NSGA3 evaluates the same point multiple times

[mschytt]

Hello👋

After its first iteration, NSGA3 seems to evaluate the objective functions at the same place approximately N/2 times.

Consider the following MWE:

using Metaheuristics

function objective(x)
    @info x
    return [sum((x .- 0.5).^2), sum((x .+ 0.5).^2)], [0.0], [0.0]
end

n = 2
N = 10
bounds = boxconstraints(lb = -ones(n), ub = ones(n))
options = Options(f_calls_limit=30, seed = 1337, verbose = true)
alg = NSGA3(N=N, options=options)

res = optimize(objective, bounds, alg)

which prints

Algorithm Parameters
====================
  NSGA3(N=10, η_cr=20.0, p_cr=0.9, η_m=20.0, p_m=-1.0, partitions=12)

Optimization Result
===================
  Empty status.


[ Info: [-0.1846656815945078, 0.2207039622817888]
[ Info: [-0.6617257513975063, 0.5195810051063896]
[ Info: [-0.8600008519021676, -0.4525735697266313]
[ Info: [0.6619126923119993, -0.8102844592899499]
[ Info: [0.34437628136171505, -0.9199862534059393]
[ Info: [0.4682413588709464, -0.7137176659081459]
[ Info: [0.6520704859020932, 0.614884883865771]
[ Info: [0.9116517810532121, -0.08297745716276861]
[ Info: [-0.6813744510917941, -0.17653930805284945]
[ Info: [0.669531010267163, -0.28043736764844707]
+-----------+------------+------------+------------+------------+
| Iteration | Num. Evals |     NDS    |  Mean CVio |    Time    |
+-----------+------------+------------+------------+------------+
|         1 |         10 |       5/10 | 0.0000e+00 |   0.0005 s | 
[ Info: [0.6706522261009393, -0.6646945997629945]
[ Info: [0.9544391771955858, -0.8785267643421679]
[ Info: [-0.2086137305927499, 0.2207039622817888]
[ Info: [-0.8631268073141017, -0.45866738194687895]
[ Info: [0.6749481247627177, -0.8251998363497399]
[ Info: [-0.675059249086544, 0.6677026560781374]
[ Info: [0.0, 0.0]
[ Info: [0.0, 0.0]
[ Info: [0.0, 0.0]
[ Info: [0.0, 0.0]
|         2 |         20 |       7/10 | 0.0000e+00 |   0.0009 s | 
[ Info: [-0.1445567175792214, 0.26853208083242375]
[ Info: [-0.8599313117016076, -0.45886403320924973]
[ Info: [0.5925739891731482, 0.6017591988536004]
[ Info: [-0.02052696868519399, -0.08142545469223275]
[ Info: [-0.5821146955091046, -0.19470510394965335]
[ Info: [-0.05076294939677822, 0.018196310337433505]
[ Info: [0.0, 0.0]
[ Info: [0.0, 0.0]
[ Info: [0.0, 0.0]
[ Info: [0.0, 0.0]
|         3 |         30 |      10/10 | 0.0000e+00 |   0.0013 s | 
Optimization Result
===================
  Iteration:       3
  Non-dominated:   10 / 10
  Function calls:  30
  Feasibles:       10 / 10 in final population
  Total time:      0.0013 s
  Stop reason:     Maximum objective function calls exceeded.