An Improved Real-Coded Genetic Algorithm Using the Heuristical Normal Distribution and Direction-Based Crossover

Algorithm 1

MOIRCGA.

	Input: population size: n; mutation probability: Pm; crossover probability: Pc; lower and upper bounds of variables: [a, b]; the number of elite individuals retained: m
	Output: the optimal value of an optimization problem
(1)	Initialize population
(2)	Calculate the objective function values of individuals and sort the individuals in descending order
(3)	While termination criterion is not met
(4)	Perform SGS
(5)	Perform HNDDBX
(6)	Perform substitution operation
(7)	Calculate the objective function values of individuals and sort the individuals in descending order
(8)	Retain m elitist members from all parents and 3n offsprings after performing the substitution operation
(9)	Perform combinational mutation
(10)	Calculate the objective function values of the individuals and sort the individuals in descending order
(11)	m elitist members, 3nPm mutated members, and 3n(1 − Pm) nonmutated members constitute the current population
(12)	Select n best members to constitute the new population, and retain m elitist members
(13)	End While
(14)	Output the average running time, the average number of iterations, and the optimal value