xavier-mayiming / ar-moea

An indicator-based multiobjective evolutionary algorithm with reference point adaptation

AR-MOEA: An indicator-based multiobjective evolutionary algorithm with reference point adaptation

Reference: Tian Y, Cheng R, Zhang X, et al. An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility[J]. IEEE Transactions on Evolutionary Computation, 2017, 22(4): 609-622.

Variables	Meaning
npop	Population size
iter	Iteration number
lb	Lower bound
ub	Upper bound
nobj	The dimension of objective space (default = 3)
eta_c	Spread factor distribution index (default = 30)
eta_m	Perturbance factor distribution index (default = 20)
nvar	The dimension of decision space
pop	Population
objs	Objectives
W	Oringinal reference vectors
arch	Archive
refs	Reference points
Range	Ideal and nadir points
pf	Pareto front

Test problem: DTLZ5

$$ \begin{aligned} & \theta_i = \frac{\pi}{4(1 + g(x_M))}(1 + 2g(x_M)x_i), \quad i = 1, \cdots, n \\ & g(x_M) = \sum_{x_i \in x_M} (x_i - 0.5) ^ 2 \\ & \min \\ & f_1(x) = (1 + g(x_M)) \cos(\theta_i \pi / 2) \cdots \cos(\theta_{M-2} \pi /2) \cos(\theta_{M - 1} \pi /2) \\ & f_2(x) = (1 + g(x_M)) \cos(\theta_i \pi / 2) \cdots \cos(\theta_{M-2} \pi /2) \sin(\theta_{M - 1} \pi /2) \\ & f_3(x) = (1 + g(x_M)) \cos(\theta_i \pi / 2) \cdots \sin(\theta_{M-2} \pi /2) \\ & \vdots \\ & f_M(x) = (1 + g(x_M)) \sin(\theta_1 \pi /2) \\ & \text{subject to} \\ & x_i \in [0, 1], \quad \forall i = 1, \cdots, n \end{aligned} $$

Example

if __name__ == '__main__':
    main(100, 300, np.array([0] * 12), np.array([1] * 12))

Output: