Note
Go to the end to download the full example code.
21a. Assisted specification¶
Example of the estimation of several versions of the model using assisted specification algorithm. The catalog of specifications is defined in 21b. 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_b21b_multiple_models_spec import PARETO_FILE_NAME, the_biogeme
logger = blog.get_screen_logger(blog.INFO)
logger.info('Example b21a_multiple_models')
income_segmentation=INCOME: [{0: 'inc-zero', 1: 'inc-under50', 2: 'inc-50-100', 3: 'inc-100+', 4: 'inc-unknown'}] ref: inc-zero
Example b21a_multiple_models
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,
)
Unable to read file b21_multiple_models.pareto. Pareto set empty.
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_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.
Analytical Hessian method: full
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 7 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.
Analytical Hessian method: full
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 1/36
Biogeme parameters read from biogeme.toml.
Model with 10 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.
Analytical Hessian method: full
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 2/36
Biogeme parameters read from biogeme.toml.
Model with 9 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.
Analytical Hessian method: full
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 ++
Model 3/36
Biogeme parameters read from biogeme.toml.
Model with 8 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.
Analytical Hessian method: full
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 4/36
Biogeme parameters read from biogeme.toml.
Model with 8 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.
Analytical Hessian method: full
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 5/36
Biogeme parameters read from biogeme.toml.
Model with 7 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.
Analytical Hessian method: full
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 6/36
Biogeme parameters read from biogeme.toml.
Model with 10 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.
Analytical Hessian method: full
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 5e-07 1e+03 1 ++
Model 7/36
Biogeme parameters read from biogeme.toml.
Model with 6 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.
Analytical Hessian method: full
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 8/36
Biogeme parameters read from biogeme.toml.
Model with 5 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.
Analytical Hessian method: full
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 9/36
Biogeme parameters read from biogeme.toml.
Model with 13 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.
Analytical Hessian method: full
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 8.7e-07 1.2e+02 1 ++
Model 10/36
Biogeme parameters read from biogeme.toml.
Model with 4 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.
Analytical Hessian method: full
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 11/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000161
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.
Analytical Hessian method: full
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 12/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000162
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.
Analytical Hessian method: full
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 13/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000163
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.
Analytical Hessian method: full
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 14/36
Model 15/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000164
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.
Analytical Hessian method: full
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 16/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000165
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.
Analytical Hessian method: full
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 17/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000166
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.
Analytical Hessian method: full
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 18/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000167
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.
Analytical Hessian method: full
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 19/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000168
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.
Analytical Hessian method: full
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 20/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000169
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.
Analytical Hessian method: full
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 21/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b07everything_000170
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.
Analytical Hessian method: full
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 0.22 0.6 0.76 -0.37 0.34 -0.29 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 1.1e-05 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 9.3e-08 1e+04 1 ++
Model 22/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000171
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.
Analytical Hessian method: full
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 23/36
Biogeme parameters read from biogeme.toml.
Model with 5 unknown parameters [max: 50]
*** Estimate b07everything_000172
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.
Analytical Hessian method: full
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 24/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b07everything_000173
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.
Analytical Hessian method: full
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 4.3e-10 1e+04 1 ++
Model 25/36
Biogeme parameters read from biogeme.toml.
Model with 6 unknown parameters [max: 50]
*** Estimate b07everything_000174
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.
Analytical Hessian method: full
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 26/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000175
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.
Analytical Hessian method: full
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 27/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000176
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.
Analytical Hessian method: full
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 28/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000177
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.
Analytical Hessian method: full
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 29/36
Biogeme parameters read from biogeme.toml.
Model with 12 unknown parameters [max: 50]
*** Estimate b07everything_000178
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.
Analytical Hessian method: full
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 0.00079 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 30/36
Biogeme parameters read from biogeme.toml.
Model with 11 unknown parameters [max: 50]
*** Estimate b07everything_000179
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.
Analytical Hessian method: full
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 31/36
Biogeme parameters read from biogeme.toml.
Model with 10 unknown parameters [max: 50]
*** Estimate b07everything_000180
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.
Analytical Hessian method: full
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 32/36
Biogeme parameters read from biogeme.toml.
Model with 8 unknown parameters [max: 50]
*** Estimate b07everything_000181
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.
Analytical Hessian method: full
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 33/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000182
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.
Analytical Hessian method: full
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 34/36
Biogeme parameters read from biogeme.toml.
Model with 9 unknown parameters [max: 50]
*** Estimate b07everything_000183
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.
Analytical Hessian method: full
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 35/36
Biogeme parameters read from biogeme.toml.
Model with 7 unknown parameters [max: 50]
*** Estimate b07everything_000184
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.
Analytical Hessian method: full
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 ++
Pareto file has been updated: b21_multiple_models.pareto
Before the algorithm: 1 models, with 1 Pareto.
After the algorithm: 36 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 __b21_multiple_models_000000.iter
Cannot read file __b21_multiple_models_000000.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 1.7992210443671005e-09
Cause of termination: Relative gradient = 1.8e-09 <= 6.1e-06
Number of function evaluations: 16
Number of gradient evaluations: 11
Number of hessian evaluations: 5
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 5
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:03.063539
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000001.iter
Cannot read file __b21_multiple_models_000001.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 1.0595595040904127e-07
Cause of termination: Relative gradient = 1.1e-07 <= 6.1e-06
Number of function evaluations: 13
Number of gradient evaluations: 9
Number of hessian evaluations: 4
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 4
Proportion of Hessian calculation: 4/4 = 100.0%
Optimization time: 0:00:01.330613
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000002.iter
Cannot read file __b21_multiple_models_000002.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 5.482794560380737e-10
Cause of termination: Relative gradient = 5.5e-10 <= 6.1e-06
Number of function evaluations: 16
Number of gradient evaluations: 11
Number of hessian evaluations: 5
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 5
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:02.513434
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000003.iter
Cannot read file __b21_multiple_models_000003.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 2.0806244413786043e-06
Cause of termination: Relative gradient = 2.1e-06 <= 6.1e-06
Number of function evaluations: 13
Number of gradient evaluations: 9
Number of hessian evaluations: 4
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 4
Proportion of Hessian calculation: 4/4 = 100.0%
Optimization time: 0:00:02.204917
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000004.iter
Cannot read file __b21_multiple_models_000004.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 3.608609221568633e-09
Cause of termination: Relative gradient = 3.6e-09 <= 6.1e-06
Number of function evaluations: 19
Number of gradient evaluations: 13
Number of hessian evaluations: 6
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 6
Proportion of Hessian calculation: 6/6 = 100.0%
Optimization time: 0:00:01.667551
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000005.iter
Cannot read file __b21_multiple_models_000005.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 5.317241977940658e-06
Cause of termination: Relative gradient = 5.3e-06 <= 6.1e-06
Number of function evaluations: 24
Number of gradient evaluations: 15
Number of hessian evaluations: 7
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 9
Proportion of Hessian calculation: 7/7 = 100.0%
Optimization time: 0:00:00.842302
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000006.iter
Cannot read file __b21_multiple_models_000006.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 8.7e-07 1.2e+02 1 ++
Optimization algorithm has converged.
Relative gradient: 8.741583096647686e-07
Cause of termination: Relative gradient = 8.7e-07 <= 6.1e-06
Number of function evaluations: 22
Number of gradient evaluations: 13
Number of hessian evaluations: 6
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 9
Proportion of Hessian calculation: 6/6 = 100.0%
Optimization time: 0:00:01.051084
Calculate final gradient and BHHH
Calculate second derivatives
Biogeme parameters provided by the user.
*** Initial values of the parameters are obtained from the file __b21_multiple_models_000007.iter
Cannot read file __b21_multiple_models_000007.iter. Statement is ignored.
Starting values for the algorithm: {}
Analytical Hessian method: full
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 ++
Optimization algorithm has converged.
Relative gradient: 3.3741323570117958e-06
Cause of termination: Relative gradient = 3.4e-06 <= 6.1e-06
Number of function evaluations: 18
Number of gradient evaluations: 11
Number of hessian evaluations: 5
Algorithm: Newton with trust region for simple bound constraints
Number of iterations: 7
Proportion of Hessian calculation: 5/5 = 100.0%
Optimization time: 0:00:00.732329
Calculate final gradient and BHHH
Calculate second derivatives
Pareto: 8
Considered: 36
Removed: 6
summary, description = compile_estimation_results(
non_dominated_models, use_short_names=True
)
print(summary)
Model_000000 ... Model_000007
Number of estimated parameters 5 ... 9
Sample size 6768 ... 6768
Final log likelihood -5292.095 ... -4881.917
Akaike Information Criterion 10594.19 ... 9781.834
Bayesian Information Criterion 10628.29 ... 9843.214
asc_train (t-test) -0.485 (-7.53) ...
b_time (t-test) -1.67 (-21.9) ... -1.69 (-21.2)
lambda_time (t-test) 0.51 (6.6) ... 0.334 (4.54)
b_cost (t-test) -1.08 (-15.9) ... -1.09 (-15)
asc_car (t-test) -0.00462 (-0.0963) ...
asc_train_ref (t-test) ... -0.219 (-2.42)
asc_train_diff_male (t-test) ... -1.15 (-13.4)
asc_train_diff_GA (t-test) ... 1.96 (21.1)
asc_car_ref (t-test) ... -0.417 (-4.23)
asc_car_diff_male (t-test) ... 0.412 (3.95)
asc_car_diff_GA (t-test) ... -0.447 (-2.19)
b_cost_ref (t-test) ...
b_cost_diff_GA (t-test) ...
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:no_seg;b_cost:no_seg;train_tt:boxcox AIC=10594.19
Model_000001: asc:no_seg;b_cost:no_seg;train_tt:linear AIC=10670.5
Model_000002: asc:MALE-GA;b_cost:no_seg;train_tt:log AIC=9817.767
Model_000003: asc:GA;b_cost:no_seg;train_tt:log AIC=10054.47
Model_000004: asc:GA;b_cost:no_seg;train_tt:boxcox AIC=10005.51
Model_000005: asc:MALE-GA;b_cost:GA;train_tt:boxcox AIC=9778.922
Model_000006: asc:MALE-GA;b_cost:INCOME;train_tt:boxcox AIC=9750.73
Model_000007: asc:MALE-GA;b_cost:no_seg;train_tt:boxcox AIC=9781.834
Total running time of the script: (1 minutes 51.343 seconds)