Re-estimate the Pareto optimal models

The assisted specification algorithm generates a file containing the pareto optimal specification. This script is designed to re-estimate the Pareto optimal models. The catalog of specifications is defined in Specification of a catalog of models .

Michel Bierlaire, EPFL Sat Jun 28 2025, 12:35:57m

from biogeme.results_processing import compile_estimation_results

try:
    import matplotlib.pyplot as plt

    can_plot = True
except ModuleNotFoundError:
    can_plot = False
from biogeme.assisted import ParetoPostProcessing
from plot_b22b_multiple_models_spec import the_biogeme, PARETO_FILE_NAME


PATH_PARETO_FILE_NAME = f'saved_results/{PARETO_FILE_NAME}'

CSV_FILE = 'b22_process_pareto.csv'
SEP_CSV = ','

The constructor of the Pareto post-processing object takes two arguments:

• the biogeme object,

• the name of the file where the algorithm has stored the estimated models.

the_pareto_post = ParetoPostProcessing(
    biogeme_object=the_biogeme,
    pareto_file_name=PATH_PARETO_FILE_NAME,
)

the_pareto_post.log_statistics()

all_results = the_pareto_post.reestimate(recycle=True)

summary, description = compile_estimation_results(all_results, use_short_names=True)
print(summary)

                                      Model_000000  ...    Model_000006
Number of estimated parameters                  10  ...               6
Sample size                                   6768  ...            6768
Final log likelihood                      -6116.33  ...         -5731.9
Akaike Information Criterion              12252.66  ...         11475.8
Bayesian Information Criterion            12320.86  ...        11516.72
asc_train_ref (t-test)                -1.2  (-5.5)  ...  -0.39  (-6.18)
asc_train_diff_male (t-test)     -0.0584  (-0.319)  ...
asc_train_diff_with_ga (t-test)        2.1  (10.2)  ...    2.14  (18.9)
b_time (t-test)                     -3.17  (-11.7)  ...  -1.63  (-11.5)
b_cost (t-test)                     -2.73  (-3.58)  ...  -1.51  (-17.8)
lambda_cost (t-test)                  1.05  (3.85)  ...
b_headway (t-test)                -0.0141  (-6.25)  ...
asc_car_ref (t-test)                -0.19  (-1.43)  ...  -0.55  (-8.69)
asc_car_diff_male (t-test)       -0.0358  (-0.335)  ...
asc_car_diff_with_ga (t-test)          1.13  (4.5)  ...  -2.01  (-4.26)
asc_train (t-test)                                  ...
asc_car (t-test)                                    ...

[17 rows x 7 columns]

print(f'Summary table available in {CSV_FILE}')
summary.to_csv(CSV_FILE, sep=SEP_CSV)

Summary table available in b22_process_pareto.csv

Explanation of the short names of the models.

with open(CSV_FILE, 'a', encoding='utf-8') as f:
    print('\n\n', file=f)
    for k, v in description.items():
        if k != v:
            print(f'{k}: {v}')
            print(f'{k}{SEP_CSV}{v}', file=f)

Model_000000: asc:MALE-GA;train_cost_catalog:boxcox;train_headway_catalog:with_headway;train_tt_catalog:sqrt
Model_000001: asc:MALE-GA;train_cost_catalog:sqrt;train_headway_catalog:with_headway;train_tt_catalog:log
Model_000002: asc:no_seg;train_cost_catalog:sqrt;train_headway_catalog:with_headway;train_tt_catalog:log
Model_000003: asc:GA;train_cost_catalog:log;train_headway_catalog:with_headway;train_tt_catalog:sqrt
Model_000004: asc:MALE-GA;train_cost_catalog:sqrt;train_headway_catalog:without_headway;train_tt_catalog:sqrt
Model_000005: asc:no_seg;train_cost_catalog:sqrt;train_headway_catalog:without_headway;train_tt_catalog:linear
Model_000006: asc:GA;train_cost_catalog:log;train_headway_catalog:without_headway;train_tt_catalog:sqrt

The following plot illustrates all models that have been estimated. Each dot corresponds to a model. The x-coordinate corresponds to the Akaike Information Criterion (AIC). The y-coordinate corresponds to the Bayesian Information Criterion (BIC). Note that there is a third objective that does not appear on this picture: the number of parameters. If the shape of the dot is a circle, it means that it corresponds to a Pareto optimal model. If the shape is a cross, it means that the model has been Pareto optimal at some point during the algorithm and later removed as a new model dominating it has been found. If the shape is a start, it means that the model has been deemed invalid.

if can_plot:
    _ = the_pareto_post.plot(label_x='AIC', label_y='BIC')
    plt.show()

It is possible to plot two different objectives: AIC and number of parameters.

if can_plot:
    _ = the_pareto_post.plot(
        objective_x=0, objective_y=2, label_x='AIC', label_y='Number of parameters'
    )
    plt.show()

It is possible to plot two different objectives: BIC and number of parameters.

if can_plot:
    _ = the_pareto_post.plot(
        objective_x=1, objective_y=2, label_x='BIC', label_y='Number of parameters'
    )
    plt.show()