Optimizing Airport Land Side Operations: Check-In, Passengers’ Migration, and Security Control Processes

Algorithm 1

The Surrogate Method.

(1)	Initialize satisfying constraints [25, 26] ( is a continuous vector, is a discrete vector, both of dimension )
(2)	Initialize , ( is the optimal solution of the continuous problem)
(3)	Initialize
(4)	while do (K and H integer parameters, Form the selection set (steps 5–13): is a set of discrete vectors)
(5)	Initialize I =  and  −  (I is the set of M integers, is a continuous vector the component is the decimal part of the component)
(6)	while I ≠  do
(7)
(8)
(9)	(integer vector, the versor with j-th component equal to 1)
(10)
(11)
(12)	end while
(13)	(Transform the continuous problem to the discrete problem, D is the set of the discrete vectors that satisfy constraints [25, 26, 28])
(14)	(Transformation function f, Gradient estimate)
(15)	(OF Objective function declared in [29], where , where k satisfies and , Update state)
(16)	(is the step size of the gradient method, Optimal solution update)
(17)	if then
(18)
(19)
(20)	else
(21)
(22)	end if
(23)	end while (Return the optimal solution )
(24)	Return