A Simplified Hypervolume-Based Evolutionary Algorithm for Many-Objective Optimization

Algorithm 1

The framework of the algorithm SHEA.

	Input:
	MaOP(1)
	A stopping criterion
	: the number of weight vectors
	: the number of external population
	: the number of weight vectors in the neighborhood of each weight vector,
	: the number of the solutions with largest hypervolume selected in neighbors,
	: a set of uniformly distributed weight vectors
	Output: External population
	Initialization: Generate an initial population randomly; set ; determine by a problem-specific method; determine closest weight vectors to each vector
	While the stopping criterion is not met do
	Calculate the proposed hypervolume of nondominated solutions.
	Fordo
	if rand < J then
	else
	end if
	Choose and from according to the selection operator in Section 2.2.
	Use and to generate offspring , and set .
	Useto Update: For , if , then set .
	End for
	Set.
	Use the updated strategy to update .
	Use the updated strategy of external population of Section 2.3 to update .
	End while