A Novel Angular-Guided Particle Swarm Optimizer for Many-Objective Optimization Problems

Algorithm 2

Angular-guided archive update (S, A, N).

(1)	combine S and A into a union set U and set
(2)	normalize all particles in U by equation (6)
(3)	for i = 1 to N
(4)	find the particle pair (xh, xu) in U with the minimum angular-distance for all particle pairs in U
(5)	find x in (xh, xu) such that x has the smaller angular-distance to U by equation (9)
(6)	add x to A, then deleted x from U
(7)	end for
(8)	for each particle
(9)	initialize an empty subset Si
(10)	add the particle xi into Si
(11)	end for
(12)	for each particle
(13)	associate xi to the particle xt in U that has the smallest angular-distance to xi
(14)	add xi into St
(15)	end for
(16)	set
(17)	for i = 1 to N
(18)	find the particle x of Si that has the best convergence performance computed by equation (5)
(19)	add x into A
(20)	end for
(21)	return A