A New Multiobjective Evolutionary Algorithm for Community Detection in Dynamic Complex Networks

Algorithm 1

Program  DNCD-MOEA

Input:  The number 𝑇 of time steps, the sequence of

dynamic network 𝑁={𝑁₁,𝑁₂,…,𝑁_𝑇}

Output:  The sequence of community structure detected in

the dynamic network 𝐶={𝐶₁,𝐶₂,…,𝐶_𝑇}

Begin

       Step 1: Set 𝑡=1. Generate the initial community structure

        𝐶₁={𝐶¹₁,𝐶²₁,…,𝐶^𝑘₁} of the network 𝑁₁using

        GA-Net algorithm. Set 𝑡=𝑡+1.

         Step 2: If 𝑡>𝑇, return the sequence of community

        structure 𝐶={𝐶₁,𝐶₂,…,𝐶_𝑇} as the output,

        algorithm stops; Else, go to Step 3.

         Step 3: Set 𝑠=1. Randomly generate individuals whose

        length equals the nodes number 𝑛_𝑡=𝑉_𝑡 of

        network 𝑁_𝑡 as an initial population 𝑃_𝑠;

         Step 4: While termination condition is not satisfied do

      Step 4.1: Create a new population 𝑄_𝑠 of offspring by

            applying the variation operators on

            population 𝑃_𝑠;

      Step 4.2: Combine the parents 𝑃_𝑠 and offspring 𝑄_𝑠 into a

            new pool 𝑅_𝑠 and;

      Step 4.3: Decode each individual 𝐼 of the population 𝑅_𝑠

            to generate the partitioning

            𝐶_𝑡={𝐶¹_𝑡,𝐶²_𝑡,…,𝐶^𝑘𝐼𝑡_𝑡} of the network 𝑁_𝑡 in

            𝑘_𝑡 connected components;

      Step 4.4: Evaluate the two fitness values of the translated

            individuals;

      Step 4.5: Partition 𝑅_𝑠 into fronts, assign a rank to each

            individual and sort them according to

            nondomination rank;

      Step 4.6: Select individuals based on rank and crowding

            length to comprise new population 𝑃_𝑠+1;

      Step 4.7: Select the dominant individuals 𝐿_𝑠 in 𝑃_𝑠+1,

      Step 4.8: Perform the local search algorithm on the

            selected individuals in 𝐿_𝑠 to generate the new

            dominant population 𝐿^′_𝑠. Update the dominant

            population 𝐿_𝑠 with 𝐿^′_𝑠 in 𝑃_𝑠+1.

      Step 4.9: 𝑠=𝑠+1

          End while

         Step 5: Select the individual which has the maximum

        Community Score on the Pareto front. Decode the

        selected individual to get the community structure

        𝐶_𝑡={𝐶¹_𝑡,𝐶²_𝑡,…,𝐶^𝑘𝑡_𝑡} of the network 𝑁_𝑡.

         Step 6: Set 𝑡=𝑡+1, go to Step 2.

End