complexity of calculating the fuzzy similarity matrix is O (N 2) (N is the number of cells in a network), and calculating the fuzzy equivalence matrix by the transitive closure method is O (N 3 log (2N)) [36]. That is, the computational complexity of fuzzy initialization is O (N 3 log (2N)) . M2M decomposition requires O (K 2 S) operators for a two-objective optimization problem, while computation of the gte values of 2KS solutions and updating of the KS solutions in each subpopulation require O (2KS + 2KS 2) operators. Therefore, the computational complexity of the proposed algorithm for the two-objective TA planning is O (N 3 log (2N ) + KS 2 + K 2 S ). As we can see, the fuzzy clustering costs a lot. Thus, we are planning to introduce more effective fuzzy clustering algorithms for initialization in our future work. In the M2M framework, the selection operator is conduced independently in each subpopulation, and those infeasible but crucial solutions are more likely to survive. fails to maintain the population diversity in the evolutionary process because of the overemphasis on feasible solutions. The final solutions tend to be clustered and the convergence of the population also decreases for the same reason. C. Computational Complexity The fuzzy initialization and selection in each subpopulation are the major costs of the proposed algorithm. The computational 21.70 3.0 21.65 × 104 M2M MOEA/D The Number of Pagings 21.60 HV-Metric 21.55 21.50 21.45 21.40 21.35 21.30 21.25 0 50 100 150 200 250 300 The Number of Generations 350 1.5 1.0 × 104 6.0 M2M MOEA/D 1.5 1.0 × 104 1.8 × 104 5.5 2.0 0.6 0.8 1.0 1.2 1.4 1.6 The Number of Location Updates Figure 9 Plot of the solutions with median hV-metric value obtained by M2M and MOeA/d for the 5 × 6 network. The Number of Pagings The Number of Pagings 2.5 2.0 0.5 0.4 400 Figure 7 Variation of hV-metric for the proposed eMO algorithm with different number of generations for multi-objective TA planning in network 1. 2.5 M2M MOEA/D 5.0 4.5 4.0 3.5 3.0 2.5 0.5 0.6 0.8 1.0 1.2 1.4 The Number of Location Updates × 104 1.6 Figure 8 Plot of the solutions with median hV-metric value obtained by M2M and MOeA/d for the 5 × 5 network. 40 IEEE ComputatIonal IntEllIgEnCE magazInE | FEbruary 2017 2.0 2.0 2.5 3.0 3.5 The Number of Location Updates × 104 4.0 Figure 10 Plot of the solutions with median hV-metric value obtained by M2M and MOeA/d for the 9 × 9 network.