A Competitive Bilevel Programming Model for Green, CLSCs in Light of Government Incentives

Algorithm 3

Adopted QBPSO algorithm.

	Step1: (Initialization)
	1.1. Set the value parameters of the QBPSO algorithm and population sizes , .
	1.2. By equation , randomly generate the initialized value of the leader’s decision variables for any particle; next, in the lower level, the follower’s problem is solved by fixing .
	Let (also ) be the optimal solution to the follower problem. Then, the leader problem is solved by fixing and optimal values of the lower level (regarding ) in the upper-level problem, while the fitness value of the current position of the r^th particle is calculated using , where is the leader’s objective function. Consider the personal best position of the r^th particle equal to and set the global best position .
	Step 2: (Updating) Change and update according to the QBPSO algorithm.
	Step 3: (Obtaining the follower’s reaction and determining the particle’s fitness) by fixing new in the lower-level problem, obtain the follower’s optimal solution . Afterwards, in the upper-level problem, the position and fitness value of is calculated by fixing .
	Step 4: (Updating the personal best position) If the fitness value of is better than that of , update .
	Step 5: (Updating the global best position) after comparing the fitness value of with that of all personal best positions, is updated with the global best position .
	Step 6: (Termination) Go to step 2 until the stopping criterion is met.