genetic algorithm - Fitness Sharing in multi objective optimization -


i'm writing genetic algorithm uses fitness sharing in tournament selection. in relevant literature found (sareni example) mentioned solution's own fitness (fi) should divided sum of niche distances (mi).

what don't understand is, optimizing multiple objectives each solution has more 1 fitness. 'fitness' fi? should see multiplication of fitness's ?

for example, in code i'm writing (processing):

float sharedfitnessa = (a.f2*a.f3) / nichecounta; 

thanks

n

for multi objective optimization goal of fitness sharing (to distribute population on number of different peaks in search space each peak receiving fraction of population in proportion height of peak) pursued in different manner.

when 2 candidates either both dominated or both non-dominated (so it's they're in same equivalence class) niche count mi used choose "best fit" candidate.

e.g.

equivalence class sharing

(here maximizing along x-axis , minimizing on y-axis)

candidates aren't dominated comparison set. pareto point of view neither preferred. using mi choose candidate2 (smallest niche count , least number of individuals in niche).

this called equivalence class sharing , isn't based on fitness degradation (i.e. fi / mi), anyway maintains diversity along front.

for further details take @ multiobjective optimization using niched pareto genetic algorithm jeffrey horn , nicholas nafpliotis (it contains implementation details).


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