.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b21c_process_pareto.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_swissmetro_plot_b21c_process_pareto.py: .. _plot_b21c_process_pareto: 21c. 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 :ref:`plot_b21b_multiple_models_spec` . Michel Bierlaire, EPFL Sat Jun 28 2025, 20:58:22 .. GENERATED FROM PYTHON SOURCE LINES 15-37 .. code-block:: Python import biogeme.biogeme_logging as blog from biogeme.results_processing import compile_estimation_results try: import matplotlib.pyplot as plt can_plot = True except ModuleNotFoundError: can_plot = False from biogeme_optimization.exceptions import OptimizationError from biogeme.assisted import ParetoPostProcessing from plot_b21b_multiple_models_spec import the_biogeme, PARETO_FILE_NAME PATH_PARETO_FILE_NAME = f'saved_results/{PARETO_FILE_NAME}' logger = blog.get_screen_logger(blog.INFO) logger.info('Example b21c_process_pareto.py') CSV_FILE = 'b21_process_pareto.csv' SEP_CSV = ',' .. rst-class:: sphx-glr-script-out .. code-block:: none Example b21c_process_pareto.py .. GENERATED FROM PYTHON SOURCE LINES 38-43 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. .. GENERATED FROM PYTHON SOURCE LINES 43-48 .. code-block:: Python the_pareto_post = ParetoPostProcessing( biogeme_object=the_biogeme, pareto_file_name=PATH_PARETO_FILE_NAME, ) .. rst-class:: sphx-glr-script-out .. code-block:: none Pareto set initialized from file with 36 elements [8 Pareto] and 0 invalid elements. .. GENERATED FROM PYTHON SOURCE LINES 49-51 .. code-block:: Python the_pareto_post.log_statistics() .. rst-class:: sphx-glr-script-out .. code-block:: none Pareto: 8 Considered: 36 Removed: 5 .. GENERATED FROM PYTHON SOURCE LINES 52-54 Complete re-estimation of the best models, including the calculation of the statistics. .. GENERATED FROM PYTHON SOURCE LINES 54-56 .. code-block:: Python all_results = the_pareto_post.reestimate(recycle=False) .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters provided by the user. *** Initial values of the parameters are obtained from the file __b21_multiple_models_000000.iter Parameter values restored from __b21_multiple_models_000000.iter Starting values for the algorithm: {'asc_train': -0.48497306751082847, 'b_time': -1.6749097004118856, 'lambda_time': 0.5100585118642703, 'b_cost': -1.0785345256538428, 'asc_car': -0.004623351582876547} 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 Optimization algorithm has converged. Relative gradient: 2.367865132130195e-09 Cause of termination: Relative gradient = 2.4e-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: 0:00:00.204035 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 Parameter values restored from __b21_multiple_models_000001.iter Starting values for the algorithm: {'asc_train': -0.7011872849436406, 'b_time': -1.2778589565196712, 'b_cost': -1.083790037120771, 'asc_car': -0.15463267198926292} 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 Optimization algorithm has converged. Relative gradient: 1.3841917138444102e-07 Cause of termination: Relative gradient = 1.4e-07 <= 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: 0:00:00.194494 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 Parameter values restored from __b21_multiple_models_000002.iter Starting values for the algorithm: {'asc_train_ref': -0.20264549785499558, 'asc_train_diff_male': -1.200728418470046, 'asc_train_diff_GA': 2.027138762017538, 'b_time': -1.7020556248823198, 'b_cost': -1.0632584808816534, 'asc_car_ref': -0.38890294740134795, 'asc_car_diff_male': 0.3766698739403544, 'asc_car_diff_GA': -0.41534549213148914} 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 -1.2 2.1 -2.7 0.46 -0.88 -0.42 -0.43 7.2e+03 0.43 1 0.78 + 1 -1.2 2.1 -2.7 0.46 -0.88 -0.42 -0.43 7.2e+03 0.43 0.5 -0.28 - 2 -1.6 2.5 -3.2 0.13 -0.69 -0.92 -0.48 6.9e+03 0.2 0.5 0.43 + 3 -1.6 2.5 -3.2 0.13 -0.69 -0.92 -0.48 6.9e+03 0.2 0.25 -0.016 - 4 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.25 0.22 + 5 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.12 -1.3 - 6 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.062 -0.95 - 7 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.031 -0.75 - 8 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.016 -0.64 - 9 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.0078 -0.59 - 10 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.0039 -0.57 - 11 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.002 -0.55 - 12 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.00098 -0.55 - 13 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.00049 -0.54 - 14 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.00024 -0.54 - 15 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 0.00012 -0.54 - 16 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 6.1e-05 -0.54 - 17 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 3.1e-05 -0.54 - 18 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 1.5e-05 -0.54 - 19 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 7.6e-06 -0.54 - 20 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 3.8e-06 -0.54 - 21 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 1.9e-06 -0.54 - 22 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 9.5e-07 -0.54 - 23 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 4.8e-07 -0.54 - 24 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 2.4e-07 -0.54 - 25 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 1.2e-07 -0.54 - 26 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 6e-08 -0.54 - 27 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 3e-08 -0.54 - 28 -1.5 2.8 -3.5 -0.12 -0.91 -0.81 -0.59 6.9e+03 0.14 1.5e-08 -0.54 - 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: 29 Proportion of Hessian calculation: 4/4 = 100.0% Optimization time: 0:00:04.742609 Calculate final gradient and BHHH Calculate second derivatives 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. Biogeme parameters provided by the user. *** Initial values of the parameters are obtained from the file __b21_multiple_models_000003.iter Parameter values restored from __b21_multiple_models_000003.iter Starting values for the algorithm: {'asc_train_ref': -1.0506235695550208, 'asc_train_diff_GA': 2.126084650203615, 'b_time': -1.6770223717911181, 'b_cost': -1.0704947507024756, 'asc_car_ref': -0.06463269501694303, 'asc_car_diff_GA': -0.2677822135309631} 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 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 1 0.21 + 1 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.5 -1.2 - 2 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.25 -0.54 - 3 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.12 -0.29 - 4 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.062 -0.23 - 5 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.031 -0.2 - 6 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.016 -0.19 - 7 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.0078 -0.18 - 8 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.0039 -0.18 - 9 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.002 -0.18 - 10 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.00098 -0.18 - 11 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.00049 -0.18 - 12 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.00024 -0.18 - 13 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 0.00012 -0.18 - 14 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 6.1e-05 -0.18 - 15 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 3.1e-05 -0.18 - 16 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 1.5e-05 -0.18 - 17 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 7.6e-06 -0.18 - 18 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 3.8e-06 -0.18 - 19 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 1.9e-06 -0.18 - 20 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 9.5e-07 -0.18 - 21 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 4.8e-07 -0.18 - 22 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 2.4e-07 -0.18 - 23 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 1.2e-07 -0.18 - 24 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 6e-08 -0.18 - 25 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 3e-08 -0.18 - 26 -1.9 -0.77 2.1 -2.7 -0.83 -0.098 0.0057 -0.27 8.8e+03 0.51 1.5e-08 -0.18 - 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: 0:00:01.765358 Calculate final gradient and BHHH Calculate second derivatives 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. Biogeme parameters provided by the user. *** Initial values of the parameters are obtained from the file __b21_multiple_models_000004.iter Parameter values restored from __b21_multiple_models_000004.iter Starting values for the algorithm: {'asc_train_ref': -1.0259779041009203, 'asc_train_diff_GA': 2.0417012426211842, 'b_time': -1.6680444783266626, 'lambda_time': 0.38240549309565697, 'b_cost': -1.0996092635678825, 'asc_car_ref': -0.06404634973454974, 'asc_car_diff_GA': -0.3133824421860232} 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 -1 0 2 -1.7 0.38 0 0 0 0 0 -0.064 0 -0.31 1.2e+04 0.51 0.5 -1.3 - 1 -1 0 2 -1.7 0.38 0 0 0 0 0 -0.064 0 -0.31 1.2e+04 0.51 0.25 0.038 - 2 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.25 0.27 + 3 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.12 -0.6 - 4 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.062 -0.48 - 5 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.031 -0.43 - 6 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.016 -0.41 - 7 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.0078 -0.4 - 8 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.0039 -0.39 - 9 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.002 -0.39 - 10 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.00098 -0.39 - 11 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.00049 -0.39 - 12 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.00024 -0.39 - 13 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 0.00012 -0.38 - 14 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 6.1e-05 -0.38 - 15 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 3.1e-05 -0.38 - 16 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 1.5e-05 -0.38 - 17 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 7.6e-06 -0.38 - 18 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 3.8e-06 -0.38 - 19 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 1.9e-06 -0.38 - 20 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 9.5e-07 -0.38 - 21 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 4.8e-07 -0.38 - 22 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 2.4e-07 -0.38 - 23 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 1.2e-07 -0.38 - 24 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 6e-08 -0.38 - 25 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 3e-08 -0.38 - 26 -1.3 -0.25 1.8 -1.9 0.63 -0.16 -0.12 -0.17 0.094 0.017 -0.31 -0.25 -0.56 1.1e+04 0.63 1.5e-08 -0.38 - 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: 0:00:02.908273 Calculate final gradient and BHHH Calculate second derivatives 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. Biogeme parameters provided by the user. *** Initial values of the parameters are obtained from the file __b21_multiple_models_000005.iter Parameter values restored from __b21_multiple_models_000005.iter Starting values for the algorithm: {'asc_train_ref': -0.22042476916949647, 'asc_train_diff_male': -1.151266094199158, 'asc_train_diff_GA': 1.9592099898038795, 'b_time': -1.6961870666166756, 'lambda_time': 0.33402590778620567, 'b_cost_ref': -1.1000257376459193, 'b_cost_diff_GA': 0.9180420289202494, 'asc_car_ref': -0.42186663330205093, 'asc_car_diff_male': 0.4127085778824223, 'asc_car_diff_GA': -1.028659959596067} 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 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 1 0.28 + 1 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.5 -0.55 - 2 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.25 -0.36 - 3 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.12 0.00036 - 4 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.062 0.078 - 5 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.031 -0.041 - 6 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.016 -0.24 - 7 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.0078 -0.26 - 8 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.0039 -0.25 - 9 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.002 -0.24 - 10 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.00098 -0.24 - 11 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.00049 -0.24 - 12 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.00024 -0.24 - 13 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 0.00012 -0.24 - 14 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 6.1e-05 -0.24 - 15 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 3.1e-05 -0.24 - 16 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 1.5e-05 -0.24 - 17 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 7.6e-06 -0.24 - 18 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 3.8e-06 -0.24 - 19 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 1.9e-06 -0.24 - 20 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 9.5e-07 -0.24 - 21 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 4.8e-07 -0.24 - 22 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 2.4e-07 -0.24 - 23 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 1.2e-07 -0.24 - 24 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 6e-08 -0.24 - 25 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 3e-08 -0.24 - 26 -0.74 2.9 -2.7 -0.85 -0.28 -1.1 6.6e+03 0.17 1.5e-08 -0.24 - 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: 0:00:02.595949 Calculate final gradient and BHHH Calculate second derivatives 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. Biogeme parameters provided by the user. *** Initial values of the parameters are obtained from the file __b21_multiple_models_000006.iter Parameter values restored from __b21_multiple_models_000006.iter Starting values for the algorithm: {'asc_train_ref': -0.2611816966101033, 'asc_train_diff_male': -1.1195242784737038, 'asc_train_diff_GA': 1.985409833363222, 'b_time': -1.7053432288614183, 'lambda_time': 0.3292415317345787, 'b_cost_ref': -1.5754489476205231, 'b_cost_diff_inc-under50': -0.58809651569771, 'b_cost_diff_inc-50-100': 0.21526355869697572, 'b_cost_diff_inc-100+': 0.6292373530301496, 'b_cost_diff_inc-unknown': 0.817483132749231, 'asc_car_ref': -0.4530857199287251, 'asc_car_diff_male': 0.44854156261935, 'asc_car_diff_GA': -0.37092707884149506} 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 -0.17 -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 -0.00057 - 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 -0.05 - 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 -0.046 - 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 0.0083 - 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 0.0087 - 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 0.029 - 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 0.035 - 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 0.039 - 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 0.042 - 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 0.044 - 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 0.045 - 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: 0:00:03.157414 Calculate final gradient and BHHH Calculate second derivatives 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. Biogeme parameters provided by the user. *** Initial values of the parameters are obtained from the file __b21_multiple_models_000007.iter Parameter values restored from __b21_multiple_models_000007.iter Starting values for the algorithm: {'asc_train_ref': -0.21902546252532915, 'asc_train_diff_male': -1.1505866349098672, 'asc_train_diff_GA': 1.9563205717629264, 'b_time': -1.694875891360683, 'lambda_time': 0.334435139283056, 'b_cost': -1.0858025498414257, 'asc_car_ref': -0.4168292296137742, 'asc_car_diff_male': 0.41179043556673484, 'asc_car_diff_GA': -0.4472956477074032} 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 Optimization algorithm has converged. Relative gradient: 4.813620336140356e-06 Cause of termination: Relative gradient = 4.8e-06 <= 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: 0:00:00.717282 Calculate final gradient and BHHH Calculate second derivatives .. GENERATED FROM PYTHON SOURCE LINES 57-60 .. code-block:: Python summary, description = compile_estimation_results(all_results, use_short_names=True) print(summary) .. rst-class:: sphx-glr-script-out .. code-block:: none 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_GA (t-test) ... 1.96 (21.1) asc_car_ref (t-test) ... -0.417 (-4.23) asc_car_diff_GA (t-test) ... -0.447 (-2.19) asc_train_diff_male (t-test) ... -1.15 (-13.4) asc_car_diff_male (t-test) ... 0.412 (3.95) b_cost_ref (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) ... b_cost_diff_GA (t-test) ... [22 rows x 8 columns] .. GENERATED FROM PYTHON SOURCE LINES 61-64 .. code-block:: Python print(f'Summary table available in {CSV_FILE}') summary.to_csv(CSV_FILE, sep=SEP_CSV) .. rst-class:: sphx-glr-script-out .. code-block:: none Summary table available in b21_process_pareto.csv .. GENERATED FROM PYTHON SOURCE LINES 65-66 Explanation of the short names of the models. .. GENERATED FROM PYTHON SOURCE LINES 66-73 .. code-block:: Python 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) .. rst-class:: sphx-glr-script-out .. code-block:: none Model_000000: asc:no_seg;b_cost:no_seg;train_tt:boxcox Model_000001: asc:no_seg;b_cost:no_seg;train_tt:linear Model_000002: asc:GA;b_cost:no_seg;train_tt:boxcox Model_000003: asc:MALE-GA;b_cost:no_seg;train_tt:log Model_000004: asc:MALE-GA;b_cost:INCOME;train_tt:boxcox Model_000005: asc:GA;b_cost:no_seg;train_tt:log Model_000006: asc:MALE-GA;b_cost:GA;train_tt:boxcox Model_000007: asc:MALE-GA;b_cost:no_seg;train_tt:boxcox .. GENERATED FROM PYTHON SOURCE LINES 74-82 The following plot illustrates all models that have been estimated. Each dot corresponds to a model. The x-coordinate corresponds to the negative log-likelihood. The y-coordinate corresponds to 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. .. GENERATED FROM PYTHON SOURCE LINES 82-90 .. code-block:: Python if can_plot: try: _ = the_pareto_post.plot( label_x='Negative loglikelihood', label_y='Number of parameters' ) plt.show() except OptimizationError as e: print(f'No plot available: {e}') .. image-sg:: /auto_examples/swissmetro/images/sphx_glr_plot_b21c_process_pareto_001.png :alt: plot b21c process pareto :srcset: /auto_examples/swissmetro/images/sphx_glr_plot_b21c_process_pareto_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 29.008 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b21c_process_pareto.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b21c_process_pareto.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b21c_process_pareto.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b21c_process_pareto.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_