.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/assisted/plot_b09post_processing.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_assisted_plot_b09post_processing.py: Re-estimation of best models ============================ After running the assisted specification algorithm for the 432 specifications in :ref:`everything_spec_section`, we use post-processing to re-estimate all Pareto optimal models, and display some information about the algorithm. See `Bierlaire and Ortelli (2023) `_. Michel Bierlaire, EPFL Sun Apr 27 2025, 18:38:57 .. GENERATED FROM PYTHON SOURCE LINES 16-38 .. code-block:: Python from IPython.core.display_functions import display from biogeme.biogeme import BIOGEME from biogeme.results_processing import get_pandas_estimated_parameters try: import matplotlib.pyplot as plt can_plot = True except ModuleNotFoundError: can_plot = False import biogeme.biogeme_logging as blog from biogeme.assisted import ParetoPostProcessing from everything_spec import model_catalog, database logger = blog.get_screen_logger(level=blog.INFO) logger.info('Example b08selected_specification') PARETO_FILE_NAME = 'saved_results/b07everything_assisted.pareto' .. rst-class:: sphx-glr-script-out .. code-block:: none Example b08selected_specification .. GENERATED FROM PYTHON SOURCE LINES 39-40 Create the biogeme object from the catalog. .. GENERATED FROM PYTHON SOURCE LINES 40-43 .. code-block:: Python the_biogeme = BIOGEME(database, model_catalog) the_biogeme.model_name = 'b09post_processing' .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. .. GENERATED FROM PYTHON SOURCE LINES 44-45 Create the post-processing object. .. GENERATED FROM PYTHON SOURCE LINES 45-49 .. code-block:: Python post_processing = ParetoPostProcessing( biogeme_object=the_biogeme, pareto_file_name=PARETO_FILE_NAME ) .. rst-class:: sphx-glr-script-out .. code-block:: none Pareto set initialized from file with 162 elements [13 Pareto] and 0 invalid elements. .. GENERATED FROM PYTHON SOURCE LINES 50-51 Re-estimate the models. .. GENERATED FROM PYTHON SOURCE LINES 51-53 .. code-block:: Python all_results = post_processing.reestimate(recycle=True) .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000000 *** Initial values of the parameters are obtained from the file __b09post_processing_000000.iter Cannot read file __b09post_processing_000000.iter. Statement is ignored. Starting values for the algorithm: {} 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_travel_t b_cost_train mu_existing asc_car_ref asc_car_diff_GA b_cost_car b_cost_swissmet Function Relgrad Radius Rho 0 -0.65 0.21 -1 1.4 -0.55 1.9 0.25 -0.26 0.14 -0.64 9.8e+03 0.23 1 0.43 + 1 -0.65 0.21 -1 1.4 -0.55 1.9 0.25 -0.26 0.14 -0.64 9.8e+03 0.23 0.5 -0.7 - 2 -0.26 0.4 -0.81 1.1 -0.4 1.8 -0.25 -0.38 -0.27 -0.46 8.6e+03 0.11 0.5 0.71 + 3 -0.42 0.67 -0.98 0.7 -0.64 2.3 -0.22 -0.51 -0.25 -0.52 8.2e+03 0.011 5 0.92 ++ 4 -0.42 0.67 -0.98 0.7 -0.64 2.3 -0.22 -0.51 -0.25 -0.52 8.2e+03 0.011 0.64 -0.68 - 5 -0.24 1.1 -1.6 0.16 -0.81 1.6 -0.03 -0.34 -0.36 -0.64 8.2e+03 0.0074 0.64 0.75 + 6 -0.32 1 -1.6 0.35 -0.81 1.6 -0.083 -0.49 -0.34 -0.64 8.2e+03 0.0021 6.4 1 ++ 7 -0.34 1 -1.5 0.36 -0.81 1.6 -0.09 -0.5 -0.34 -0.64 8.2e+03 1.6e-05 64 1 ++ 8 -0.34 1 -1.5 0.36 -0.81 1.6 -0.09 -0.5 -0.34 -0.64 8.2e+03 1.6e-08 64 1 ++ Optimization algorithm has converged. Relative gradient: 1.558341176595387e-08 Cause of termination: Relative gradient = 1.6e-08 <= 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: 0:00:04.278932 Calculate second derivatives and BHHH File b09post_processing_000000.html has been generated. File b09post_processing_000000.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000001 *** Initial values of the parameters are obtained from the file __b09post_processing_000001.iter Cannot read file __b09post_processing_000001.iter. Statement is ignored. Starting values for the algorithm: {} Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time_ref b_time_diff_1st b_cost asc_car Function Relgrad Radius Rho 0 -0.75 -0.56 -0.47 -0.73 -0.27 8.7e+03 0.038 10 1.1 ++ 1 -0.71 -0.88 -0.64 -0.84 -0.0093 8.6e+03 0.0053 1e+02 1.1 ++ 2 -0.71 -0.92 -0.69 -0.87 0.0087 8.6e+03 0.00011 1e+03 1 ++ 3 -0.71 -0.92 -0.69 -0.87 0.0087 8.6e+03 7.3e-08 1e+03 1 ++ Optimization algorithm has converged. Relative gradient: 7.3355295711836e-08 Cause of termination: Relative gradient = 7.3e-08 <= 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: 0:00:00.417032 Calculate second derivatives and BHHH File b09post_processing_000001.html has been generated. File b09post_processing_000001.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000002 *** Initial values of the parameters are obtained from the file __b09post_processing_000002.iter Cannot read file __b09post_processing_000002.iter. Statement is ignored. Starting values for the algorithm: {} 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_ref b_time_diff_1st square_tt_coef cube_tt_coef b_cost_train b_cost_swissmet asc_car_ref asc_car_diff_GA b_cost_car Function Relgrad Radius Rho 0 0 0 0 0 0 0 0 0 0 0 0 1.1e+04 0.26 0.5 -1.5 - 1 0 0 0 0 0 0 0 0 0 0 0 1.1e+04 0.26 0.25 -0.051 - 2 -0.25 -0.00017 -0.25 -0.19 0 0 -0.25 0.25 0.0078 -0.023 -0.0062 9.4e+03 1.4 2.5 1 ++ 3 -0.25 -0.00017 -0.25 -0.19 0 0 -0.25 0.25 0.0078 -0.023 -0.0062 9.4e+03 1.4 1.2 -5.6 - 4 -0.25 -0.00017 -0.25 -0.19 0 0 -0.25 0.25 0.0078 -0.023 -0.0062 9.4e+03 1.4 0.62 -3 - 5 -0.25 -0.00017 -0.25 -0.19 0 0 -0.25 0.25 0.0078 -0.023 -0.0062 9.4e+03 1.4 0.31 -1.4 - 6 -0.25 -0.00017 -0.25 -0.19 0 0 -0.25 0.25 0.0078 -0.023 -0.0062 9.4e+03 1.4 0.16 0.032 - 7 -0.36 0.019 -0.41 -0.26 0.15 -0.0031 -0.36 0.21 0.041 -0.052 0.022 9.2e+03 9.1 0.16 0.54 + 8 -0.36 0.019 -0.41 -0.26 0.15 -0.0031 -0.36 0.21 0.041 -0.052 0.022 9.2e+03 9.1 0.078 0.085 - 9 -0.38 0.037 -0.48 -0.27 0.12 0.0023 -0.38 0.13 0.059 -0.07 0.042 9.1e+03 5.4 0.078 0.16 + 10 -0.38 0.037 -0.48 -0.27 0.12 0.0023 -0.38 0.13 0.059 -0.07 0.042 9.1e+03 5.4 0.039 -4.2 - 11 -0.38 0.037 -0.48 -0.27 0.12 0.0023 -0.38 0.13 0.059 -0.07 0.042 9.1e+03 5.4 0.02 -2.8 - 12 -0.38 0.037 -0.48 -0.27 0.12 0.0023 -0.38 0.13 0.059 -0.07 0.042 9.1e+03 5.4 0.0098 -2 - 13 -0.38 0.037 -0.48 -0.27 0.12 0.0023 -0.38 0.13 0.059 -0.07 0.042 9.1e+03 5.4 0.0049 -1.1 - 14 -0.39 0.042 -0.48 -0.28 0.11 -0.0026 -0.39 0.13 0.061 -0.075 0.045 9e+03 11 0.0049 0.15 + 15 -0.39 0.043 -0.48 -0.28 0.11 0.0012 -0.39 0.12 0.061 -0.076 0.045 9e+03 5.3 0.0049 0.14 + 16 -0.39 0.043 -0.48 -0.28 0.11 0.0012 -0.39 0.12 0.061 -0.076 0.045 9e+03 5.3 0.0024 -0.6 - 17 -0.39 0.046 -0.49 -0.28 0.11 -0.0013 -0.39 0.12 0.064 -0.078 0.048 8.9e+03 4.2 0.0024 0.65 + 18 -0.39 0.047 -0.49 -0.28 0.11 -0.00081 -0.39 0.12 0.064 -0.079 0.048 8.9e+03 2.4 0.024 1.3 ++ 19 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.024 0.63 + 20 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.012 -3.8 - 21 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.0061 -3.9 - 22 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.0031 -3.1 - 23 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.0015 -1.7 - 24 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.00076 -0.72 - 25 -0.4 0.056 -0.5 -0.28 0.12 -0.00053 -0.4 0.093 0.064 -0.088 0.05 8.9e+03 5.5 0.00038 -0.11 - 26 -0.4 0.056 -0.5 -0.29 0.12 -0.00091 -0.4 0.092 0.064 -0.088 0.05 8.9e+03 2.6 0.00038 0.32 + 27 -0.4 0.056 -0.5 -0.29 0.12 -0.00091 -0.4 0.092 0.064 -0.088 0.05 8.9e+03 2.6 0.00019 -0.56 - 28 -0.4 0.056 -0.5 -0.29 0.12 -0.00072 -0.4 0.092 0.063 -0.088 0.05 8.9e+03 1.9 0.00019 0.62 + 29 -0.4 0.056 -0.5 -0.29 0.12 -0.00075 -0.4 0.092 0.063 -0.088 0.05 8.9e+03 0.054 0.0019 1 ++ 30 -0.4 0.057 -0.5 -0.29 0.12 -0.00076 -0.4 0.09 0.063 -0.089 0.05 8.9e+03 0.16 0.019 1 ++ 31 -0.4 0.064 -0.51 -0.29 0.12 -0.00078 -0.41 0.071 0.063 -0.096 0.051 8.8e+03 0.051 0.19 1 ++ 32 -0.44 0.14 -0.61 -0.33 0.18 -0.001 -0.49 -0.12 0.051 -0.17 0.052 8.7e+03 0.12 1.9 0.99 ++ 33 -0.44 0.14 -0.61 -0.33 0.18 -0.001 -0.49 -0.12 0.051 -0.17 0.052 8.7e+03 0.12 0.95 -67 - 34 -0.44 0.14 -0.61 -0.33 0.18 -0.001 -0.49 -0.12 0.051 -0.17 0.052 8.7e+03 0.12 0.48 -3.4 - 35 -0.5 0.57 -0.82 -0.41 -0.011 -0.00022 -0.82 -0.6 -0.33 -0.5 -0.22 8.4e+03 0.32 0.48 0.89 + 36 -0.65 1 -1.2 -0.61 -0.022 -0.00017 -1.1 -0.85 -0.41 -0.72 -0.29 8.2e+03 0.15 4.8 1.1 ++ 37 -0.65 1 -1.2 -0.61 -0.022 -0.00017 -1.1 -0.85 -0.41 -0.72 -0.29 8.2e+03 0.15 2.4 -3.2e+02 - 38 -0.65 1 -1.2 -0.61 -0.022 -0.00017 -1.1 -0.85 -0.41 -0.72 -0.29 8.2e+03 0.15 1.2 -1.1e+02 - 39 -0.65 1 -1.2 -0.61 -0.022 -0.00017 -1.1 -0.85 -0.41 -0.72 -0.29 8.2e+03 0.15 0.6 -22 - 40 -0.65 1 -1.2 -0.61 -0.022 -0.00017 -1.1 -0.85 -0.41 -0.72 -0.29 8.2e+03 0.15 0.3 -3.1 - 41 -0.65 1 -1.2 -0.61 -0.022 -0.00017 -1.1 -0.85 -0.41 -0.72 -0.29 8.2e+03 0.15 0.15 0.054 - 42 -0.77 1.1 -1.3 -0.69 -0.095 0.00018 -1.2 -0.78 -0.39 -0.75 -0.3 8.2e+03 8.8 0.15 0.74 + 43 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.15 0.59 + 44 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.075 -0.81 - 45 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.037 -0.61 - 46 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.019 -0.48 - 47 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.0093 -0.52 - 48 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.0047 -0.51 - 49 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.0023 -0.36 - 50 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.0012 -0.31 - 51 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.00058 -0.3 - 52 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.00029 -0.29 - 53 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 0.00015 -0.29 - 54 -0.69 1.2 -1.5 -0.75 -0.08 1.6e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.2e+03 14 7.3e-05 -0.29 - 55 -0.69 1.2 -1.5 -0.75 -0.079 8.9e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.1e+03 8.3 7.3e-05 0.62 + 56 -0.69 1.2 -1.5 -0.75 -0.08 7e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.1e+03 2 7.3e-05 0.81 + 57 -0.69 1.2 -1.5 -0.75 -0.08 7.4e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.1e+03 0.071 0.00073 0.98 ++ 58 -0.69 1.2 -1.5 -0.75 -0.08 7.7e-05 -1.1 -0.87 -0.41 -0.8 -0.34 8.1e+03 0.015 0.0073 1 ++ 59 -0.7 1.2 -1.5 -0.75 -0.086 0.0001 -1.2 -0.87 -0.4 -0.8 -0.34 8.1e+03 0.14 0.073 0.99 ++ 60 -0.74 1.2 -1.5 -0.78 -0.096 0.00015 -1.2 -0.85 -0.38 -0.81 -0.33 8.1e+03 1.9 0.73 1 ++ 61 -0.73 1.4 -1.8 -0.77 -0.11 0.00019 -1.1 -0.86 -0.31 -1 -0.33 8.1e+03 1.9 7.3 0.99 ++ 62 -0.72 1.4 -1.8 -0.77 -0.1 0.00019 -1.1 -0.86 -0.3 -1 -0.32 8.1e+03 0.035 73 1 ++ 63 -0.72 1.4 -1.8 -0.77 -0.1 0.00019 -1.1 -0.86 -0.3 -1 -0.32 8.1e+03 7.9e-05 7.3e+02 1 ++ 64 -0.72 1.4 -1.8 -0.77 -0.1 0.00019 -1.1 -0.86 -0.3 -1 -0.32 8.1e+03 8e-08 7.3e+02 1 ++ Optimization algorithm has converged. Relative gradient: 7.973438777139777e-08 Cause of termination: Relative gradient = 8e-08 <= 6.1e-06 Number of function evaluations: 122 Number of gradient evaluations: 57 Number of hessian evaluations: 28 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 65 Proportion of Hessian calculation: 28/28 = 100.0% Optimization time: 0:00:00.985973 Calculate second derivatives and BHHH File b09post_processing_000002.html has been generated. File b09post_processing_000002.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000003 *** Initial values of the parameters are obtained from the file __b09post_processing_000003.iter Cannot read file __b09post_processing_000003.iter. Statement is ignored. Starting values for the algorithm: {} 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_ asc_train_diff_ b_time square_tt_coef cube_tt_coef b_cost_train mu_existing asc_car_ref asc_car_diff_GA asc_car_diff_on asc_car_diff_se b_cost_car b_cost_swissmet Function Relgrad Radius Rho 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.1e+04 0.26 0.5 -2.7 - 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.1e+04 0.26 0.25 -0.39 - 2 -0.25 -0.0003 -0.25 -0.0098 -0.25 0 0 -0.25 1.2 0.013 -0.039 -0.011 -0.0031 -0.011 0.25 9.3e+03 2.1 2.5 1 ++ 3 -0.25 -0.0003 -0.25 -0.0098 -0.25 0 0 -0.25 1.2 0.013 -0.039 -0.011 -0.0031 -0.011 0.25 9.3e+03 2.1 1.2 1 - 4 -0.25 -0.0003 -0.25 -0.0098 -0.25 0 0 -0.25 1.2 0.013 -0.039 -0.011 -0.0031 -0.011 0.25 9.3e+03 2.1 0.62 1 - 5 -0.25 -0.0003 -0.25 -0.0098 -0.25 0 0 -0.25 1.2 0.013 -0.039 -0.011 -0.0031 -0.011 0.25 9.3e+03 2.1 0.31 -1.7 - 6 -0.25 -0.0003 -0.25 -0.0098 -0.25 0 0 -0.25 1.2 0.013 -0.039 -0.011 -0.0031 -0.011 0.25 9.3e+03 2.1 0.16 -0.12 - 7 -0.32 0.037 -0.25 -0.011 -0.41 0.11 -0.0031 -0.35 1.3 0.047 -0.076 -0.018 -0.0056 0.017 0.18 9.2e+03 11 0.16 0.3 + 8 -0.32 0.037 -0.25 -0.011 -0.41 0.11 -0.0031 -0.35 1.3 0.047 -0.076 -0.018 -0.0056 0.017 0.18 9.2e+03 11 0.078 -0.51 - 9 -0.32 0.037 -0.25 -0.011 -0.41 0.11 -0.0031 -0.35 1.3 0.047 -0.076 -0.018 -0.0056 0.017 0.18 9.2e+03 11 0.039 -0.42 - 10 -0.32 0.037 -0.25 -0.011 -0.41 0.11 -0.0031 -0.35 1.3 0.047 -0.076 -0.018 -0.0056 0.017 0.18 9.2e+03 11 0.02 -0.36 - 11 -0.32 0.037 -0.25 -0.011 -0.41 0.11 -0.0031 -0.35 1.3 0.047 -0.076 -0.018 -0.0056 0.017 0.18 9.2e+03 11 0.0098 -0.34 - 12 -0.32 0.037 -0.25 -0.011 -0.41 0.11 -0.0031 -0.35 1.3 0.047 -0.076 -0.018 -0.0056 0.017 0.18 9.2e+03 11 0.0049 -0.32 - 13 -0.32 0.042 -0.24 -0.01 -0.4 0.11 0.0018 -0.35 1.3 0.045 -0.081 -0.023 -0.0096 0.02 0.17 9.1e+03 5.3 0.0049 0.17 + 14 -0.32 0.042 -0.24 -0.01 -0.4 0.11 0.0018 -0.35 1.3 0.045 -0.081 -0.023 -0.0096 0.02 0.17 9.1e+03 5.3 0.0024 -0.18 - 15 -0.32 0.044 -0.24 -0.0097 -0.4 0.11 -0.00066 -0.35 1.3 0.046 -0.084 -0.026 -0.012 0.021 0.17 9e+03 2.7 0.024 0.99 ++ 16 -0.32 0.055 -0.23 -0.0095 -0.42 0.12 -0.00076 -0.36 1.3 0.045 -0.093 -0.032 -0.013 0.021 0.14 8.9e+03 0.55 0.24 1 ++ 17 -0.3 0.17 -0.12 -0.0078 -0.57 0.22 -0.0011 -0.44 1.4 0.036 -0.18 -0.097 -0.02 0.015 -0.1 8.6e+03 0.52 2.4 0.97 ++ 18 -0.3 0.17 -0.12 -0.0078 -0.57 0.22 -0.0011 -0.44 1.4 0.036 -0.18 -0.097 -0.02 0.015 -0.1 8.6e+03 0.52 1.2 0.97 - 19 -0.3 0.17 -0.12 -0.0078 -0.57 0.22 -0.0011 -0.44 1.4 0.036 -0.18 -0.097 -0.02 0.015 -0.1 8.6e+03 0.52 0.61 -33 - 20 -0.43 0.72 0.27 0.013 -0.93 -0.11 0.0002 -0.93 2 -0.17 -0.58 -0.31 -0.077 -0.18 -0.64 8.5e+03 7.3 0.61 0.3 + 21 -0.47 0.59 0.16 0.029 -1.5 -0.034 -0.00011 -0.63 1.9 -0.18 -0.48 -0.051 -0.11 -0.31 -0.68 8.2e+03 7.8 0.61 0.68 + 22 -0.47 0.59 0.16 0.029 -1.5 -0.034 -0.00011 -0.63 1.9 -0.18 -0.48 -0.051 -0.11 -0.31 -0.68 8.2e+03 7.8 0.31 -5.7 - 23 -0.47 0.59 0.16 0.029 -1.5 -0.034 -0.00011 -0.63 1.9 -0.18 -0.48 -0.051 -0.11 -0.31 -0.68 8.2e+03 7.8 0.15 -2.8 - 24 -0.47 0.59 0.16 0.029 -1.5 -0.034 -0.00011 -0.63 1.9 -0.18 -0.48 -0.051 -0.11 -0.31 -0.68 8.2e+03 7.8 0.076 -0.71 - 25 -0.49 0.6 0.16 0.03 -1.6 -0.11 0.00021 -0.66 2 -0.17 -0.48 -0.05 -0.11 -0.3 -0.65 8.1e+03 19 0.076 0.65 + 26 -0.49 0.67 0.23 0.039 -1.6 -0.1 0.00017 -0.72 2 -0.15 -0.48 -0.06 -0.12 -0.26 -0.59 8.1e+03 0.71 0.76 1 ++ 27 -0.6 0.92 0.34 0.19 -2 -0.11 0.00019 -0.81 1.5 -0.16 -0.45 -0.057 -0.31 -0.27 -0.68 8.1e+03 1 0.76 0.87 + 28 -0.59 0.9 0.35 0.22 -2 -0.11 0.0002 -0.79 1.6 -0.17 -0.46 -0.063 -0.36 -0.24 -0.67 8.1e+03 0.27 7.6 1 ++ 29 -0.59 0.9 0.35 0.22 -2 -0.11 0.0002 -0.78 1.6 -0.17 -0.45 -0.063 -0.37 -0.24 -0.66 8.1e+03 0.0069 76 1 ++ 30 -0.59 0.9 0.35 0.21 -2 -0.11 0.0002 -0.78 1.6 -0.17 -0.45 -0.063 -0.37 -0.24 -0.66 8.1e+03 0.081 7.6e+02 1 ++ 31 -0.59 0.9 0.35 0.21 -2 -0.11 0.0002 -0.78 1.6 -0.17 -0.45 -0.063 -0.37 -0.24 -0.66 8.1e+03 0.0051 7.6e+03 1 ++ 32 -0.59 0.9 0.35 0.21 -2 -0.11 0.0002 -0.78 1.6 -0.17 -0.45 -0.063 -0.38 -0.24 -0.66 8.1e+03 0.00066 7.6e+04 1 ++ 33 -0.59 0.9 0.35 0.21 -2 -0.11 0.0002 -0.78 1.6 -0.17 -0.45 -0.063 -0.38 -0.24 -0.66 8.1e+03 5.8e-06 7.6e+04 1 ++ Optimization algorithm has converged. Relative gradient: 5.817355202609906e-06 Cause of termination: Relative gradient = 5.8e-06 <= 6.1e-06 Number of function evaluations: 69 Number of gradient evaluations: 35 Number of hessian evaluations: 17 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 34 Proportion of Hessian calculation: 17/17 = 100.0% Optimization time: 0:00:03.824482 Calculate second derivatives and BHHH File b09post_processing_000003.html has been generated. File b09post_processing_000003.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000004 *** Initial values of the parameters are obtained from the file __b09post_processing_000004.iter Cannot read file __b09post_processing_000004.iter. Statement is ignored. Starting values for the algorithm: {} 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 -0.76 -0.77 -0.7 -0.29 8.8e+03 0.04 10 1.1 ++ 1 -0.66 -1.2 -0.77 -0.0015 8.7e+03 0.0064 1e+02 1.1 ++ 2 -0.65 -1.3 -0.79 0.016 8.7e+03 0.00012 1e+03 1 ++ 3 -0.65 -1.3 -0.79 0.016 8.7e+03 4e-08 1e+03 1 ++ Optimization algorithm has converged. Relative gradient: 3.954408093567457e-08 Cause of termination: Relative gradient = 4e-08 <= 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: 0:00:00.333908 Calculate second derivatives and BHHH File b09post_processing_000004.html has been generated. File b09post_processing_000004.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000005 *** Initial values of the parameters are obtained from the file __b09post_processing_000005.iter Cannot read file __b09post_processing_000005.iter. Statement is ignored. Starting values for the algorithm: {} Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. Function Relgrad Radius Rho 0 1.1e+04 0.4 0.5 -0.56 - 1 1e+04 1.5 0.5 0.2 + 2 1e+04 1.5 0.25 0.2 - 3 1e+04 1.5 0.12 0.2 - 4 1e+04 1.5 0.062 -4.2 - 5 9.9e+03 7.1 0.062 0.48 + 6 9.9e+03 7.1 0.031 0.0017 - 7 9.6e+03 1.2 0.031 0.12 + 8 9.6e+03 1.2 0.016 -0.32 - 9 9.3e+03 0.58 0.16 0.92 ++ 10 9.3e+03 0.58 0.078 0.92 - 11 9.3e+03 0.58 0.039 -15 - 12 9.3e+03 0.58 0.02 -16 - 13 9.3e+03 0.58 0.0098 -6.7 - 14 9.3e+03 3.5 0.0098 0.56 + 15 9.3e+03 0.11 0.0098 0.88 + 16 9.2e+03 0.44 0.098 0.97 ++ 17 9.1e+03 0.41 0.98 1 ++ 18 9.1e+03 0.41 0.49 -0.77 - 19 8.7e+03 10 0.49 0.45 + 20 8.7e+03 10 0.24 0.45 - 21 8.7e+03 10 0.12 0.45 - 22 8.7e+03 10 0.061 0.45 - 23 8.7e+03 10 0.031 0.45 - 24 8.7e+03 10 0.015 0.45 - 25 8.7e+03 10 0.0076 0.45 - 26 8.7e+03 10 0.0038 -1.7 - 27 8.7e+03 10 0.0019 -1.1 - 28 8.7e+03 10 0.00095 -0.63 - 29 8.7e+03 10 0.00048 -0.36 - 30 8.7e+03 10 0.00024 -0.065 - 31 8.7e+03 6.6 0.00024 0.51 + 32 8.7e+03 7.8 0.00024 0.3 + 33 8.7e+03 1.4 0.00024 0.85 + 34 8.7e+03 0.19 0.0024 1 ++ 35 8.7e+03 1.2 0.024 1 ++ 36 8.6e+03 0.16 0.24 1 ++ 37 8.3e+03 0.89 0.24 0.62 + 38 8.2e+03 0.22 2.4 0.98 ++ 39 8.1e+03 0.091 24 1.1 ++ 40 8.1e+03 0.77 24 0.75 + 41 8e+03 0.5 2.4e+02 1.1 ++ 42 8e+03 0.5 1.2e+02 1.1 - 43 8e+03 0.5 60 1.1 - 44 8e+03 0.5 30 1.1 - 45 8e+03 0.5 15 1.1 - 46 8e+03 0.5 7.5 1.1 - 47 8e+03 0.5 3.7 1.1 - 48 8e+03 0.5 1.9 -4.9e+02 - 49 8e+03 0.5 0.93 -2e+02 - 50 8e+03 0.5 0.47 -19 - 51 8e+03 0.5 0.23 -1.2 - 52 8e+03 2.4 0.23 0.72 + 53 8e+03 3.2 2.3 1 ++ 54 8e+03 3.2 0.39 -3.9 - 55 8e+03 2.4 0.39 0.47 + 56 8e+03 8.4 3.9 0.94 ++ 57 8e+03 0.1 39 1 ++ 58 8e+03 0.00059 3.9e+02 1 ++ 59 8e+03 9.3e-06 3.9e+03 1 ++ 60 8e+03 3.1e-06 3.9e+03 1 ++ Optimization algorithm has converged. Relative gradient: 3.120917028152968e-06 Cause of termination: Relative gradient = 3.1e-06 <= 6.1e-06 Number of function evaluations: 118 Number of gradient evaluations: 57 Number of hessian evaluations: 28 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 61 Proportion of Hessian calculation: 28/28 = 100.0% Optimization time: 0:00:07.476546 Calculate second derivatives and BHHH File b09post_processing_000005.html has been generated. File b09post_processing_000005.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000006 *** Initial values of the parameters are obtained from the file __b09post_processing_000006.iter Cannot read file __b09post_processing_000006.iter. Statement is ignored. Starting values for the algorithm: {} 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_ref b_time_diff_1st b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.93 1 -0.56 -0.4 -0.66 -0.29 -0.4 8.5e+03 0.041 10 1.1 ++ 1 -1.1 1.4 -0.84 -0.56 -0.75 -0.01 -1.1 8.3e+03 0.0076 1e+02 1.1 ++ 2 -1.2 1.5 -0.87 -0.62 -0.78 0.0051 -1.2 8.3e+03 0.00034 1e+03 1 ++ 3 -1.2 1.5 -0.87 -0.62 -0.78 0.0051 -1.2 8.3e+03 6.4e-07 1e+03 1 ++ Optimization algorithm has converged. Relative gradient: 6.381936270565892e-07 Cause of termination: Relative gradient = 6.4e-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: 0:00:00.493179 Calculate second derivatives and BHHH File b09post_processing_000006.html has been generated. File b09post_processing_000006.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000007 *** Initial values of the parameters are obtained from the file __b09post_processing_000007.iter Cannot read file __b09post_processing_000007.iter. Statement is ignored. Starting values for the algorithm: {} 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_ref b_time_diff_com square_tt_coef cube_tt_coef b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 0 0 0 0 0 0 0 0 0 1.1e+04 0.26 0.5 -0.12 - 1 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 5 1.1 ++ 2 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 2.5 -4.7 - 3 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 1.2 -4.3 - 4 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.62 -3.9 - 5 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.31 -3.6 - 6 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.16 -3.5 - 7 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.078 -3.7 - 8 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.039 -4.1 - 9 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.02 -4.3 - 10 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.0098 -3.1 - 11 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.0049 -2.4 - 12 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.0024 -2 - 13 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.0012 -1.5 - 14 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.00061 -0.87 - 15 -0.5 -0.0018 -0.5 -0.5 0 0 -0.41 0.082 -0.24 9.1e+03 9.7 0.00031 -0.074 - 16 -0.5 -0.0015 -0.5 -0.5 0.00031 -0.00031 -0.41 0.081 -0.24 9.1e+03 6.1 0.00031 0.69 + 17 -0.5 -0.0015 -0.5 -0.5 0.00031 -0.00031 -0.41 0.081 -0.24 9.1e+03 6.1 0.00015 -1.3 - 18 -0.5 -0.0015 -0.5 -0.5 0.00031 -0.00031 -0.41 0.081 -0.24 9.1e+03 6.1 7.6e-05 -0.74 - 19 -0.5 -0.0014 -0.5 -0.5 0.00038 -0.00023 -0.41 0.081 -0.24 9.1e+03 5.6 7.6e-05 0.4 + 20 -0.5 -0.0014 -0.5 -0.5 0.00046 -0.00026 -0.41 0.081 -0.24 9.1e+03 1.3 7.6e-05 0.84 + 21 -0.5 -0.0014 -0.5 -0.5 0.00053 -0.00025 -0.41 0.081 -0.24 9.1e+03 0.14 0.00076 0.99 ++ 22 -0.5 -0.0013 -0.5 -0.5 0.0013 -0.00026 -0.41 0.081 -0.24 9.1e+03 0.35 0.0076 1 ++ 23 -0.5 -0.00013 -0.51 -0.5 0.0089 -0.00029 -0.41 0.079 -0.24 9.1e+03 0.14 0.076 1 ++ 24 -0.54 0.012 -0.57 -0.51 0.085 -0.0006 -0.42 0.064 -0.24 8.9e+03 0.53 0.76 0.98 ++ 25 -0.72 0.77 -0.95 -0.3 0.13 -0.00078 -0.82 0.03 -0.55 8.4e+03 9.1 7.6 1 ++ 26 -0.72 0.77 -0.95 -0.3 0.13 -0.00078 -0.82 0.03 -0.55 8.4e+03 9.1 3.8 -1.2e+02 - 27 -0.72 0.77 -0.95 -0.3 0.13 -0.00078 -0.82 0.03 -0.55 8.4e+03 9.1 1.9 -1e+02 - 28 -0.72 0.77 -0.95 -0.3 0.13 -0.00078 -0.82 0.03 -0.55 8.4e+03 9.1 0.95 -70 - 29 -0.72 0.77 -0.95 -0.3 0.13 -0.00078 -0.82 0.03 -0.55 8.4e+03 9.1 0.48 -15 - 30 -0.72 0.77 -0.95 -0.3 0.13 -0.00078 -0.82 0.03 -0.55 8.4e+03 9.1 0.24 -2.2 - 31 -0.96 0.95 -1.2 -0.29 -0.096 0.00012 -0.7 -0.0011 -0.62 8.4e+03 17 0.24 0.43 + 32 -1 1.1 -1.4 -0.34 -0.073 6.6e-05 -0.68 -0.066 -0.66 8.3e+03 10 2.4 0.94 ++ 33 -1 1.1 -1.4 -0.34 -0.073 6.6e-05 -0.68 -0.066 -0.66 8.3e+03 10 0.62 -4 - 34 -0.93 1.7 -1.9 -0.54 -0.11 0.00021 -0.76 0.11 -0.87 8.2e+03 38 0.62 0.71 + 35 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.62 0.62 + 36 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.087 -2.1 - 37 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.044 -1.9 - 38 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.022 -2 - 39 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.011 -1.9 - 40 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.0055 -1.8 - 41 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.0027 -1.8 - 42 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.0014 -1.8 - 43 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.00068 -1.7 - 44 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.00034 -1.7 - 45 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 0.00017 -1.6 - 46 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 8.5e-05 -1.6 - 47 -0.82 1.6 -2.1 -1.2 -0.1 0.00022 -0.69 0.21 -1.2 8.2e+03 27 4.3e-05 -1.2 - 48 -0.82 1.6 -2.1 -1.2 -0.1 0.00018 -0.69 0.21 -1.2 8.2e+03 26 4.3e-05 0.55 + 49 -0.82 1.6 -2.1 -1.2 -0.1 0.00019 -0.69 0.21 -1.2 8.2e+03 0.64 0.00043 0.95 ++ 50 -0.82 1.6 -2.1 -1.2 -0.1 0.00019 -0.69 0.21 -1.2 8.2e+03 0.033 0.0043 1 ++ 51 -0.83 1.6 -2.1 -1.2 -0.11 0.00021 -0.7 0.21 -1.2 8.2e+03 0.55 0.043 0.99 ++ 52 -0.87 1.6 -2.1 -1.2 -0.11 0.00021 -0.72 0.18 -1.2 8.2e+03 0.091 0.43 1 ++ 53 -0.9 1.6 -2 -1.2 -0.11 0.0002 -0.71 0.17 -1.3 8.2e+03 0.14 4.3 1 ++ 54 -0.9 1.6 -2 -1.2 -0.11 0.0002 -0.71 0.17 -1.3 8.2e+03 0.021 43 1 ++ 55 -0.9 1.6 -2 -1.2 -0.11 0.0002 -0.71 0.17 -1.3 8.2e+03 0.0096 4.3e+02 1 ++ 56 -0.9 1.6 -2 -1.2 -0.11 0.0002 -0.71 0.17 -1.3 8.2e+03 0.0092 4.3e+03 1 ++ 57 -0.9 1.6 -2 -1.2 -0.11 0.0002 -0.71 0.17 -1.3 8.2e+03 3.9e-07 4.3e+03 1 ++ Optimization algorithm has converged. Relative gradient: 3.897850964533427e-07 Cause of termination: Relative gradient = 3.9e-07 <= 6.1e-06 Number of function evaluations: 105 Number of gradient evaluations: 47 Number of hessian evaluations: 23 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 58 Proportion of Hessian calculation: 23/23 = 100.0% Optimization time: 0:00:02.862128 Calculate second derivatives and BHHH File b09post_processing_000007.html has been generated. File b09post_processing_000007.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000008 *** Initial values of the parameters are obtained from the file __b09post_processing_000008.iter Cannot read file __b09post_processing_000008.iter. Statement is ignored. Starting values for the algorithm: {} 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_train b_cost_swissmet asc_car b_cost_car Function Relgrad Radius Rho 0 -0.59 -0.75 -0.92 -0.69 -0.42 -0.57 8.7e+03 0.053 10 1.1 ++ 1 -0.19 -1.2 -1.5 -0.78 -0.39 -0.39 8.5e+03 0.021 1e+02 1.2 ++ 2 -0.064 -1.3 -1.9 -0.82 -0.41 -0.38 8.4e+03 0.0039 1e+03 1.1 ++ 3 -0.046 -1.3 -1.9 -0.82 -0.42 -0.38 8.4e+03 0.00012 1e+04 1 ++ 4 -0.046 -1.3 -1.9 -0.82 -0.42 -0.38 8.4e+03 1e-07 1e+04 1 ++ Optimization algorithm has converged. Relative gradient: 1.0424282105589559e-07 Cause of termination: Relative gradient = 1e-07 <= 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: 0:00:00.340770 Calculate second derivatives and BHHH File b09post_processing_000008.html has been generated. File b09post_processing_000008.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000009 *** Initial values of the parameters are obtained from the file __b09post_processing_000009.iter Cannot read file __b09post_processing_000009.iter. Statement is ignored. Starting values for the algorithm: {} 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_ref b_time_diff_com square_tt_coef cube_tt_coef b_cost_train mu_existing asc_car_ref asc_car_diff_GA b_cost_car b_cost_swissmet Function Relgrad Radius Rho 0 0 0 0 0 0 0 0 1 0 0 0 0 1.1e+04 0.26 0.5 -2.9 - 1 0 0 0 0 0 0 0 1 0 0 0 0 1.1e+04 0.26 0.25 -0.22 - 2 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 2.5 1 ++ 3 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 1.2 1 - 4 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.62 1 - 5 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.31 1 - 6 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.16 1 - 7 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.078 1 - 8 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.039 -3 - 9 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.02 -3.4 - 10 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.0098 -3.7 - 11 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.0049 -4.2 - 12 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.0024 -2.3 - 13 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.0012 -1.6 - 14 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.00061 -0.94 - 15 -0.25 -0.0082 -0.25 -0.25 0 0 -0.25 1.2 0.25 -0.25 -0.025 0.25 9.2e+03 5.6 0.00031 -0.17 - 16 -0.25 -0.0079 -0.25 -0.25 0.00031 -0.00031 -0.25 1.3 0.25 -0.25 -0.025 0.25 9.2e+03 3.7 0.00031 0.63 + 17 -0.25 -0.0079 -0.25 -0.25 0.00051 -0.00021 -0.25 1.3 0.25 -0.25 -0.025 0.25 9.2e+03 2.9 0.00031 0.56 + 18 -0.25 -0.0078 -0.25 -0.25 0.00072 -0.00026 -0.25 1.3 0.25 -0.25 -0.025 0.25 9.2e+03 0.6 0.0031 0.92 ++ 19 -0.25 -0.0073 -0.25 -0.25 0.0028 -0.00026 -0.25 1.3 0.25 -0.25 -0.026 0.25 9.2e+03 0.1 0.031 1 ++ 20 -0.27 -0.0022 -0.28 -0.25 0.024 -0.00035 -0.27 1.3 0.24 -0.26 -0.03 0.25 9.1e+03 0.5 0.31 1 ++ 21 -0.4 0.058 -0.59 -0.29 0.23 -0.0012 -0.43 1.4 0.2 -0.33 -0.07 0.19 8.9e+03 1.9 0.31 0.55 + 22 -0.29 0.17 -0.59 -0.26 0.1 -0.00065 -0.42 1.5 0.13 -0.42 -0.097 -0.11 8.5e+03 0.3 3.1 0.9 ++ 23 -0.54 1 -0.98 -0.48 -0.13 0.00028 -0.68 1.8 -0.26 -0.43 -0.27 -0.56 8.3e+03 26 3.1 0.74 + 24 -0.54 1 -0.98 -0.48 -0.13 0.00028 -0.68 1.8 -0.26 -0.43 -0.27 -0.56 8.3e+03 26 0.88 -2.2 - 25 -0.54 1 -0.98 -0.48 -0.13 0.00028 -0.68 1.8 -0.26 -0.43 -0.27 -0.56 8.3e+03 26 0.44 -0.096 - 26 -0.6 0.94 -1.4 -0.57 -0.062 2.6e-05 -0.64 1.9 -0.26 -0.41 -0.3 -0.58 8.2e+03 27 0.44 0.55 + 27 -0.6 0.94 -1.4 -0.57 -0.062 2.6e-05 -0.64 1.9 -0.26 -0.41 -0.3 -0.58 8.2e+03 27 0.22 -3.7 - 28 -0.6 0.94 -1.4 -0.57 -0.062 2.6e-05 -0.64 1.9 -0.26 -0.41 -0.3 -0.58 8.2e+03 27 0.11 -1.6 - 29 -0.6 0.94 -1.4 -0.57 -0.062 2.6e-05 -0.64 1.9 -0.26 -0.41 -0.3 -0.58 8.2e+03 27 0.055 -0.51 - 30 -0.59 0.94 -1.4 -0.57 -0.12 0.00023 -0.64 1.9 -0.26 -0.41 -0.29 -0.59 8.1e+03 43 0.055 0.39 + 31 -0.53 0.96 -1.4 -0.58 -0.092 0.00014 -0.62 1.9 -0.26 -0.41 -0.28 -0.63 8.1e+03 14 0.055 0.88 + 32 -0.53 0.97 -1.5 -0.59 -0.1 0.00017 -0.65 1.9 -0.25 -0.41 -0.27 -0.6 8.1e+03 3.2 0.55 0.96 ++ 33 -0.37 1 -1.9 -0.91 -0.11 0.0002 -0.86 1.5 -0.16 -0.53 -0.31 -0.69 8.1e+03 3.7 5.5 0.91 ++ 34 -0.36 1 -1.9 -0.93 -0.11 0.0002 -0.82 1.5 -0.17 -0.56 -0.27 -0.67 8.1e+03 0.76 55 1 ++ 35 -0.35 1 -1.9 -0.93 -0.11 0.0002 -0.82 1.6 -0.17 -0.56 -0.27 -0.66 8.1e+03 0.019 5.5e+02 1 ++ 36 -0.35 1 -1.9 -0.93 -0.11 0.0002 -0.82 1.6 -0.17 -0.55 -0.27 -0.66 8.1e+03 1.8e-05 5.5e+03 1 ++ 37 -0.35 1 -1.9 -0.93 -0.11 0.0002 -0.82 1.6 -0.17 -0.55 -0.27 -0.66 8.1e+03 8.4e-05 5.5e+04 1 ++ 38 -0.35 1 -1.9 -0.93 -0.11 0.0002 -0.82 1.6 -0.17 -0.55 -0.27 -0.66 8.1e+03 9.9e-07 5.5e+04 1 ++ Optimization algorithm has converged. Relative gradient: 9.9074111913857e-07 Cause of termination: Relative gradient = 9.9e-07 <= 6.1e-06 Number of function evaluations: 78 Number of gradient evaluations: 39 Number of hessian evaluations: 19 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 39 Proportion of Hessian calculation: 19/19 = 100.0% Optimization time: 0:00:03.075296 Calculate second derivatives and BHHH File b09post_processing_000009.html has been generated. File b09post_processing_000009.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000010 *** Initial values of the parameters are obtained from the file __b09post_processing_000010.iter Cannot read file __b09post_processing_000010.iter. Statement is ignored. Starting values for the algorithm: {} Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. Function Relgrad Radius Rho 0 8.6e+03 0.055 1 0.68 + 1 8.6e+03 0.13 1 0.15 + 2 8.6e+03 0.13 0.5 -0.35 - 3 8.1e+03 0.014 5 0.98 ++ 4 8.1e+03 0.014 0.91 -1.3 - 5 8.1e+03 0.021 9.1 0.91 ++ 6 8e+03 0.0027 91 1.1 ++ 7 8e+03 0.00081 9.1e+02 1 ++ 8 8e+03 4.3e-06 9.1e+02 1 ++ Optimization algorithm has converged. Relative gradient: 4.3017252378782595e-06 Cause of termination: Relative gradient = 4.3e-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: 0:00:05.560448 Calculate second derivatives and BHHH File b09post_processing_000010.html has been generated. File b09post_processing_000010.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000011 *** Initial values of the parameters are obtained from the file __b09post_processing_000011.iter Cannot read file __b09post_processing_000011.iter. Statement is ignored. Starting values for the algorithm: {} Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. Function Relgrad Radius Rho 0 9.1e+03 0.25 1 0.7 + 1 8.5e+03 0.12 1 0.54 + 2 8.2e+03 0.034 1 0.83 + 3 8.1e+03 0.017 1 0.66 + 4 8.1e+03 0.0038 10 1 ++ 5 8.1e+03 0.0053 10 0.88 + 6 8.1e+03 5.8e-05 1e+02 1 ++ 7 8.1e+03 6.3e-07 1e+02 1 ++ Optimization algorithm has converged. Relative gradient: 6.345269858865713e-07 Cause of termination: Relative gradient = 6.3e-07 <= 6.1e-06 Number of function evaluations: 25 Number of gradient evaluations: 17 Number of hessian evaluations: 8 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 8 Proportion of Hessian calculation: 8/8 = 100.0% Optimization time: 0:00:02.639345 Calculate second derivatives and BHHH File b09post_processing_000011.html has been generated. File b09post_processing_000011.yaml has been generated. Biogeme parameters provided by the user. No yaml file has been found for model b09post_processing_000012 *** Initial values of the parameters are obtained from the file __b09post_processing_000012.iter Cannot read file __b09post_processing_000012.iter. Statement is ignored. Starting values for the algorithm: {} Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. Function Relgrad Radius Rho 0 9.2e+03 0.2 1 0.61 + 1 9.2e+03 0.2 0.5 -0.84 - 2 9.1e+03 0.24 0.5 0.11 + 3 8.5e+03 0.099 0.5 0.54 + 4 8.3e+03 0.085 0.5 0.65 + 5 8.1e+03 0.012 5 1 ++ 6 8.1e+03 0.012 1.2 -2.8 - 7 8.1e+03 0.022 12 0.93 ++ 8 8e+03 0.007 1.2e+02 1.2 ++ 9 8e+03 0.0023 1.2e+03 1.1 ++ 10 8e+03 0.00012 1.2e+04 1 ++ 11 8e+03 1.4e-06 1.2e+04 1 ++ Optimization algorithm has converged. Relative gradient: 1.3617002739334765e-06 Cause of termination: Relative gradient = 1.4e-06 <= 6.1e-06 Number of function evaluations: 33 Number of gradient evaluations: 21 Number of hessian evaluations: 10 Algorithm: Newton with trust region for simple bound constraints Number of iterations: 12 Proportion of Hessian calculation: 10/10 = 100.0% Optimization time: 0:00:08.464501 Calculate second derivatives and BHHH File b09post_processing_000012.html has been generated. File b09post_processing_000012.yaml has been generated. .. GENERATED FROM PYTHON SOURCE LINES 54-55 We retrieve the first estimation results for illustration. .. GENERATED FROM PYTHON SOURCE LINES 55-57 .. code-block:: Python spec, results = next(iter(all_results.items())) .. GENERATED FROM PYTHON SOURCE LINES 58-60 .. code-block:: Python print(spec) .. rst-class:: sphx-glr-script-out .. code-block:: none asc:GA;b_cost_gen_altspec:altspec;b_time:no_seg;b_time_gen_altspec:generic;model_catalog:nested existing;train_tt_catalog:boxcox .. GENERATED FROM PYTHON SOURCE LINES 61-63 .. code-block:: Python print(results.short_summary()) .. rst-class:: sphx-glr-script-out .. code-block:: none Results for model b09post_processing_000000 Nbr of parameters: 10 Sample size: 10719 Excluded data: 9 Final log likelihood: -8159.232 Akaike Information Criterion: 16338.46 Bayesian Information Criterion: 16411.26 .. GENERATED FROM PYTHON SOURCE LINES 64-67 .. code-block:: Python estimated_parameters = get_pandas_estimated_parameters(estimation_results=results) display(estimated_parameters) .. rst-class:: sphx-glr-script-out .. code-block:: none Name Value ... Robust t-stat. Robust p-value 0 asc_train_ref -0.337820 ... -4.295228 1.745137e-05 1 asc_train_diff_GA 1.049716 ... 11.124844 0.000000e+00 2 b_time -1.548603 ... -26.610823 0.000000e+00 3 lambda_travel_time 0.359844 ... 5.295211 1.188789e-07 4 b_cost_train -0.813968 ... -8.817720 0.000000e+00 5 mu_existing 1.598688 ... 18.413032 0.000000e+00 6 asc_car_ref -0.090481 ... -1.454429 1.458275e-01 7 asc_car_diff_GA -0.502957 ... -4.009956 6.073007e-05 8 b_cost_car -0.339878 ... -4.951261 7.373413e-07 9 b_cost_swissmetro -0.642446 ... -13.224771 0.000000e+00 [10 rows x 5 columns] .. GENERATED FROM PYTHON SOURCE LINES 68-79 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. .. GENERATED FROM PYTHON SOURCE LINES 79-86 .. code-block:: Python if can_plot: _ = post_processing.plot( label_x='Nbr of parameters', label_y='Negative log likelihood', objective_x=1, objective_y=0, ) .. image-sg:: /auto_examples/assisted/images/sphx_glr_plot_b09post_processing_001.png :alt: plot b09post processing :srcset: /auto_examples/assisted/images/sphx_glr_plot_b09post_processing_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 58.688 seconds) .. _sphx_glr_download_auto_examples_assisted_plot_b09post_processing.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b09post_processing.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b09post_processing.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b09post_processing.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_