Xavier-MaYiMing / AMPSO

A modified particle swarm optimizer (AMPSO) for multi-modal multi-objective optimization (MMO)

AMOPSO: A modified particle swarm optimizer (AMPSO) for multi-modal multi-objective optimization (MMO) problems

Reference: Zhang X W, Liu H, Tu L P. A modified particle swarm optimization for multimodal multi-objective optimization[J]. Engineering Applications of Artificial Intelligence, 2020, 95: 103905.

The AMOPSO belongs to the category of multi-objective evolutionary algorithms (MOEAs). AMOPSO is an algorithm to solve the multi-modal multi-objective optimization (MMO) problems.

Variables	Meaning
npop	Population size
iter	Iteration number
lb	Lower bound
ub	Upper bound
omega	Inertia weight
c1	Acceleration constant 1 (default = 2)
c2	Acceleration constant 2 (default = 2)
dim	Dimension
pos	Position
vmin	Minimum velocity
vmax	Maximum velocity
vel	Velocity
objs	Objectives
nvar	The dimension of decision space
nobj	The dimension of objective space
PA	Personal archive
NA	Neighborhood archive
PA_objs	The objectives of PA
NA_objs	The objective of NA
off	Offspring
off_objs	The objectives of offsprings
scd	Special crowding distance
pf	Pareto front
ps	Pareto set

Test problem: MMF1

$$ \left{ \begin{aligned} &f_1(x)=|x_1-2|\\ &f_2(x)=1-\sqrt{|x_1 - 2|}+2(x_2-\sin{(6 \pi |x_1 - 2| + \pi)})^2\\ &1 \leq x_1 \leq 3, -1 \leq x_2 \leq 1 \end{aligned} \right. $$

Example

if __name__ == '__main__':
    t_npop = 800
    t_iter = 100
    t_lb = np.array([1, -1])
    t_ub = np.array([3, 1])
    main(t_npop, t_iter, t_lb, t_ub)

Output:

Iteration 10 completed.
Iteration 20 completed.
Iteration 30 completed.
Iteration 40 completed.
Iteration 50 completed.
Iteration 60 completed.
Iteration 70 completed.
Iteration 80 completed.
Iteration 90 completed.
Iteration 100 completed.