Xavier-MaYiMing / IBEA

Indicator-based evolutionary algorithm (IBEA) is a classic multi-objective evolutionary algorithm (MOEA).

IBEA: Indicator-based evolutionary algorithm

Reference: Zitzler E, Künzli S. Indicator-based selection in multiobjective search[C]//International Conference on Parallel Problem Solving from Nature. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004: 832-842.

IBEA is a classic multi-objective evolutionary algorithm (MOEA).

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 = 20)
eta_m	Perturbance factor distribution index (default = 20)
nvar	The dimension of decision space
pop	Population
objs	Objectives
off	Offspring
off_objs	The objectives of offspring
pf	Pareto front

Test problem: DTLZ2

$$ \begin{aligned} & k = nvar - nobj + 1, \text{ the last $k$ variables is represented as $x_M$} \\ & g(x_M) = \sum_{x_i \in x_M}(x_i - 0.5)^2 \\ & \min \\ & f_1(x) = (1 + g(x_M)) \cos{\frac{x_1 \pi}{2}} \cdots \cos{\frac{x_{M - 2} \pi}{2}} \cos{\frac{x_{M - 1} \pi}{2}} \\ & f_2(x) = (1 + g(x_M)) \cos{\frac{x_1 \pi}{2}} \cdots \cos{\frac{x_{M - 2} \pi}{2}} \sin{\frac{x_{M - 1} \pi}{2}} \\ & f_3(x) = (1 + g(x_M)) \cos{\frac{x_1 \pi}{2}} \cdots \sin{\frac{x_{M - 2} \pi}{2}} \\ & \vdots \\ & f_M(x) = (1 + g(x_M)) \sin(\frac{x_1 \pi}{2}) \\ & \text{subject to} \\ & x_i \in [0, 1], \quad \forall i = 1, \cdots, n \end{aligned} $$

Example

if __name__ == '__main__':
    main(100, 150, np.array([0] * 7), np.array([1] * 7))

Output: