Termination with number of iterations with no change in optimal solutions defined by a custom optimal function #529

dinohsu1019 · 2023-12-15T12:50:08Z

dinohsu1019
Dec 15, 2023

Hi Julian,

The following is an example of my NSGA-II execution, where we can see why I need a new approach of termination. I have defined a ftol of 0.0001 with period of 10, but it takes 36 iterations (from n_gen 22 to 47) with the same optimal solution before it terminates. The optimal solution of an iteration is a custom optimal function taking the non-dominated solutions and calcuate a value with the highest (or lowest) as the optimal solution. To fix this problem, I suggest to add a termination approach with number of iterations with no change in optimal solutions defined by a custom optimal function (highest or lowest as the optimal one) Thanks in advance.

2023-12-15 18:09:50 search started.
computer_name='DINONB2023' nb_fname='search_0002.小資族'
Objective variables: (4), to minimize
f1: annual_return, maximize => -annual_return
f2: annual_sharpe, maximize => -annual_sharpe
f3: annual_sortino, maximize => -anual_sortino
f4: annual_calmar, maximize => -annual_calmar
Solution variables: (12)
x1: 0-1 (binary): condition1 = (市值 < 1e10)
x2: 0-1 (binary): condition2 = 自由現金流 > 0
x3: 0-1 (binary): condition3 = 股東權益報酬率 > 0
x4: 0-1 (binary): condition4 = 營業利益成長率 > 0
x5: 0-1 (binary): condition5 = 市值營收比 < 2
x6: 0-3, 0=無, 1=100000, 2=200000, 3=500000, condition6 = vol_ma10 > (value)
x7: 1-6, 選股數量 1=5, 2=10, 3=15, 4=20, 5=25, 6=30
x8: 0-5: 選股數量依據, 0=無, 1=rsv5 (is_largest), 2=rsv10 (is_largest), 
    3=rsv20 (is_largest), 4=rsv60 (is_largest), 5=peg (is_smallest)
x9: 0-5, stop_loss 0=None, 1=0.08, 2=0.1, 3=0.12, 4=0.15, 5=0.20
x10: 0-5, take_profit 0=None, 1=0.1, 2=0.2, 3=0.3, 4=0.4, 5=0.5 
x11: 0-5, trail_stop, 0=None, 1=0.08, 2=0.1, 3=0.12, 4=0.15, 5=0.20 
x12: 0-5, position_limit, 0=1, 1=1/2, 2=1/3, 3=1/4, 4=1/5, 5=1/10
N_VAR=12 N_OBJ=4 N_IEQ_CONSTR=0 N_EQ_CONSTR=0 SBX_PROB=1.0 SBX_ETA=3.0 PM_PROB=1.0 PM_ETA=3.0
POP_SIZE=60 N_OFFSPRINGS=30 FTOL=0.0001 PERIOD=10 N_MAX_GEN=50 N_MAX_EVALS=3000 ELIMINATE_DUPLICATES=False
XL=array([0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]) XU=array([1, 1, 1, 1, 1, 3, 6, 5, 5, 5, 5, 5])
2023-12-15 18:09:53 download and prepare data started.
2023-12-15 18:10:09 download and prepare data finished.
n_gen=1 n_eval=60 opt_F=array([-0.29367264, -1.327737  , -2.22197711, -0.89303128]) opt_X=array([0, 1, 0, 0, 1, 0, 1, 4, 0, 5, 4, 0]) opt_index=1 hypervol=0.0
n_gen=2 n_eval=90 opt_F=array([-0.30347474, -1.45741012, -2.19618437, -1.13566507]) opt_X=array([1, 1, 0, 1, 1, 2, 4, 3, 3, 0, 0, 5]) opt_index=1 hypervol=0.0
n_gen=3 n_eval=120 opt_F=array([-0.32345957, -1.4943235 , -2.29350228, -1.01661837]) opt_X=array([1, 0, 0, 0, 1, 1, 4, 3, 0, 5, 0, 3]) opt_index=1 hypervol=0.0
n_gen=4 n_eval=150 opt_F=array([-0.3866844 , -1.67943024, -2.98000541, -1.32724968]) opt_X=array([1, 1, 0, 0, 1, 0, 1, 4, 0, 5, 4, 0]) opt_index=0 hypervol=0.0
n_gen=5 n_eval=180 opt_F=array([-0.3866844 , -1.67943024, -2.98000541, -1.32724968]) opt_X=array([1, 1, 0, 0, 1, 0, 1, 4, 0, 5, 4, 0]) opt_index=0 hypervol=0.0
n_gen=6 n_eval=210 opt_F=array([-0.3866844 , -1.67943024, -2.98000541, -1.32724968]) opt_X=array([1, 1, 0, 0, 1, 0, 1, 4, 0, 5, 4, 0]) opt_index=0 hypervol=0.0
n_gen=7 n_eval=240 opt_F=array([-0.42176911, -1.92894911, -3.33300419, -2.09232507]) opt_X=array([1, 1, 1, 1, 1, 0, 1, 3, 0, 2, 0, 2]) opt_index=1 hypervol=0.0
n_gen=8 n_eval=270 opt_F=array([-0.42176911, -1.92894911, -3.33300419, -2.09232507]) opt_X=array([1, 1, 1, 1, 1, 0, 1, 3, 0, 2, 0, 2]) opt_index=2 hypervol=0.0
n_gen=9 n_eval=300 opt_F=array([-0.42176911, -1.92894911, -3.33300419, -2.09232507]) opt_X=array([1, 1, 1, 1, 1, 0, 1, 3, 0, 2, 0, 2]) opt_index=3 hypervol=0.0
n_gen=10 n_eval=330 opt_F=array([-0.46852203, -1.73466163, -3.05369106, -1.47482932]) opt_X=array([1, 1, 0, 0, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=9 hypervol=0.0
n_gen=11 n_eval=360 opt_F=array([-0.46852203, -1.73466163, -3.05369106, -1.47482932]) opt_X=array([1, 1, 0, 0, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=9 hypervol=0.0
n_gen=12 n_eval=390 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=13 hypervol=0.0
n_gen=13 n_eval=420 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=12 hypervol=0.0
n_gen=14 n_eval=450 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=32 hypervol=0.0
n_gen=15 n_eval=480 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=40 hypervol=0.0
n_gen=16 n_eval=510 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=26 hypervol=0.0
n_gen=17 n_eval=540 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=41 hypervol=0.0
n_gen=18 n_eval=570 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=2 hypervol=0.0
n_gen=19 n_eval=600 opt_F=array([-0.51890862, -1.77028758, -3.10377309, -1.69585051]) opt_X=array([1, 1, 0, 0, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=3 hypervol=0.0
n_gen=20 n_eval=630 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=49 hypervol=0.0
n_gen=21 n_eval=660 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=2 hypervol=0.0
n_gen=22 n_eval=690 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=0 hypervol=0.0
n_gen=23 n_eval=720 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=2 hypervol=0.0
n_gen=24 n_eval=750 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=2 hypervol=0.0
n_gen=25 n_eval=780 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=1 hypervol=0.0
n_gen=26 n_eval=810 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=3 hypervol=0.0
n_gen=27 n_eval=840 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=36 hypervol=0.0
n_gen=28 n_eval=870 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=0 hypervol=0.0
n_gen=29 n_eval=900 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=0 hypervol=0.0
n_gen=30 n_eval=930 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=58 hypervol=0.0
n_gen=31 n_eval=960 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=29 hypervol=0.0
n_gen=32 n_eval=990 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=4 hypervol=0.0
n_gen=33 n_eval=1020 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=45 hypervol=0.0
n_gen=34 n_eval=1050 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=6 hypervol=0.0
n_gen=35 n_eval=1080 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=1 hypervol=0.0
n_gen=36 n_eval=1110 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=50 hypervol=0.0
n_gen=37 n_eval=1140 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=29 hypervol=0.0
n_gen=38 n_eval=1170 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=5 hypervol=0.0
n_gen=39 n_eval=1200 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=3 hypervol=0.0
n_gen=40 n_eval=1230 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=59 hypervol=0.0
n_gen=41 n_eval=1260 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=1 hypervol=0.0
n_gen=42 n_eval=1290 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=1 hypervol=0.0
n_gen=43 n_eval=1320 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=57 hypervol=0.0
n_gen=44 n_eval=1350 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=56 hypervol=0.0
n_gen=45 n_eval=1380 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=1 hypervol=0.0
n_gen=46 n_eval=1410 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=2 hypervol=0.0
n_gen=47 n_eval=1440 opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=3 hypervol=0.0

2023-12-15 20:38:44 search finished.
n_gen=47 n_eval=1440 exec_time=8914.59 secs.
opt_F=array([-0.51894508, -1.83975937, -3.17334784, -2.15496542]) opt_X=array([1, 1, 1, 1, 1, 2, 1, 4, 0, 5, 0, 4]) opt_index=3
annual_return=0.519 annual_sharpe=1.840 mdd=-0.277 annual_sortino=3.173 annual_return/abs(mdd)=1.872
tneagle_ratio=5.940 win_ratio=0.55 calmar_ratio=2.155 cagr=0.597 n_trades=479 n_trades_per_year=50

==========================================================
n_gen  |  n_eval  | n_nds  |      eps      |   indicator  
==========================================================
     1 |       60 |      2 |             - |             -
     2 |       90 |      2 |  1.0000000000 |         ideal
     3 |      120 |      2 |  1.0000000000 |         ideal
     4 |      150 |      1 |  0.6865031215 |         ideal
     5 |      180 |      4 |  1.0000000000 |         ideal
     6 |      210 |      2 |  1.0000000000 |         ideal
     7 |      240 |      2 |  1.0000000000 |         ideal
     8 |      270 |      3 |  0.000000E+00 |             f
     9 |      300 |      5 |  0.000000E+00 |             f
    10 |      330 |     10 |  0.3496830797 |         ideal
    11 |      360 |     14 |  0.0660458320 |             f
    12 |      390 |     23 |  0.2737100802 |         ideal
    13 |      420 |     29 |  0.1418642450 |         nadir
    14 |      450 |     39 |  0.000000E+00 |             f
    15 |      480 |     41 |  0.1330075528 |         ideal
    16 |      510 |     48 |  0.0859158054 |         ideal
    17 |      540 |     60 |  0.0091757835 |             f
    18 |      570 |     41 |  0.4475885853 |         nadir
    19 |      600 |     49 |  0.0193538661 |             f
    20 |      630 |     51 |  0.0251633301 |         ideal
    21 |      660 |     60 |  0.0281710442 |         ideal
    22 |      690 |     60 |  0.2025591851 |         ideal
    23 |      720 |     60 |  0.0477965905 |         ideal
    24 |      750 |     60 |  0.000000E+00 |             f
    25 |      780 |     60 |  0.000000E+00 |             f
    26 |      810 |     60 |  0.000000E+00 |             f
    27 |      840 |     60 |  0.000000E+00 |             f
    28 |      870 |     60 |  0.000000E+00 |             f
    29 |      900 |     60 |  0.000000E+00 |             f
    30 |      930 |     60 |  0.0072192396 |         ideal
    31 |      960 |     60 |  0.000000E+00 |             f
    32 |      990 |     60 |  0.0070917429 |             f
    33 |     1020 |     60 |  0.000000E+00 |             f
    34 |     1050 |     60 |  0.000000E+00 |             f
    35 |     1080 |     60 |  0.0003357997 |             f
    36 |     1110 |     60 |  0.0003357997 |             f
    37 |     1140 |     60 |  0.0003357997 |             f
    38 |     1170 |     60 |  0.0139423480 |         ideal
    39 |     1200 |     60 |  0.000000E+00 |             f
    40 |     1230 |     60 |  0.0207953887 |         ideal
    41 |     1260 |     60 |  0.2278720282 |         nadir
    42 |     1290 |     60 |  0.000000E+00 |             f
    43 |     1320 |     60 |  0.000000E+00 |             f
    44 |     1350 |     60 |  0.000000E+00 |             f
    45 |     1380 |     60 |  0.000000E+00 |             f
    46 |     1410 |     60 |  0.000000E+00 |             f
    47 |     1440 |     60 |  0.0025609098 |             f

blankjul · 2023-12-17T20:52:07Z

blankjul
Dec 17, 2023
Maintainer

This seems to be exactly what you have already asked in #527. Unfortunatly, I will not be able to review all your code solving an application problem because of my own time limitation.

I hope implementing a custom termination criterion will resolve this issue though!

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Termination with number of iterations with no change in optimal solutions defined by a custom optimal function #529

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Termination with number of iterations with no change in optimal solutions defined by a custom optimal function #529

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dinohsu1019 Dec 15, 2023

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blankjul Dec 17, 2023 Maintainer

dinohsu1019
Dec 15, 2023

blankjul
Dec 17, 2023
Maintainer