NSGA-II: Why some solution variables don't change over many iterations? #528

dinohsu1019 · 2023-12-15T07:28:11Z

dinohsu1019
Dec 15, 2023

I am running a discrete problem with 3 objectives and 12 solution varables with NSGA-II algorithm.

The best solution this time is: opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4])

But I know there's a better solution from earilyer execution: opt_F=array([-0.52725378, -1.8748386 , -3.29617812]) opt_X=array([1, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 0])

Here are part of the code:

# Hyperparameters
N_VAR = 12
N_OBJ = 3
N_IEQ_CONSTR = 0
N_EQ_CONSTR = 0
XL = np.array([0,0,0,0,0,0,1,0,0,0,0,0])  # Lower bounds for variables
XU = np.array([1,1,1,1,1,3,6,5,5,5,5,5])  # Upper bounds for variables
POP_SIZE = 60
# POP_SIZE = 100
N_OFFSPRINGS = 30
# N_OFFSPRINGS = 50
FTOL = 0.00001
PERIOD = 20
N_MAX_GEN = 100
N_MAX_EVALS = 5000
# SBX_PROB = 1.0
# SBX_ETA = 3.0
# PM_PROB = 1.0
# PM_ETA = 3.0
ELIMINATE_DUPLICATES = True

# NSGA-II algorithm setup
algorithm = NSGA2(
    pop_size = POP_SIZE,
    n_offsprings = N_OFFSPRINGS,
    sampling=IntegerRandomSampling(),
    crossover=SBX(repair=RoundingRepair()),
    mutation=PM(repair=RoundingRepair()),
    eliminate_duplicates = ELIMINATE_DUPLICATES
)

termination = DefaultMultiObjectiveTermination(
    # xtol = 0,
    # cvtol = 0,
    ftol = FTOL,
    period = PERIOD,
    n_max_gen = N_MAX_GEN,
    n_max_evals = N_MAX_EVALS
)

The strange thing I see is during iteration 26 to 46 there are no change in variables x1-x5 (all are 0,1,0,1,1) in any of the populations (they are all 0-1's), only the other 7 variables have variations, and unfortunately the better solution comes with x1-x5 = 1,1,1,0,1. My question is why all the crossovers and mutations do not add any variations to x1-x5 for 21 straight iterations? Does this make sense at all? Are there any mistakes with my parameters?

2023-12-15 06:40:31 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=3 N_IEQ_CONSTR=0 N_EQ_CONSTR=0
POP_SIZE=100 N_OFFSPRINGS=50 FTOL=1e-05 PERIOD=20 N_MAX_GEN=100 N_MAX_EVALS=5000
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 06:40:32 download and prepare data started.
2023-12-15 06:40:48 download and prepare data finished.
n_gen=1 n_eval=100 opt_F=array([-0.26832001, -1.16359147, -1.87592461]) opt_X=array([0, 1, 0, 1, 1, 2, 1, 3, 1, 5, 5, 3]) opt_index=1 hypervol=0.0
n_gen=2 n_eval=150 opt_F=array([-0.31331382, -1.28976581, -2.08948021]) opt_X=array([0, 1, 0, 1, 1, 2, 1, 3, 0, 4, 5, 2]) opt_index=1 hypervol=0.0
n_gen=3 n_eval=200 opt_F=array([-0.31331382, -1.28976581, -2.08948021]) opt_X=array([0, 1, 0, 1, 1, 2, 1, 3, 0, 4, 5, 2]) opt_index=1 hypervol=0.0
n_gen=4 n_eval=250 opt_F=array([-0.33689316, -1.69157224, -2.58681223]) opt_X=array([0, 1, 0, 1, 1, 2, 4, 4, 3, 5, 0, 2]) opt_index=1 hypervol=0.0
n_gen=5 n_eval=300 opt_F=array([-0.34177646, -1.87845937, -2.86711499]) opt_X=array([0, 1, 0, 1, 1, 0, 4, 4, 3, 4, 0, 2]) opt_index=0 hypervol=0.0
n_gen=6 n_eval=350 opt_F=array([-0.36776235, -1.46315355, -2.34168857]) opt_X=array([1, 0, 0, 1, 1, 2, 2, 4, 0, 3, 0, 3]) opt_index=2 hypervol=0.0
n_gen=7 n_eval=400 opt_F=array([-0.36776235, -1.46315355, -2.34168857]) opt_X=array([1, 0, 0, 1, 1, 2, 2, 4, 0, 3, 0, 3]) opt_index=2 hypervol=0.0
n_gen=8 n_eval=450 opt_F=array([-0.37250788, -1.49696886, -2.34331391]) opt_X=array([0, 0, 0, 1, 1, 1, 2, 4, 0, 4, 0, 3]) opt_index=2 hypervol=0.0
n_gen=9 n_eval=500 opt_F=array([-0.37250788, -1.49696886, -2.34331391]) opt_X=array([0, 0, 0, 1, 1, 1, 2, 4, 0, 4, 0, 3]) opt_index=1 hypervol=0.0
n_gen=10 n_eval=550 opt_F=array([-0.41163291, -1.53267767, -2.51721255]) opt_X=array([0, 1, 0, 1, 1, 2, 1, 4, 0, 4, 0, 2]) opt_index=3 hypervol=0.0
n_gen=11 n_eval=600 opt_F=array([-0.41163291, -1.53267767, -2.51721255]) opt_X=array([0, 1, 0, 1, 1, 2, 1, 4, 0, 4, 0, 2]) opt_index=2 hypervol=0.0
n_gen=12 n_eval=650 opt_F=array([-0.41163291, -1.53267767, -2.51721255]) opt_X=array([0, 1, 0, 1, 1, 2, 1, 4, 0, 4, 0, 2]) opt_index=0 hypervol=0.0
n_gen=13 n_eval=700 opt_F=array([-0.41637168, -1.94682486, -3.00992466]) opt_X=array([0, 1, 0, 1, 1, 0, 3, 4, 0, 0, 0, 0]) opt_index=1 hypervol=0.0
n_gen=14 n_eval=750 opt_F=array([-0.41637168, -1.94682486, -3.00992466]) opt_X=array([0, 1, 0, 1, 1, 0, 3, 4, 0, 0, 0, 0]) opt_index=1 hypervol=0.0
n_gen=15 n_eval=800 opt_F=array([-0.42083945, -1.60017311, -2.65154339]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 0, 0, 4]) opt_index=3 hypervol=0.0
n_gen=16 n_eval=850 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=17 n_eval=900 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=18 n_eval=950 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=19 n_eval=1000 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=20 n_eval=1050 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=21 n_eval=1100 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=22 n_eval=1150 opt_F=array([-0.4335514 , -1.70383116, -2.83360958]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 4, 0, 4]) opt_index=3 hypervol=0.0
n_gen=23 n_eval=1200 opt_F=array([-0.44005371, -1.71019984, -2.85228078]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 2]) opt_index=2 hypervol=0.0
n_gen=24 n_eval=1250 opt_F=array([-0.44005371, -1.71019984, -2.85228078]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 2]) opt_index=2 hypervol=0.0
n_gen=25 n_eval=1300 opt_F=array([-0.44005371, -1.71019984, -2.85228078]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 2]) opt_index=2 hypervol=0.0
n_gen=26 n_eval=1350 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=27 n_eval=1400 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=28 n_eval=1450 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=29 n_eval=1500 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=30 n_eval=1550 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=31 n_eval=1600 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=32 n_eval=1650 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=33 n_eval=1700 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=34 n_eval=1750 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=35 n_eval=1800 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=36 n_eval=1850 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=37 n_eval=1900 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=38 n_eval=1950 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=39 n_eval=2000 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=40 n_eval=2050 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=41 n_eval=2100 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=42 n_eval=2150 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=43 n_eval=2200 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=44 n_eval=2250 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=45 n_eval=2300 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0
n_gen=46 n_eval=2350 opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8 hypervol=0.0

2023-12-15 11:41:57 search finished.
n_gen=46 n_eval=2350 exec_time=18068.81 secs.
opt_F=array([-0.44153224, -1.71889729, -2.86858502]) opt_X=array([0, 1, 0, 1, 1, 0, 1, 4, 0, 5, 0, 4]) opt_index=8
annual_return=0.442 annual_sharpe=1.719 mdd=-0.299 annual_sortino=2.869 annual_return/abs(mdd)=1.474
tneagle_ratio=4.229 win_ratio=0.56 calmar_ratio=1.640 cagr=0.491 n_trades=519 n_trades_per_year=54
==========================================================
n_gen  |  n_eval  | n_nds  |      eps      |   indicator  
==========================================================
     1 |      100 |      2 |             - |             -
     2 |      150 |      2 |  0.9428204150 |         ideal
     3 |      200 |      4 |  0.9561809900 |         ideal
     4 |      250 |      2 |  1.7028406136 |         ideal
     5 |      300 |      1 |  0.1183295487 |         ideal
     6 |      350 |      3 |  0.5676020335 |         ideal
     7 |      400 |      4 |  0.1518478191 |             f
     8 |      450 |      3 |  0.1659256047 |         ideal
     9 |      500 |      3 |  0.0571136176 |         ideal
    10 |      550 |      4 |  0.5777007831 |         ideal
    11 |      600 |      8 |  0.0654974473 |         ideal
    12 |      650 |      3 |  0.1807352163 |         ideal
    13 |      700 |      2 |  0.0971341278 |         ideal
    14 |      750 |      2 |  0.000000E+00 |             f
    15 |      800 |      5 |  0.4048075295 |         ideal
    16 |      850 |      7 |  0.5352690079 |         ideal
    17 |      900 |     11 |  0.3311860321 |         ideal
    18 |      950 |     13 |  0.000000E+00 |             f
    19 |     1000 |     15 |  0.000000E+00 |             f
    20 |     1050 |     16 |  0.000000E+00 |             f
    21 |     1100 |     11 |  0.0485869744 |         ideal
    22 |     1150 |     12 |  0.000000E+00 |             f
    23 |     1200 |      3 |  0.1173827498 |         ideal
    24 |     1250 |      6 |  0.000000E+00 |             f
    25 |     1300 |      9 |  0.2656327107 |         ideal
    26 |     1350 |     11 |  0.0248383551 |         ideal
    27 |     1400 |     14 |  0.000000E+00 |             f
    28 |     1450 |     16 |  0.000000E+00 |             f
    29 |     1500 |     16 |  0.000000E+00 |             f
    30 |     1550 |     16 |  0.000000E+00 |             f
    31 |     1600 |     16 |  0.000000E+00 |             f
    32 |     1650 |     16 |  0.000000E+00 |             f
    33 |     1700 |     16 |  0.000000E+00 |             f
    34 |     1750 |     16 |  0.000000E+00 |             f
    35 |     1800 |     16 |  0.000000E+00 |             f
    36 |     1850 |     16 |  0.000000E+00 |             f
    37 |     1900 |     16 |  0.000000E+00 |             f
    38 |     1950 |     16 |  0.000000E+00 |             f
    39 |     2000 |     16 |  0.000000E+00 |             f
    40 |     2050 |     16 |  0.000000E+00 |             f
    41 |     2100 |     16 |  0.000000E+00 |             f
    42 |     2150 |     16 |  0.000000E+00 |             f
    43 |     2200 |     16 |  0.000000E+00 |             f
    44 |     2250 |     17 |  0.000000E+00 |             f
    45 |     2300 |     17 |  0.000000E+00 |             f
    46 |     2350 |     18 |  0.000000E+00 |             f

Answered by blankjul

Dec 17, 2023

Keep in mind that evolutionary algorithms are probabilistic algorithms. Not in every run the same solution will be found. In some runs, you might get stuck in a local optima and when the diversity in the population is lost it will be hard to get out of it.

For some applications, implementing a restart strategy might make sense too!

View full answer

blankjul · 2023-12-17T20:48:51Z

blankjul
Dec 17, 2023
Maintainer

Keep in mind that evolutionary algorithms are probabilistic algorithms. Not in every run the same solution will be found. In some runs, you might get stuck in a local optima and when the diversity in the population is lost it will be hard to get out of it.

For some applications, implementing a restart strategy might make sense too!

2 replies

dinohsu1019 Dec 18, 2023
Author

I have asked ChatGPT 3.5 about "restart strategy", there are options of adaptive or periodic resetting of populations and changes of parameters, and this is a topic that we can come back on later.
As an update, after I changed the probabilities and eta's of SBX and PM to 1.0 and 3.0, the NSGA-II coverges faster with the better objectives, and I am testing more solution varialbes (30-50) and see if it still works well.
Thanks again.

blankjul Dec 18, 2023
Maintainer

Yes, you can play with all parameters to fine-tune them for your problem. Basically you are doing hyper-parameter optimization. You can also be more systemetic and use algorithms for this.

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NSGA-II: Why some solution variables don't change over many iterations? #528

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NSGA-II: Why some solution variables don't change over many iterations? #528

dinohsu1019 Dec 15, 2023

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blankjul Dec 17, 2023 Maintainer

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