird size (M): 100100 and 200200• number of nodes: 100, 200, and 300

• Parameters:Parameter Value Meaning

Evaporation factorInitial pheromoneWeight factorTransmission rangeNumber of antsNumber of generation

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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.

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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

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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

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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.

THANK YOU FOR YOUR ATTENTION

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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.

Black: headsGray: members

Redundant headRandom choosing the heads

𝑠𝑐𝑜𝑟𝑒𝑣=𝑤 ∙𝑝𝑜𝑤𝑒𝑟 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛𝑜𝑓 𝑣+ (1−𝑤 ) ∙ 𝑙𝑜𝑎𝑑𝑖𝑚𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑜𝑓 𝑣