A Kriging Model-Based Expensive Multiobjective Optimization Algorithm Using R2 Indicator of Expectation Improvement

Algorithm 1

EIR2-MOEA.

	Input:
	: Maximum number of evaluations by expensive function
	: Ratio of the number of initial samples to
	: Integer used to generate weight vector
	Output:
	: Nondominated solution set
	(1) Initialization: Obtain design variable limits and , number of objective , etc. according to MOP to be solved. Set and .
	(2) Generate sample points in design space using optimal Latin hypercube sampling.
	(3) for = 1 to do
	(4) Calculate the expensive objective function values for sample point
	(5) , i.e., add sample point to
	(6) end for
	(7) Generate weight vectors in objective space and save them in set .
	(8) Find non-dominated solutions in and put them into
	(9) fordo
	(10) fordo
	(11) Using PSO to find the best hyperparameter
	(12) Build Kriging model of the -th objective function based on
	(13) end for
	(14) According to EIR2 indicator, apply PSO to find the best infilling point
	(15) Calculate expensive objective function
	(16) Update
	(17) Find the non-dominated solutions in and put them into
	(18) end for return Output as approximated Pareto set