All-Domain Fusion-Based Time Synchronization Protocol in SD-ATSN

Algorithm 2

Mixed mutation operator NSGA-II.

Notations:: dominance set of solution; : solution of the population; : this is the number of solutions that dominate ; : front; : crowding distance; : size of child population; : size of the old population considered for execution; : rank of solution; : number of generations used for looping; : max number of generations; : old population; : child population
Input:; ;
(1)	Near the virtual centroid . Generate initial population of size by random distribution of decision variable in given range [, ]. Save one copy of population as
(2)	For each
(a)	Calculate Multiobjective using equation (11)
(b)	Meet the relevant constraints using equation (12)
End for
(3)	While ()
Nondominated_sorting()
(4)	For each
Calculate
End for
,
(5)	For each
If ()
End If
End For
(6)	For each
If ()
End If
End for
Crowing_distance ()
Assume from boundary point to for any solution
(7)	For each
calculate from all point excluding boundary points
End For
(8)	Select the best half elite population as using Binary tournament selection approach.
(9)	While ()
(a)	Randomly select two chromosomes from the
(b)	Perform crossover to produce two child chromosomes
(c)	Mutate chromosome to produce a child chromosome using Mixed mutation operator (13)
Update and
End While
(10)	Generate new population of size (2 × ) by
(11)	Non-dominated_sorting()
(12)	Crowing_distance ( )
(13)	Select again the best half elite population as using rank and
End While
(14)	Select the minimum sum of Multiobjective
(15)	Exit
Output: optimized chromosomes