associate function

Association Operation in Non-Dominated Genetic Algorithms III

Function that associates each member of the population with a reference point. The function calculates the perpendicular distance of each individual from each of the reference lines. This code section corresponds to Algorithm 3 of the referenced paper.

associate_to_niches(object, utopian_epsilon = 0)
  compute_perpendicular_distance(x, y)
  compute_niche_count(n_niches, niche_of_individuals)

Arguments

• object: An object of class "nsga3".
• utopian_epsilon: The epsilon used for decrease the ideal point to get the utopian point.
• x: Individuals to calculate their niche.
• y: Reference points.
• n_niches: Number of reference points.
• niche_of_individuals: The niche count of individuals, except the last front.

Returns

Returns a list with the niche count of individuals and the distances between them.

References

J. Blank and K. Deb, "Pymoo: Multi-Objective Optimization in Python," in IEEE Access, vol. 8, pp. 89497-89509, 2020, doi: 10.1109/ACCESS.2020.2990567.

K. Deb and H. Jain, "An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints," in IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 577-601, Aug. 2014, doi: 10.1109/TEVC.2013.2281535.

Author(s)

Francisco Benitez