Assisted specificationΒΆ

Example of the estimation of several versions of the model using assisted specification algorithm. The catalog of specifications is defined in Specification of a catalog of models . All specifications are estimated. Have a look at Assisted specification for an example where the number of specifications is too high to be enumerated.

Michel Bierlaire, EPFL Sat Jun 28 2025, 19:21:26

import biogeme.biogeme_logging as blog
from biogeme.assisted import AssistedSpecification
from biogeme.multiobjectives import loglikelihood_dimension
from biogeme.results_processing import compile_estimation_results

from plot_b21multiple_models_spec import PARETO_FILE_NAME, the_biogeme

logger = blog.get_screen_logger(blog.INFO)
logger.info('Example b21multipleModels')
income_segmentation=INCOME: [{0: 'inc-zero', 1: 'inc-under50', 2: 'inc-50-100', 3: 'inc-100+', 4: 'inc-unknown'}] ref: inc-zero
Example b21multipleModels

Creation of the object capturing the assisted specification algorithm. Its constructor takes three arguments:

  • the biogeme object containing the specifications and the database,

  • an object defining the objectives to minimize. Here, we use the opposite of the log likelihood and the number of estimated parameters.

  • the name of the file where the estimated are saved, and organized into a Pareto set.

assisted_specification = AssistedSpecification(
    biogeme_object=the_biogeme,
    multi_objectives=loglikelihood_dimension,
    pareto_file_name=PARETO_FILE_NAME,
)
Biogeme parameters read from biogeme.toml.
Pareto set initialized from file with 36 elements [8 Pareto] and 0 invalid elements.

The algorithm is run.

non_dominated_models = assisted_specification.run()
Biogeme parameters read from biogeme.toml.
Model with 4 unknown parameters [max: 50]
*** Estimate b07everything_000125
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0           -0.92           -0.67           -0.88           -0.49      5.4e+03      0.041       10      1.1   ++
    1           -0.73            -1.2              -1           -0.18      5.3e+03     0.0072    1e+02      1.1   ++
    2            -0.7            -1.3            -1.1           -0.16      5.3e+03    0.00018    1e+03        1   ++
    3            -0.7            -1.3            -1.1           -0.16      5.3e+03    1.1e-07    1e+03        1   ++
default_specification=asc:no_seg;b_cost:no_seg;train_tt:linear
We consider all possible combinations of the catalogs.
Model 0/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000126
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc         asc_car     Function    Relgrad   Radius      Rho
    0           -0.75              -1           -0.36          -0.045           -0.13           -0.14          -0.023           -0.29      5.5e+03      0.035       10        1   ++
    1           -0.54            -1.6            -1.4           -0.17            0.37             0.6            0.73          0.0049      5.3e+03     0.0064    1e+02      1.1   ++
    2           -0.51            -1.7            -1.5           -0.64            0.28            0.63            0.75           0.011      5.3e+03    0.00037    1e+03        1   ++
    3           -0.51            -1.7            -1.5           -0.64            0.28            0.63            0.75           0.011      5.3e+03    2.2e-06    1e+03        1   ++
Model 1/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000127
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time      b_cost_ref  b_cost_diff_GA         asc_car     Function    Relgrad   Radius      Rho
    0           -0.74              -1           -0.39          -0.095            -0.3      5.5e+03      0.043       10        1   ++
    1           -0.52            -1.6           -0.88           -0.53           0.037      5.3e+03     0.0053    1e+02      1.1   ++
    2           -0.48            -1.7           -0.95           -0.97           0.061      5.3e+03    0.00033    1e+03      1.1   ++
    3           -0.48            -1.7           -0.95            -1.1           0.063      5.3e+03    1.1e-05    1e+04        1   ++
    4           -0.48            -1.7           -0.95            -1.1           0.063      5.3e+03    1.7e-08    1e+04        1   ++
Model 2/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000128
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.78            0.18              -1           -0.34          -0.042           -0.13           -0.14          -0.021           -0.27           -0.11      5.4e+03      0.036       10        1   ++
    1           -0.98             2.4            -1.6            -1.5          -0.066            0.41            0.65            0.77          -0.072          -0.068        5e+03      0.028    1e+02     0.94   ++
    2            -1.1             2.1            -1.7            -1.6           -0.76            0.28            0.66            0.78           -0.07            -0.2        5e+03    0.00071    1e+03        1   ++
    3            -1.1             2.1            -1.7            -1.6           -0.76            0.28            0.66            0.78           -0.07            -0.2        5e+03    5.1e-06    1e+03        1   ++
Model 3/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000129
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time     lambda_time          b_cost     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.43           -0.62           -0.89             1.8              -1           -0.45           -0.24      5.6e+03      0.083        1     0.72    +
    1            0.39            -1.5            -1.6            0.85              -1           -0.65            0.58      5.2e+03      0.028       10     0.94   ++
    2            0.48            -1.3            -1.9            0.42            -1.1           -0.21             0.3      5.1e+03     0.0096    1e+02     0.95   ++
    3            0.36            -1.3            -1.7            0.45            -1.1           -0.29             0.3      5.1e+03     0.0004    1e+03     0.98   ++
    4            0.36            -1.3            -1.7            0.45            -1.1           -0.29             0.3      5.1e+03    6.7e-07    1e+03        1   ++
Model 4/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000130
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.37           -0.59              -1           -0.89           -0.33           -0.13      5.3e+03      0.036       10        1   ++
    1             0.4            -1.3            -1.6              -1           -0.22            0.22      5.2e+03     0.0091    1e+02        1   ++
    2             0.4            -1.3            -1.7              -1           -0.24            0.25      5.2e+03    0.00022    1e+03        1   ++
    3             0.4            -1.3            -1.7              -1           -0.24            0.25      5.2e+03    2.4e-07    1e+03        1   ++
Model 5/36
Biogeme parameters read from biogeme.toml.
Model with 13 unknown parameters [max: 50]
*** Estimate b07everything_000131
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time     lambda_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.48           -0.69            0.63           -0.93               2              -1           -0.11           -0.35           -0.42           -0.06           -0.43           -0.22           -0.25      5.6e+03        0.1        1     0.69    +
    1           -0.46            -1.1             1.6           -0.92             1.5            -0.7           -0.23           -0.38            0.05         -0.0044           -0.35            0.26           -0.33      5.1e+03      0.014       10      1.1   ++
    2           -0.46            -1.1             1.6           -0.92             1.5            -0.7           -0.23           -0.38            0.05         -0.0044           -0.35            0.26           -0.33      5.1e+03      0.014        5 -1.4e+03    -
    3           -0.46            -1.1             1.6           -0.92             1.5            -0.7           -0.23           -0.38            0.05         -0.0044           -0.35            0.26           -0.33      5.1e+03      0.014      2.5      -23    -
    4           -0.46            -1.1             1.6           -0.92             1.5            -0.7           -0.23           -0.38            0.05         -0.0044           -0.35            0.26           -0.33      5.1e+03      0.014      1.2     -1.8    -
    5           -0.31           -0.96             2.1              -2            0.26            -1.3           -0.44           -0.44           -0.14           0.074           -0.44            0.53           -0.41      4.9e+03      0.022      1.2     0.69    +
    6           -0.26            -1.1               2            -1.7            0.31            -1.5           -0.58            0.23            0.66            0.89           -0.45            0.44           -0.36      4.9e+03     0.0046       12     0.91   ++
    7           -0.26            -1.1               2            -1.7            0.33            -1.6           -0.59            0.22            0.63            0.82           -0.45            0.45           -0.37      4.9e+03     0.0001  1.2e+02        1   ++
    8           -0.26            -1.1               2            -1.7            0.33            -1.6           -0.59            0.22            0.63            0.82           -0.45            0.45           -0.37      4.9e+03    5.2e-07  1.2e+02        1   ++
Model 6/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b07everything_000132
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.44            -0.6            0.47              -1           -0.69          -0.075           -0.25           -0.28          -0.042           -0.34           -0.16           -0.18      5.2e+03      0.036       10        1   ++
    1           -0.24           -0.98               2            -1.6            -1.5            -0.3            0.23             0.6            0.76           -0.37            0.34           -0.28      4.9e+03      0.018    1e+02        1   ++
    2           -0.25            -1.1               2            -1.7            -1.5           -0.59            0.21            0.63            0.78           -0.43            0.41           -0.34      4.9e+03     0.0011    1e+03        1   ++
    3           -0.25            -1.2             2.1            -1.7            -1.6           -0.61            0.21            0.63            0.78           -0.43            0.42           -0.34      4.9e+03      9e-06    1e+04        1   ++
    4           -0.25            -1.2             2.1            -1.7            -1.6           -0.61            0.21            0.63            0.78           -0.43            0.42           -0.34      4.9e+03    4.2e-08    1e+04        1   ++
Model 7/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000133
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time     lambda_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.73            0.39              -1             1.6           -0.73           -0.15           -0.45            -0.2      5.5e+03       0.05        1     0.83    +
    1            -1.1             1.4            -1.3            0.91            -1.1            -0.2           -0.19           -0.33      5.1e+03      0.021       10      1.1   ++
    2           -0.87               2            -1.9            0.26            -1.1             1.3           0.034            -1.1        5e+03      0.013       10     0.81    +
    3              -1               2            -1.7            0.36            -1.1               1          -0.066           -0.95        5e+03     0.0012    1e+02        1   ++
    4              -1               2            -1.7            0.38            -1.1            0.92          -0.068           -0.89        5e+03    3.3e-05    1e+03        1   ++
    5              -1               2            -1.7            0.38            -1.1            0.92          -0.068           -0.89        5e+03    8.2e-08    1e+03        1   ++
Model 8/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b07everything_000134
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time     lambda_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.44           -0.66            -0.9               2              -1           -0.11           -0.35           -0.42           -0.06           -0.43           -0.22      5.7e+03      0.095        1     0.68    +
    1            0.56            -1.4            -1.6             1.1           -0.96           -0.51           -0.49             0.3           0.066           -0.52            0.77      5.3e+03       0.02        1     0.84    +
    2            0.66            -1.2            -2.2            0.34            -1.6           -0.36            0.25            0.62            0.96           -0.14            0.38      5.1e+03      0.029        1     0.87    +
    3            0.33            -1.3            -1.7            0.42            -1.5           -0.37            0.23            0.59            0.84            -0.3            0.32      5.1e+03     0.0026       10     0.96   ++
    4            0.35            -1.3            -1.7            0.45            -1.6           -0.37            0.23            0.59            0.85            -0.3            0.32      5.1e+03    7.5e-05    1e+02     0.98   ++
    5            0.35            -1.3            -1.7            0.45            -1.6           -0.37            0.23            0.59            0.85            -0.3            0.32      5.1e+03    9.3e-08    1e+02        1   ++
Model 9/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000135
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.36           -0.78           -0.63              -1            0.12           -0.03            0.16            0.29           -0.56           0.012      5.3e+03      0.043       10      1.1   ++
    1           0.017            -1.1            -1.2            -1.4           -0.28            0.17            0.49            0.72           -0.48             0.3      5.2e+03     0.0097    1e+02      1.1   ++
    2           0.069            -1.2            -1.3            -1.5           -0.41            0.18            0.53            0.78           -0.47            0.33      5.2e+03    0.00037    1e+03        1   ++
    3           0.069            -1.2            -1.3            -1.5           -0.41            0.18            0.53            0.78           -0.47            0.33      5.2e+03    5.1e-07    1e+03        1   ++
Model 10/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000136
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc         asc_car     Function    Relgrad   Radius      Rho
    0           -0.92           -0.66              -1           0.026         -0.0026             0.2            0.21           -0.49      5.4e+03      0.041       10      1.1   ++
    1           -0.74            -1.2            -1.4           -0.53            0.22            0.52            0.69           -0.17      5.3e+03     0.0075    1e+02      1.1   ++
    2           -0.71            -1.3            -1.5           -0.66            0.24            0.56            0.75           -0.15      5.3e+03     0.0002    1e+03        1   ++
    3           -0.71            -1.3            -1.5           -0.66            0.24            0.56            0.75           -0.15      5.3e+03    1.5e-07    1e+03        1   ++
Model 11/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000137
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.76            0.19              -1           -0.36          -0.089           -0.27           -0.12      5.4e+03      0.044       10        1   ++
    1           -0.98             2.4            -1.6           -0.98            0.71           -0.08           -0.61        5e+03      0.027    1e+02     0.93   ++
    2            -1.1             2.1            -1.7            -1.1            0.92          -0.071           -0.87        5e+03    0.00067    1e+03        1   ++
    3            -1.1             2.1            -1.7            -1.1            0.92          -0.071           -0.87        5e+03      2e-06    1e+03        1   ++
Model 12/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000138
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.37           -0.59              -1           -0.89           -0.15           -0.32           -0.12      5.3e+03      0.036       10        1   ++
    1            0.41            -1.3            -1.7           -0.94           -0.88           -0.17            0.22      5.2e+03     0.0094    1e+02        1   ++
    2            0.42            -1.3            -1.7           -0.96              -1           -0.18            0.25      5.2e+03    0.00022    1e+03        1   ++
    3            0.42            -1.3            -1.7           -0.96              -1           -0.18            0.25      5.2e+03    2.3e-07    1e+03        1   ++
Model 13/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000139
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0              -1            0.85            -0.7           -0.75           -0.11           -0.31           -0.21          -0.052           -0.41           -0.23      5.2e+03      0.049       10      1.1   ++
    1            -1.2             1.9            -1.1            -1.5           -0.54            0.19            0.54            0.71           -0.28           -0.19        5e+03      0.012    1e+02      1.1   ++
    2            -1.3               2            -1.2            -1.6           -0.78            0.23            0.59            0.78           -0.26           -0.21        5e+03     0.0006    1e+03        1   ++
    3            -1.3               2            -1.2            -1.6           -0.78            0.23            0.59            0.78           -0.26           -0.21        5e+03    1.8e-06    1e+03        1   ++
Model 14/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000140
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time     lambda_time      b_cost_ref  b_cost_diff_GA         asc_car     Function    Relgrad   Radius      Rho
    0           -0.71              -1             1.7           -0.82           -0.17            -0.5      5.6e+03      0.059        1     0.77    +
    1           -0.78            -1.6            0.69            -1.3           -0.38           -0.33      5.4e+03      0.049       10        1   ++
    2           -0.44            -1.7            0.53           -0.96            -1.2           0.085      5.3e+03      0.002    1e+02     0.96   ++
    3           -0.46            -1.7            0.51              -1            -1.1            0.06      5.3e+03      1e-05    1e+03        1   ++
    4           -0.46            -1.7            0.51              -1            -1.1            0.06      5.3e+03    7.2e-10    1e+03        1   ++
Model 15/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000141
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.51            -0.8               1            -0.6           -0.88         -0.0059           -0.46           -0.15           -0.19      5.1e+03      0.045       10      1.1   ++
    1           -0.54           -0.97             1.7            -1.1            -1.1            0.93           -0.61            0.36           -0.93      4.9e+03      0.012    1e+02      1.1   ++
    2           -0.54            -1.1             1.9            -1.2            -1.1            0.89           -0.62            0.41           -0.98      4.9e+03     0.0007    1e+03        1   ++
    3           -0.54            -1.1             1.9            -1.2            -1.1            0.89           -0.62            0.41           -0.98      4.9e+03    4.4e-06    1e+03        1   ++
Model 16/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000142
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.33           -0.81           -0.63           -0.91            0.11           -0.52           -0.04      5.3e+03      0.043       10      1.1   ++
    1           0.052            -1.1            -1.2           -0.98           -0.72           -0.42            0.29      5.2e+03     0.0097    1e+02      1.1   ++
    2            0.11            -1.2            -1.3              -1              -1           -0.41            0.31      5.2e+03    0.00036    1e+03        1   ++
    3            0.11            -1.2            -1.3              -1              -1           -0.41            0.31      5.2e+03    9.1e-07    1e+03        1   ++
Model 17/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000143
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time     lambda_time          b_cost     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.73            0.39              -1             1.6           -0.73           -0.45           -0.21      5.5e+03      0.049        1     0.83    +
    1            -1.1             1.4            -1.3             0.9            -1.1            -0.2           -0.35      5.1e+03      0.022       10      1.1   ++
    2           -0.87               2            -1.9            0.26            -1.1           0.037           -0.36        5e+03      0.012       10     0.82    +
    3              -1               2            -1.7            0.36            -1.1          -0.061           -0.31        5e+03     0.0012    1e+02        1   ++
    4              -1               2            -1.7            0.38            -1.1          -0.064           -0.31        5e+03    3.1e-05    1e+03        1   ++
    5              -1               2            -1.7            0.38            -1.1          -0.064           -0.31        5e+03    3.6e-09    1e+03        1   ++
Model 18/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000144
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0              -1             0.9            -0.7           -0.93          -0.072           -0.43           -0.22      5.2e+03      0.046       10      1.1   ++
    1            -1.2             1.9            -1.1            -1.1            0.98           -0.28           -0.87      5.1e+03      0.011    1e+02      1.1   ++
    2            -1.3               2            -1.2            -1.1            0.89           -0.25           -0.87        5e+03    0.00055    1e+03        1   ++
    3            -1.3               2            -1.2            -1.1            0.89           -0.25           -0.87        5e+03    1.5e-06    1e+03        1   ++
Model 19/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000145
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time     lambda_time          b_cost     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.46           -0.64            0.57           -0.92             1.9              -1           -0.45           -0.25           -0.24      5.5e+03      0.087        1     0.73    +
    1           -0.56            -1.1             1.6              -1             1.2           -0.95           -0.47            0.12           -0.36        5e+03      0.019       10      1.2   ++
    2           -0.56            -1.1             1.6              -1             1.2           -0.95           -0.47            0.12           -0.36        5e+03      0.019      1.6      -11    -
    3           -0.56            -1.1             1.6              -1             1.2           -0.95           -0.47            0.12           -0.36        5e+03      0.019      0.8    -0.46    -
    4           -0.55            -1.2             1.9            -1.5            0.42            -1.1           -0.48             0.3            -0.4      4.9e+03      0.017        8     0.99   ++
    5           -0.21            -1.1             1.9            -1.7            0.33            -1.1           -0.42            0.41           -0.45      4.9e+03    0.00079       80     0.98   ++
    6           -0.21            -1.1             1.9            -1.7            0.33            -1.1           -0.42            0.41           -0.45      4.9e+03    3.4e-06       80        1   ++
Model 20/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000146
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time     lambda_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.43           -0.62           -0.89             1.9              -1           -0.18           -0.44           -0.23      5.6e+03      0.084        1     0.72    +
    1            0.39            -1.5            -1.6            0.86           -0.97           -0.42           -0.63            0.58      5.2e+03      0.028       10     0.94   ++
    2            0.51            -1.3            -1.9             0.4              -1              -1           -0.14             0.3      5.1e+03      0.011    1e+02     0.93   ++
    3            0.39            -1.3            -1.7            0.44              -1            -1.1           -0.23            0.31      5.1e+03    0.00049    1e+03     0.98   ++
    4            0.39            -1.3            -1.7            0.44              -1            -1.1           -0.23            0.31      5.1e+03    1.9e-06    1e+03        1   ++
Model 21/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b07everything_000147
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time     lambda_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.73            0.37              -1             1.6           -0.67          -0.082           -0.23           -0.28          -0.042           -0.43           -0.19      5.4e+03      0.039        1     0.86    +
    1            -1.1             1.4            -1.3            0.83           -0.84           -0.21           -0.37           -0.12          -0.031           -0.19           -0.32      5.1e+03      0.023       10      1.1   ++
    2           -0.93             2.1            -1.9            0.28            -1.6           -0.57            0.26            0.63            0.83          0.0088           -0.24        5e+03     0.0077    1e+02     0.91   ++
    3              -1             2.1            -1.7            0.36            -1.6           -0.78            0.28            0.67            0.84          -0.065           -0.22        5e+03    0.00067    1e+03        1   ++
    4              -1             2.1            -1.7            0.37            -1.6           -0.79            0.28            0.66            0.84          -0.068           -0.22        5e+03    9.8e-06    1e+04        1   ++
    5              -1             2.1            -1.7            0.37            -1.6           -0.79            0.28            0.66            0.84          -0.068           -0.22        5e+03    4.6e-10    1e+04        1   ++
Model 22/36
Biogeme parameters read from biogeme.toml.
Model with 4 unknown parameters [max: 50]
*** Estimate b07everything_000148
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0           -0.74              -1           -0.39            -0.3      5.5e+03      0.044       10        1   ++
    1           -0.54            -1.6           -0.93         -0.0041      5.3e+03     0.0052    1e+02      1.1   ++
    2           -0.51            -1.7              -1          0.0019      5.3e+03    0.00015    1e+03        1   ++
    3           -0.51            -1.7              -1          0.0019      5.3e+03    1.4e-07    1e+03        1   ++
Model 23/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000149
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.76            0.19              -1           -0.37           -0.27           -0.12      5.4e+03      0.044       10        1   ++
    1           -0.97             2.4            -1.6           -0.96          -0.072           -0.11        5e+03      0.027    1e+02     0.94   ++
    2              -1             2.1            -1.7            -1.1          -0.067           -0.29        5e+03    0.00066    1e+03        1   ++
    3              -1             2.1            -1.7            -1.1          -0.067           -0.29        5e+03    2.1e-06    1e+03        1   ++
Model 24/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b07everything_000150
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.51           -0.82               1           -0.59           -0.69          -0.094           -0.32           -0.15          -0.041           -0.47           -0.15           -0.21      5.1e+03      0.045       10      1.1   ++
    1           -0.57           -0.94             1.8            -1.1            -1.4           -0.37            0.15            0.51            0.71           -0.62            0.38           -0.29      4.9e+03      0.012    1e+02      1.1   ++
    2           -0.58            -1.1             1.9            -1.2            -1.5            -0.6            0.17            0.56            0.75           -0.65            0.44           -0.33      4.9e+03    0.00078    1e+03        1   ++
    3           -0.58            -1.1             1.9            -1.2            -1.5            -0.6            0.17            0.56            0.75           -0.65            0.44           -0.33      4.9e+03    4.5e-06    1e+03        1   ++
Model 25/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000151
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time      b_cost_ref  b_cost_diff_GA         asc_car     Function    Relgrad   Radius      Rho
    0           -0.92           -0.67            -0.9           0.097            -0.5      5.4e+03      0.041       10      1.1   ++
    1           -0.71            -1.2           -0.98           -0.74           -0.13      5.3e+03     0.0075    1e+02      1.1   ++
    2           -0.68            -1.3              -1              -1          -0.097      5.3e+03     0.0002    1e+03        1   ++
    3           -0.68            -1.3              -1              -1          -0.097      5.3e+03    1.2e-06    1e+03        1   ++
Model 26/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000152
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time     lambda_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0           -0.71              -1             1.7           -0.82            -0.5      5.6e+03      0.058        1     0.77    +
    1           -0.77            -1.7            0.69            -1.3           -0.35      5.4e+03      0.049       10        1   ++
    2           -0.47            -1.7            0.53              -1           0.017      5.3e+03      0.002    1e+02     0.96   ++
    3           -0.48            -1.7            0.51            -1.1         -0.0043      5.3e+03    1.3e-05    1e+03        1   ++
    4           -0.48            -1.7            0.51            -1.1         -0.0043      5.3e+03    1.8e-09    1e+03        1   ++
Model 27/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000153
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time     lambda_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc         asc_car     Function    Relgrad   Radius      Rho
    0           -0.72              -1             1.6           -0.74          -0.092           -0.26           -0.31          -0.047           -0.48      5.6e+03      0.044        1     0.81    +
    1           -0.64            -1.6            0.65           -0.91           -0.36           -0.47            0.12          -0.013           -0.22      5.3e+03      0.038       10        1   ++
    2           -0.49            -1.7            0.51            -1.5           -0.59            0.27             0.6             0.8           0.012      5.3e+03    0.00074    1e+02        1   ++
    3           -0.49            -1.7             0.5            -1.6           -0.65            0.28            0.62            0.81          0.0042      5.3e+03      7e-06    1e+03        1   ++
    4           -0.49            -1.7             0.5            -1.6           -0.65            0.28            0.62            0.81          0.0042      5.3e+03    1.3e-09    1e+03        1   ++
Model 28/36
Model 29/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000154
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.37            -0.6              -1           -0.72          -0.082           -0.27           -0.28          -0.045           -0.32           -0.13      5.3e+03      0.036       10        1   ++
    1            0.38            -1.3            -1.6            -1.4           -0.22            0.22            0.56            0.76           -0.22            0.24      5.2e+03     0.0092    1e+02        1   ++
    2            0.38            -1.3            -1.7            -1.5           -0.36            0.23             0.6            0.81           -0.25            0.27      5.2e+03    0.00022    1e+03        1   ++
    3            0.38            -1.3            -1.7            -1.5           -0.36            0.23             0.6            0.81           -0.25            0.27      5.2e+03    2.4e-07    1e+03        1   ++
Model 30/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000155
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.88            0.66           -0.79              -1           -0.36           -0.25      5.2e+03      0.047       10      1.1   ++
    1            -1.2             1.9            -1.1            -1.1           -0.28           -0.28      5.1e+03      0.014    1e+02      1.1   ++
    2            -1.3               2            -1.2            -1.1           -0.25            -0.3      5.1e+03     0.0007    1e+03        1   ++
    3            -1.3               2            -1.2            -1.1           -0.25            -0.3      5.1e+03    2.4e-06    1e+03        1   ++
Model 31/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000156
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_ma     Function    Relgrad   Radius      Rho
    0           -0.33           -0.81           -0.63           -0.89           -0.52          -0.039      5.3e+03      0.043       10      1.1   ++
    1           0.038            -1.2            -1.2              -1           -0.47            0.28      5.2e+03     0.0093    1e+02      1.1   ++
    2           0.089            -1.2            -1.2            -1.1           -0.46            0.31      5.2e+03    0.00033    1e+03        1   ++
    3           0.089            -1.2            -1.2            -1.1           -0.46            0.31      5.2e+03    4.1e-07    1e+03        1   ++
Model 32/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000157
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.44           -0.59            0.47              -1           -0.76           -0.34           -0.17           -0.18      5.2e+03      0.044       10        1   ++
    1           -0.21              -1               2            -1.6              -1           -0.36            0.33           -0.35      4.9e+03      0.018    1e+02        1   ++
    2            -0.2            -1.2               2            -1.7            -1.1           -0.39            0.37           -0.42      4.9e+03     0.0011    1e+03        1   ++
    3            -0.2            -1.2               2            -1.7            -1.1           -0.39            0.38           -0.42      4.9e+03    8.5e-06    1e+04        1   ++
    4            -0.2            -1.2               2            -1.7            -1.1           -0.39            0.38           -0.42      4.9e+03    5.5e-10    1e+04        1   ++
Model 33/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000158
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.51            -0.8               1            -0.6           -0.88           -0.46           -0.15           -0.21      5.1e+03      0.045       10      1.1   ++
    1           -0.54           -0.96             1.7            -1.1            -1.1            -0.6            0.36           -0.37        5e+03      0.012    1e+02      1.1   ++
    2           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.41      4.9e+03     0.0007    1e+03        1   ++
    3           -0.53            -1.1             1.9            -1.2            -1.1           -0.61            0.41           -0.41      4.9e+03    4.3e-06    1e+03        1   ++
Model 34/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000159
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time     lambda_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.46           -0.65            0.57           -0.92             1.9              -1           -0.17           -0.44           -0.24           -0.24      5.5e+03      0.088        1     0.73    +
    1           -0.55            -1.1             1.6              -1             1.2           -0.94           -0.19           -0.47            0.13           -0.33        5e+03      0.019       10      1.2   ++
    2           -0.55            -1.1             1.6              -1             1.2           -0.94           -0.19           -0.47            0.13           -0.33        5e+03      0.019      1.8      -14    -
    3           -0.55            -1.1             1.6              -1             1.2           -0.94           -0.19           -0.47            0.13           -0.33        5e+03      0.019     0.88    -0.88    -
    4           -0.56            -1.2             1.9            -1.6            0.36            -1.2           -0.16           -0.46            0.34           -0.35      4.9e+03      0.023      8.8     0.91   ++
    5           -0.21            -1.1             1.9            -1.7            0.34            -1.1             1.6           -0.43            0.41            -1.3      4.9e+03     0.0036      8.8     0.82    +
    6           -0.22            -1.2               2            -1.7            0.33            -1.1             1.2           -0.42            0.41            -1.2      4.9e+03    0.00065       88      1.2   ++
    7           -0.22            -1.2               2            -1.7            0.33            -1.1            0.98           -0.42            0.41            -1.1      4.9e+03    0.00011  8.8e+02      1.1   ++
    8           -0.22            -1.2               2            -1.7            0.33            -1.1            0.98           -0.42            0.41            -1.1      4.9e+03    5.3e-06  8.8e+02        1   ++
Model 35/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000160
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.43           -0.59            0.47              -1           -0.76           -0.12           -0.34           -0.16           -0.18      5.2e+03      0.042       10        1   ++
    1           -0.21              -1               2            -1.6              -1            0.89           -0.36            0.33           -0.91      4.9e+03      0.018    1e+02        1   ++
    2            -0.2            -1.2               2            -1.7            -1.1            0.91           -0.39            0.37           -0.99      4.9e+03     0.0011    1e+03        1   ++
    3            -0.2            -1.2               2            -1.7            -1.1            0.91           -0.39            0.38           -0.99      4.9e+03    8.4e-06    1e+04        1   ++
    4            -0.2            -1.2               2            -1.7            -1.1            0.91           -0.39            0.38           -0.99      4.9e+03    5.4e-10    1e+04        1   ++
Pareto file has been updated: b21multiple_models.pareto
Before the algorithm: 36 models, with 8 Pareto.
After the algorithm: 42 models, with 8 Pareto.
VNS algorithm completed. Postprocessing of the Pareto optimal solutions
Pareto set initialized from file with 36 elements [8 Pareto] and 0 invalid elements.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000000.iter
Parameter values restored from __b21multiple_models_000000.iter
Starting values for the algorithm: {'asc_train_ref': -0.26118949275010445, 'asc_train_diff_male': -1.1195205183536523, 'asc_train_diff_GA': 1.9854139084913025, 'b_time': -1.7053348387931921, 'lambda_time': 0.3292434856239473, 'b_cost_ref': -1.575519605716697, 'b_cost_diff_inc-under50': -0.5878741661013013, 'b_cost_diff_inc-50-100': 0.21532146660967305, 'b_cost_diff_inc-100+': 0.6293032493669737, 'b_cost_diff_inc-unknown': 0.8175262402491592, 'asc_car_ref': -0.4531117907224833, 'asc_car_diff_male': 0.44856560098379494, 'asc_car_diff_GA': -0.37087421631981377}
As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time     lambda_time      b_cost_ref  b_cost_diff_GA     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.17            -1.2               2            -1.7            0.32              -1               1           -0.35            0.35            -1.1      4.9e+03     0.0067        1     0.84    +
    1           -0.23            -1.2               2            -1.7            0.33            -1.1               2            -0.3            0.29            -1.7      4.9e+03      0.002        1     0.36    +
    2           -0.23            -1.2               2            -1.7            0.33            -1.1               2            -0.3            0.29            -1.7      4.9e+03      0.002      0.5   -0.033    -
    3           -0.23            -1.2               2            -1.7            0.33            -1.1               2            -0.3            0.29            -1.7      4.9e+03      0.002     0.25   -0.049    -
    4           -0.23            -1.2               2            -1.7            0.33            -1.1               2            -0.3            0.29            -1.7      4.9e+03      0.002     0.12 -0.00017    -
    5           -0.23            -1.2               2            -1.7            0.33            -1.1               2            -0.3            0.29            -1.7      4.9e+03      0.002    0.062   -0.051    -
    6           -0.23            -1.1             1.9            -1.7            0.34            -1.1             2.1           -0.27            0.26            -1.8      4.9e+03     0.0013    0.062     0.13    +
    7           -0.23            -1.1             1.9            -1.7            0.34            -1.1             2.1           -0.27            0.26            -1.8      4.9e+03     0.0013    0.031   -0.044    -
    8           -0.23            -1.1             1.9            -1.7            0.34            -1.1             2.1           -0.27            0.26            -1.8      4.9e+03     0.0013    0.016    -0.12    -
    9           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.25            -1.8      4.9e+03     0.0015    0.016      0.2    +
   10           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.25            -1.8      4.9e+03     0.0015   0.0078   0.0082    -
   11           -0.23            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014   0.0078     0.23    +
   12           -0.23            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014   0.0039  -0.0066    -
   13           -0.23            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014    0.002      0.1    -
   14           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014    0.002     0.22    +
   15           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  0.00098   0.0089    -
   16           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  0.00049    0.014    -
   17           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  0.00024    0.019    -
   18           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  0.00012     0.03    -
   19           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  6.1e-05    0.036    -
   20           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  3.1e-05     0.04    -
   21           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  1.5e-05    0.043    -
   22           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  7.6e-06    0.045    -
   23           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  3.8e-06    0.045    -
   24           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  1.9e-06    0.046    -
   25           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  9.5e-07    0.046    -
   26           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  4.8e-07    0.046    -
   27           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  2.4e-07    0.046    -
   28           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  1.2e-07    0.046    -
   29           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014    6e-08    0.046    -
   30           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014    3e-08    0.046    -
   31           -0.22            -1.1               2            -1.7            0.34            -1.1             2.1           -0.27            0.24            -1.8      4.9e+03     0.0014  1.5e-08    0.046    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 32
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:02.229331
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000000~01.html has been generated.
File b21multiple_models_000000~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000001.iter
Parameter values restored from __b21multiple_models_000001.iter
Starting values for the algorithm: {'asc_train': -3.5, 'b_time': -5.17702237179112, 'lambda_time': -0.3521469872880427, 'b_cost': -0.23692086340664398, 'asc_car': -0.52618542015524}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0               0               0            -5.2           -0.24               0               0      6.9e+03        1.2      0.5   -0.089    -
    1            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1      0.5     0.46    +
    2            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1     0.25    -0.48    -
    3            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1     0.12     -0.2    -
    4            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1    0.062    -0.16    -
    5            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1    0.031    -0.13    -
    6            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1    0.016    -0.12    -
    7            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1   0.0078    -0.12    -
    8            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1   0.0039    -0.11    -
    9            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1    0.002    -0.11    -
   10            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  0.00098    -0.11    -
   11            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  0.00049    -0.11    -
   12            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  0.00024    -0.11    -
   13            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  0.00012    -0.11    -
   14            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  6.1e-05    -0.11    -
   15            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  3.1e-05    -0.11    -
   16            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  1.5e-05    -0.11    -
   17            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  7.6e-06    -0.11    -
   18            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  3.8e-06    -0.11    -
   19            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  1.9e-06    -0.11    -
   20            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  9.5e-07    -0.11    -
   21            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  4.8e-07    -0.11    -
   22            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  2.4e-07    -0.11    -
   23            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  1.2e-07    -0.11    -
   24            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1    6e-08    -0.11    -
   25            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1    3e-08    -0.11    -
   26            -0.5           0.065            -5.7           -0.37          -0.082            -0.5      6.4e+03          1  1.5e-08    -0.11    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 27
Proportion of Hessian calculation: 2/2 = 100.0%
Optimization time: 0:00:00.647344
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000001~01.html has been generated.
File b21multiple_models_000001~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000002.iter
Parameter values restored from __b21multiple_models_000002.iter
Starting values for the algorithm: {'asc_train_ref': -0.5580850460270373, 'asc_train_diff_male': -0.874038274510957, 'asc_train_diff_GA': 0.875, 'b_time': -2.549909700411886, 'lambda_time': 0.8850585118642702, 'b_cost': -0.20353452565384322, 'asc_car_ref': -0.875, 'asc_car_diff_male': -0.875, 'asc_car_diff_GA': -0.4700120362966725}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time          b_cost     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0            0.26           -0.52             1.4            -1.5            -1.2            0.12            0.12           -0.43      5.6e+03       0.11        1     0.44    +
    1         -0.0037           -0.85             1.5            -1.6            -2.2             0.4            0.55            -0.5      5.5e+03       0.24        1     0.22    +
    2         -0.0037           -0.85             1.5            -1.6            -2.2             0.4            0.55            -0.5      5.5e+03       0.24      0.5    -0.21    -
    3          -0.028            -1.2             1.8            -1.7            -2.7            0.16               1           -0.93      5.4e+03       0.25      0.5     0.32    +
    4            0.23            -1.2             1.9            -1.6            -3.2           -0.26             1.5            -1.2      5.3e+03       0.13      0.5      0.2    +
    5           0.099            -1.4             1.8            -1.9            -3.7           -0.68             1.6            -1.2      5.2e+03      0.075      0.5      0.4    +
    6           0.099            -1.4             1.8            -1.9            -3.7           -0.68             1.6            -1.2      5.2e+03      0.075     0.25    -0.47    -
    7             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029      2.5      1.2   ++
    8             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029     0.91      -16    -
    9             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029     0.46       -5    -
   10             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029     0.23     -1.7    -
   11             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029     0.11     -1.1    -
   12             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029    0.057    -0.75    -
   13             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029    0.029    -0.59    -
   14             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029    0.014    -0.42    -
   15             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029   0.0071    -0.42    -
   16             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029   0.0036    -0.35    -
   17             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029   0.0018    -0.32    -
   18             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  0.00089    -0.31    -
   19             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  0.00045     -0.3    -
   20             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  0.00022     -0.3    -
   21             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  0.00011     -0.3    -
   22             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  5.6e-05     -0.3    -
   23             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  2.8e-05     -0.3    -
   24             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  1.4e-05     -0.3    -
   25             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029    7e-06    -0.29    -
   26             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  3.5e-06    -0.29    -
   27             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  1.7e-06    -0.29    -
   28             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  8.7e-07    -0.29    -
   29             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  4.4e-07    -0.29    -
   30             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  2.2e-07    -0.29    -
   31             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  1.1e-07    -0.29    -
   32             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  5.5e-08    -0.29    -
   33             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  2.7e-08    -0.29    -
   34             0.3            -1.3             1.9              -2              -4           -0.93             1.5            -1.3      5.1e+03      0.029  1.4e-08    -0.29    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.3630393080385081e-08
Number of iterations: 35
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:00.779081
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000002~01.html has been generated.
File b21multiple_models_000002~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000003.iter
Parameter values restored from __b21multiple_models_000003.iter
Starting values for the algorithm: {'asc_train_ref': 0.12501564761290923, 'asc_train_diff_male': -1.302939379720285, 'asc_train_diff_GA': 1.9430273190823513, 'b_time': -1.8819982158039121, 'b_cost': -1.8121332737470164, 'asc_car_ref': -0.8012014693839187, 'asc_car_diff_male': 0.8872036748436755, 'asc_car_diff_GA': -0.7764521690057898}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time     lambda_time          b_cost     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19      0.5   -0.046    -
    1            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19     0.25    -0.11    -
    2            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19     0.12   -0.098    -
    3            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19    0.062    -0.16    -
    4            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19    0.031    -0.15    -
    5            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19    0.016    -0.15    -
    6            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19   0.0078    -0.15    -
    7            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19   0.0039    -0.15    -
    8            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19    0.002    -0.15    -
    9            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  0.00098    -0.14    -
   10            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  0.00049    -0.14    -
   11            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  0.00024    -0.14    -
   12            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  0.00012    -0.14    -
   13            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  6.1e-05    -0.14    -
   14            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  3.1e-05    -0.14    -
   15            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  1.5e-05    -0.14    -
   16            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  7.6e-06    -0.14    -
   17            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  3.8e-06    -0.14    -
   18            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  1.9e-06    -0.14    -
   19            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  9.5e-07    -0.14    -
   20            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  4.8e-07    -0.14    -
   21            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  2.4e-07    -0.14    -
   22            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  1.2e-07    -0.14    -
   23            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19    6e-08    -0.14    -
   24            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19    3e-08    -0.14    -
   25            0.13            -1.3             1.9            -1.9               1            -1.8            -0.8            0.89           -0.78      9.2e+03       0.19  1.5e-08    -0.14    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 26
Proportion of Hessian calculation: 1/1 = 100.0%
Optimization time: 0:00:02.255554
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000003~01.html has been generated.
File b21multiple_models_000003~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000004.iter
Parameter values restored from __b21multiple_models_000004.iter
Starting values for the algorithm: {'asc_train_ref': -1.0259779041009203, 'asc_train_diff_GA': 2.0417012426211842, 'b_time': -1.6680444783266624, 'lambda_time': 0.38240549309565697, 'b_cost': -1.0996092635678825, 'asc_car_ref': -0.06404634973454987, 'asc_car_diff_GA': -0.31338244218602307}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Optimization algorithm has converged.
Relative gradient: 5.030820226203682e-09
Cause of termination: Relative gradient = 5e-09 <= 6.1e-06
Number of function evaluations: 1
Number of gradient evaluations: 1
Number of hessian evaluations: 0
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 0
Optimization time: 0:00:00.701514
Calculate second derivatives and BHHH
File b21multiple_models_000004~01.html has been generated.
File b21multiple_models_000004~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000005.iter
Parameter values restored from __b21multiple_models_000005.iter
Starting values for the algorithm: {'asc_train_ref': -0.20264549785499536, 'asc_train_diff_GA': 2.0271387620175396, 'b_time': -1.7020556248822927, 'b_cost': -1.0632584808816732, 'asc_car_ref': -0.38890294740129805, 'asc_car_diff_GA': -0.4153454921314874}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19        1     0.14    +
    1           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19      0.5     -1.7    -
    2           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19     0.25     -1.5    -
    3           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19     0.12       -1    -
    4           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19    0.062     -0.8    -
    5           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19    0.031    -0.71    -
    6           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19    0.016    -0.67    -
    7           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19   0.0078    -0.65    -
    8           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19   0.0039    -0.64    -
    9           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19    0.002    -0.64    -
   10           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  0.00098    -0.64    -
   11           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  0.00049    -0.64    -
   12           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  0.00024    -0.63    -
   13           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  0.00012    -0.63    -
   14           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  6.1e-05    -0.63    -
   15           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  3.1e-05    -0.63    -
   16           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  1.5e-05    -0.63    -
   17           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  7.6e-06    -0.63    -
   18           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  3.8e-06    -0.63    -
   19           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  1.9e-06    -0.63    -
   20           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  9.5e-07    -0.63    -
   21           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  4.8e-07    -0.63    -
   22           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  2.4e-07    -0.63    -
   23           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  1.2e-07    -0.63    -
   24           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19    6e-08    -0.63    -
   25           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19    3e-08    -0.63    -
   26           -0.67            -1.8            -2.1           -0.14      5.7e+03       0.19  1.5e-08    -0.63    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 27
Proportion of Hessian calculation: 2/2 = 100.0%
Optimization time: 0:00:00.509600
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000005~01.html has been generated.
File b21multiple_models_000005~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000006.iter
Parameter values restored from __b21multiple_models_000006.iter
Starting values for the algorithm: {'asc_train_ref': -0.2204187987317722, 'asc_train_diff_male': -1.151262135247798, 'asc_train_diff_GA': 1.9592103270125723, 'b_time': -1.696198863769209, 'lambda_time': 0.3340292133468033, 'b_cost_ref': -1.1000273249513268, 'b_cost_diff_GA': 0.9150724693206711, 'asc_car_ref': -0.42185727184552724, 'asc_car_diff_male': 0.4127039445438218, 'asc_car_diff_GA': -1.026915244358154}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.   asc_train_ref asc_train_diff_ asc_train_diff_          b_time     lambda_time      b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc     asc_car_ref asc_car_diff_ma asc_car_diff_GA     Function    Relgrad   Radius      Rho
    0           -0.22            -1.2               2            -1.7            0.33            -1.1               0               0               0               0           -0.42            0.41              -1      5.1e+03      0.054      0.5     -0.6    -
    1           -0.22            -1.2               2            -1.7            0.33            -1.1               0               0               0               0           -0.42            0.41              -1      5.1e+03      0.054     0.25   -0.058    -
    2           -0.21            -1.2               2            -1.8            0.36           -0.94           -0.01          -0.078            0.25           0.012           -0.58            0.31              -1      5.1e+03      0.056     0.25      0.2    +
    3           -0.21            -1.2               2            -1.8            0.36           -0.94           -0.01          -0.078            0.25           0.012           -0.58            0.31              -1      5.1e+03      0.056     0.12   -0.013    -
    4           -0.14            -1.1               2            -1.9            0.47           -0.81          -0.088            -0.2            0.38           0.089            -0.7            0.19            -1.2      5.1e+03      0.047     0.12     0.17    +
    5           -0.11            -1.1               2            -1.9            0.44           -0.73          -0.096           -0.26             0.5           0.091           -0.83           0.076            -1.2        5e+03      0.046     0.12     0.15    +
    6           -0.11            -1.1               2            -1.9            0.44           -0.73          -0.096           -0.26             0.5           0.091           -0.83           0.076            -1.2        5e+03      0.046    0.062   0.0044    -
    7          -0.047            -1.1               2              -2            0.38           -0.67           -0.13           -0.32            0.56           0.092           -0.89           0.014            -1.2        5e+03      0.046    0.062     0.12    +
    8          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042    0.062     0.27    +
    9          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042    0.031   -0.016    -
   10          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042    0.016   0.0078    -
   11          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042   0.0078    0.041    -
   12          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042   0.0039    0.052    -
   13          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042    0.002    0.057    -
   14          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  0.00098     0.06    -
   15          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  0.00049    0.061    -
   16          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  0.00024    0.061    -
   17          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  0.00012    0.062    -
   18          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  6.1e-05    0.062    -
   19          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  3.1e-05    0.062    -
   20          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  1.5e-05    0.062    -
   21          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  7.6e-06    0.062    -
   22          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  3.8e-06    0.062    -
   23          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  1.9e-06    0.062    -
   24          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  9.5e-07    0.062    -
   25          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  4.8e-07    0.062    -
   26          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  2.4e-07    0.062    -
   27          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  1.2e-07    0.062    -
   28          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042    6e-08    0.062    -
   29          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042    3e-08    0.062    -
   30          -0.062            -1.1               2            -2.1            0.37           -0.61           -0.14           -0.38            0.62           0.089           -0.95          -0.049            -1.2        5e+03      0.042  1.5e-08    0.062    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 31
Proportion of Hessian calculation: 6/6 = 100.0%
Optimization time: 0:00:02.363975
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000006~01.html has been generated.
File b21multiple_models_000006~01.yaml has been generated.
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21multiple_models_000007.iter
Parameter values restored from __b21multiple_models_000007.iter
Starting values for the algorithm: {'asc_train': -0.7011872849436401, 'b_time': -1.2778589565196719, 'b_cost': -1.0837900371207714, 'asc_car': -0.15463267198926273}
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.       asc_train          b_time     lambda_time          b_cost         asc_car     Function    Relgrad   Radius      Rho
    0            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15      0.5     -0.7    -
    1            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15     0.25    -0.58    -
    2            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15     0.12    -0.71    -
    3            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15    0.062    -0.63    -
    4            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15    0.031     -0.6    -
    5            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15    0.016    -0.58    -
    6            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15   0.0078    -0.57    -
    7            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15   0.0039    -0.57    -
    8            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15    0.002    -0.56    -
    9            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  0.00098    -0.56    -
   10            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  0.00049    -0.56    -
   11            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  0.00024    -0.56    -
   12            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  0.00012    -0.56    -
   13            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  6.1e-05    -0.56    -
   14            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  3.1e-05    -0.56    -
   15            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  1.5e-05    -0.56    -
   16            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  7.6e-06    -0.56    -
   17            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  3.8e-06    -0.56    -
   18            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  1.9e-06    -0.56    -
   19            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  9.5e-07    -0.56    -
   20            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  4.8e-07    -0.56    -
   21            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  2.4e-07    -0.56    -
   22            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  1.2e-07    -0.56    -
   23            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15    6e-08    -0.56    -
   24            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15    3e-08    -0.56    -
   25            -0.7            -1.3               1            -1.1           -0.15      7.1e+03       0.15  1.5e-08    -0.56    -
Optimization algorithm has *not* converged.
Algorithm: Newton with trust region for simple bound constraints
Cause of termination: Trust region is too small: 1.4901161193847656e-08
Number of iterations: 26
Proportion of Hessian calculation: 1/1 = 100.0%
Optimization time: 0:00:01.816486
Calculate second derivatives and BHHH
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
File b21multiple_models_000007~01.html has been generated.
File b21multiple_models_000007~01.yaml has been generated.
Pareto: 8
Considered: 36
Removed: 5
summary, description = compile_estimation_results(
    non_dominated_models, use_short_names=True
)
print(summary)
                                     Model_000000  ...     Model_000007
Number of estimated parameters                 10  ...                5
Sample size                                  6768  ...             6768
Final log likelihood                    -4893.717  ...        -5331.252
Akaike Information Criterion             9807.434  ...          10672.5
Bayesian Information Criterion           9875.633  ...          10706.6
asc_train_ref (t-test)            -0.225  (-2.45)  ...
asc_train_diff_male (t-test)       -1.14  (-13.2)  ...
asc_train_diff_GA (t-test)             1.96  (21)  ...
b_time (t-test)                     -1.7  (-21.3)  ...   -1.28  (-11.4)
lambda_time (t-test)                 0.335  (4.6)  ...        1  (6.72)
b_cost_ref (t-test)                  -1.09  (-15)  ...
b_cost_diff_GA (t-test)              2.09  (7.05)  ...
asc_car_ref (t-test)              -0.268  (-2.88)  ...
asc_car_diff_male (t-test)           0.238  (2.4)  ...
asc_car_diff_GA (t-test)           -1.79  (-5.26)  ...
b_cost (t-test)                                    ...     -1.08  (-16)
asc_train (t-test)                                 ...  -0.701  (-9.28)
asc_car (t-test)                                   ...  -0.155  (-2.78)
b_cost_diff_inc-under50 (t-test)                   ...
b_cost_diff_inc-50-100 (t-test)                    ...
b_cost_diff_inc-100+ (t-test)                      ...
b_cost_diff_inc-unknown (t-test)                   ...

[22 rows x 8 columns]

Explanation of the short names of the model.

for k, v in description.items():
    if k != v:
        print(f'{k}: {v} AIC={summary.at["Akaike Information Criterion", k]}')
Model_000000: asc:MALE-GA;b_cost:GA;train_tt:boxcox AIC=9807.434
Model_000001: asc:GA;b_cost:no_seg;train_tt:log AIC=17391.1
Model_000002: asc:MALE-GA;b_cost:no_seg;train_tt:log AIC=12910.5
Model_000003: asc:MALE-GA;b_cost:no_seg;train_tt:boxcox AIC=10216.17
Model_000004: asc:GA;b_cost:no_seg;train_tt:boxcox AIC=10005.51
Model_000005: asc:no_seg;b_cost:no_seg;train_tt:linear AIC=11020.15
Model_000006: asc:MALE-GA;b_cost:INCOME;train_tt:boxcox AIC=11625.66
Model_000007: asc:no_seg;b_cost:no_seg;train_tt:boxcox AIC=10672.5

Total running time of the script: (1 minutes 23.782 seconds)

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