.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/swissmetro/plot_b21a_multiple_models.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_b21a_multiple_models.py: .. _plot_b21a_multiple_models: 21a. Assisted specification =========================== Example of the estimation of several versions of the model using assisted specification algorithm. The catalog of specifications is defined in :ref:`plot_b21b_multiple_models_spec`. All specifications are estimated. Have a look at :ref:`plot_b22a_multiple_models` for an example where the number of specifications is too high to be enumerated. Michel Bierlaire, EPFL Sat Jun 28 2025, 19:21:26 .. GENERATED FROM PYTHON SOURCE LINES 16-27 .. code-block:: Python 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') .. rst-class:: sphx-glr-script-out .. code-block:: none 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 .. GENERATED FROM PYTHON SOURCE LINES 28-38 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. .. GENERATED FROM PYTHON SOURCE LINES 38-44 .. code-block:: Python assisted_specification = AssistedSpecification( biogeme_object=the_biogeme, multi_objectives=loglikelihood_dimension, pareto_file_name=PARETO_FILE_NAME, ) .. rst-class:: sphx-glr-script-out .. code-block:: none Unable to read file b21_multiple_models.pareto. Pareto set empty. .. GENERATED FROM PYTHON SOURCE LINES 45-46 The algorithm is run. .. GENERATED FROM PYTHON SOURCE LINES 46-48 .. code-block:: Python non_dominated_models = assisted_specification.run() .. rst-class:: sphx-glr-script-out .. code-block:: none Biogeme parameters read from biogeme.toml. Model with 4 unknown parameters [max: 50] *** Estimate b21_multiple_models_000000 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost asc_car Function Relgrad Radius Rho 0 -0.92 -0.67 -0.88 -0.49 5.4e+03 0.041 10 1.1 ++ 1 -0.73 -1.2 -1 -0.18 5.3e+03 0.0072 1e+02 1.1 ++ 2 -0.7 -1.3 -1.1 -0.16 5.3e+03 0.00018 1e+03 1 ++ 3 -0.7 -1.3 -1.1 -0.16 5.3e+03 1.1e-07 1e+03 1 ++ default_specification=asc:no_seg;b_cost:no_seg;train_tt:linear We consider all possible combinations of the catalogs. Model 0/36 Biogeme parameters read from biogeme.toml. Model with 11 unknown parameters [max: 50] *** Estimate b21_multiple_models_000001 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.44 -0.66 -0.9 2 -1 -0.11 -0.35 -0.42 -0.06 -0.43 -0.22 5.7e+03 0.095 1 0.68 + 1 0.56 -1.4 -1.6 1.1 -0.96 -0.51 -0.49 0.3 0.066 -0.52 0.77 5.3e+03 0.02 1 0.84 + 2 0.66 -1.2 -2.2 0.34 -1.6 -0.36 0.25 0.62 0.96 -0.14 0.38 5.1e+03 0.029 1 0.87 + 3 0.33 -1.3 -1.7 0.42 -1.5 -0.37 0.23 0.59 0.84 -0.3 0.32 5.1e+03 0.0026 10 0.96 ++ 4 0.35 -1.3 -1.7 0.45 -1.6 -0.37 0.23 0.59 0.85 -0.3 0.32 5.1e+03 7.5e-05 1e+02 0.98 ++ 5 0.35 -1.3 -1.7 0.45 -1.6 -0.37 0.23 0.59 0.85 -0.3 0.32 5.1e+03 9e-08 1e+02 1 ++ Model 1/36 Biogeme parameters read from biogeme.toml. Model with 7 unknown parameters [max: 50] *** Estimate b21_multiple_models_000002 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.43 -0.62 -0.89 1.8 -1 -0.45 -0.24 5.6e+03 0.083 1 0.72 + 1 0.39 -1.5 -1.6 0.85 -1 -0.65 0.58 5.2e+03 0.028 10 0.94 ++ 2 0.48 -1.3 -1.9 0.42 -1.1 -0.21 0.3 5.1e+03 0.0096 1e+02 0.95 ++ 3 0.36 -1.3 -1.7 0.45 -1.1 -0.29 0.3 5.1e+03 0.0004 1e+03 0.98 ++ 4 0.36 -1.3 -1.7 0.45 -1.1 -0.29 0.3 5.1e+03 6.7e-07 1e+03 1 ++ Model 2/36 Biogeme parameters read from biogeme.toml. Model with 8 unknown parameters [max: 50] *** Estimate b21_multiple_models_000003 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.43 -0.62 -0.89 1.9 -1 -0.18 -0.44 -0.23 5.6e+03 0.084 1 0.72 + 1 0.39 -1.5 -1.6 0.86 -0.97 -0.42 -0.63 0.58 5.2e+03 0.028 10 0.94 ++ 2 0.51 -1.3 -1.9 0.4 -1 -1 -0.14 0.3 5.1e+03 0.011 1e+02 0.93 ++ 3 0.39 -1.3 -1.7 0.44 -1 -1.1 -0.23 0.31 5.1e+03 0.00049 1e+03 0.98 ++ 4 0.39 -1.3 -1.7 0.44 -1 -1.1 -0.23 0.31 5.1e+03 1.9e-06 1e+03 1 ++ Model 3/36 Biogeme parameters read from biogeme.toml. Model with 11 unknown parameters [max: 50] *** Estimate b21_multiple_models_000004 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.73 0.37 -1 1.6 -0.67 -0.082 -0.23 -0.28 -0.042 -0.43 -0.19 5.4e+03 0.039 1 0.86 + 1 -1.1 1.4 -1.3 0.83 -0.84 -0.21 -0.37 -0.12 -0.031 -0.19 -0.32 5.1e+03 0.023 10 1.1 ++ 2 -0.93 2.1 -1.9 0.28 -1.6 -0.57 0.26 0.63 0.83 0.0088 -0.24 5e+03 0.0077 1e+02 0.91 ++ 3 -1 2.1 -1.7 0.36 -1.6 -0.78 0.28 0.67 0.84 -0.065 -0.22 5e+03 0.00067 1e+03 1 ++ 4 -1 2.1 -1.7 0.37 -1.6 -0.79 0.28 0.66 0.84 -0.068 -0.22 5e+03 9.8e-06 1e+04 1 ++ 5 -1 2.1 -1.7 0.37 -1.6 -0.79 0.28 0.66 0.84 -0.068 -0.22 5e+03 5.8e-10 1e+04 1 ++ Model 4/36 Biogeme parameters read from biogeme.toml. Model with 5 unknown parameters [max: 50] *** Estimate b21_multiple_models_000005 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time lambda_time b_cost asc_car Function Relgrad Radius Rho 0 -0.71 -1 1.7 -0.82 -0.5 5.6e+03 0.058 1 0.77 + 1 -0.77 -1.7 0.69 -1.3 -0.35 5.4e+03 0.049 10 1 ++ 2 -0.47 -1.7 0.53 -1 0.017 5.3e+03 0.002 1e+02 0.96 ++ 3 -0.48 -1.7 0.51 -1.1 -0.0043 5.3e+03 1.3e-05 1e+03 1 ++ 4 -0.48 -1.7 0.51 -1.1 -0.0043 5.3e+03 1.8e-09 1e+03 1 ++ Model 5/36 Biogeme parameters read from biogeme.toml. Model with 13 unknown parameters [max: 50] *** Estimate b21_multiple_models_000006 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 9.9e-05 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 9.3e-08 1.2e+02 1 ++ Model 6/36 Biogeme parameters read from biogeme.toml. Model with 10 unknown parameters [max: 50] *** Estimate b21_multiple_models_000007 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.36 -0.78 -0.63 -1 0.12 -0.03 0.16 0.29 -0.56 0.012 5.3e+03 0.043 10 1.1 ++ 1 0.017 -1.1 -1.2 -1.4 -0.28 0.17 0.49 0.72 -0.48 0.3 5.2e+03 0.0097 1e+02 1.1 ++ 2 0.069 -1.2 -1.3 -1.5 -0.41 0.18 0.53 0.78 -0.47 0.33 5.2e+03 0.00037 1e+03 1 ++ 3 0.069 -1.2 -1.3 -1.5 -0.41 0.18 0.53 0.78 -0.47 0.33 5.2e+03 5.1e-07 1e+03 1 ++ Model 7/36 Biogeme parameters read from biogeme.toml. Model with 10 unknown parameters [max: 50] *** Estimate b21_multiple_models_000008 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.78 0.18 -1 -0.34 -0.042 -0.13 -0.14 -0.021 -0.27 -0.11 5.4e+03 0.036 10 1 ++ 1 -0.98 2.4 -1.6 -1.5 -0.066 0.41 0.65 0.77 -0.072 -0.068 5e+03 0.028 1e+02 0.94 ++ 2 -1.1 2.1 -1.7 -1.6 -0.76 0.28 0.66 0.78 -0.07 -0.2 5e+03 0.00071 1e+03 1 ++ 3 -1.1 2.1 -1.7 -1.6 -0.76 0.28 0.66 0.78 -0.07 -0.2 5e+03 5.1e-06 1e+03 1 ++ Model 8/36 Biogeme parameters read from biogeme.toml. Model with 7 unknown parameters [max: 50] *** Estimate b21_multiple_models_000009 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.37 -0.59 -1 -0.89 -0.15 -0.32 -0.12 5.3e+03 0.036 10 1 ++ 1 0.41 -1.3 -1.7 -0.94 -0.88 -0.17 0.22 5.2e+03 0.0094 1e+02 1 ++ 2 0.42 -1.3 -1.7 -0.96 -1 -0.18 0.25 5.2e+03 0.00022 1e+03 1 ++ 3 0.42 -1.3 -1.7 -0.96 -1 -0.18 0.25 5.2e+03 2.3e-07 1e+03 1 ++ Model 9/36 Biogeme parameters read from biogeme.toml. Model with 8 unknown parameters [max: 50] *** Estimate b21_multiple_models_000010 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.51 -0.8 1 -0.6 -0.88 -0.46 -0.15 -0.21 5.1e+03 0.045 10 1.1 ++ 1 -0.54 -0.96 1.7 -1.1 -1.1 -0.6 0.36 -0.37 5e+03 0.012 1e+02 1.1 ++ 2 -0.53 -1.1 1.9 -1.2 -1.1 -0.61 0.41 -0.41 4.9e+03 0.0007 1e+03 1 ++ 3 -0.53 -1.1 1.9 -1.2 -1.1 -0.61 0.41 -0.41 4.9e+03 4.3e-06 1e+03 1 ++ Model 10/36 Biogeme parameters read from biogeme.toml. Model with 4 unknown parameters [max: 50] *** Estimate b21_multiple_models_000011 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost asc_car Function Relgrad Radius Rho 0 -0.74 -1 -0.39 -0.3 5.5e+03 0.044 10 1 ++ 1 -0.54 -1.6 -0.93 -0.0041 5.3e+03 0.0052 1e+02 1.1 ++ 2 -0.51 -1.7 -1 0.0019 5.3e+03 0.00015 1e+03 1 ++ 3 -0.51 -1.7 -1 0.0019 5.3e+03 1.4e-07 1e+03 1 ++ Model 11/36 Biogeme parameters read from biogeme.toml. Model with 12 unknown parameters [max: 50] *** Estimate b21_multiple_models_000012 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.44 -0.6 0.47 -1 -0.69 -0.075 -0.25 -0.28 -0.042 -0.34 -0.16 -0.18 5.2e+03 0.036 10 1 ++ 1 -0.24 -0.98 2 -1.6 -1.5 -0.3 0.23 0.6 0.76 -0.37 0.34 -0.28 4.9e+03 0.018 1e+02 1 ++ 2 -0.25 -1.1 2 -1.7 -1.5 -0.59 0.21 0.63 0.78 -0.43 0.41 -0.34 4.9e+03 0.0011 1e+03 1 ++ 3 -0.25 -1.2 2.1 -1.7 -1.6 -0.61 0.21 0.63 0.78 -0.43 0.42 -0.34 4.9e+03 9e-06 1e+04 1 ++ 4 -0.25 -1.2 2.1 -1.7 -1.6 -0.61 0.21 0.63 0.78 -0.43 0.42 -0.34 4.9e+03 4.2e-08 1e+04 1 ++ Model 12/36 Biogeme parameters read from biogeme.toml. Model with 6 unknown parameters [max: 50] *** Estimate b21_multiple_models_000013 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.33 -0.81 -0.63 -0.89 -0.52 -0.039 5.3e+03 0.043 10 1.1 ++ 1 0.038 -1.2 -1.2 -1 -0.47 0.28 5.2e+03 0.0093 1e+02 1.1 ++ 2 0.089 -1.2 -1.2 -1.1 -0.46 0.31 5.2e+03 0.00033 1e+03 1 ++ 3 0.089 -1.2 -1.2 -1.1 -0.46 0.31 5.2e+03 4.1e-07 1e+03 1 ++ Model 13/36 Biogeme parameters read from biogeme.toml. Model with 5 unknown parameters [max: 50] *** Estimate b21_multiple_models_000014 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost_ref b_cost_diff_GA asc_car Function Relgrad Radius Rho 0 -0.74 -1 -0.39 -0.095 -0.3 5.5e+03 0.043 10 1 ++ 1 -0.52 -1.6 -0.88 -0.53 0.037 5.3e+03 0.0053 1e+02 1.1 ++ 2 -0.48 -1.7 -0.95 -0.97 0.061 5.3e+03 0.00033 1e+03 1.1 ++ 3 -0.48 -1.7 -0.95 -1.1 0.063 5.3e+03 1.1e-05 1e+04 1 ++ 4 -0.48 -1.7 -0.95 -1.1 0.063 5.3e+03 1.7e-08 1e+04 1 ++ Model 14/36 Biogeme parameters read from biogeme.toml. Model with 9 unknown parameters [max: 50] *** Estimate b21_multiple_models_000015 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.51 -0.8 1 -0.6 -0.88 -0.0059 -0.46 -0.15 -0.19 5.1e+03 0.045 10 1.1 ++ 1 -0.54 -0.97 1.7 -1.1 -1.1 0.93 -0.61 0.36 -0.93 4.9e+03 0.012 1e+02 1.1 ++ 2 -0.54 -1.1 1.9 -1.2 -1.1 0.89 -0.62 0.41 -0.98 4.9e+03 0.0007 1e+03 1 ++ 3 -0.54 -1.1 1.9 -1.2 -1.1 0.89 -0.62 0.41 -0.98 4.9e+03 4.4e-06 1e+03 1 ++ Model 15/36 Biogeme parameters read from biogeme.toml. Model with 10 unknown parameters [max: 50] *** Estimate b21_multiple_models_000016 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.46 -0.65 0.57 -0.92 1.9 -1 -0.17 -0.44 -0.24 -0.24 5.5e+03 0.088 1 0.73 + 1 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 10 1.2 ++ 2 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 1.8 -14 - 3 -0.55 -1.1 1.6 -1 1.2 -0.94 -0.19 -0.47 0.13 -0.33 5e+03 0.019 0.88 -0.88 - 4 -0.56 -1.2 1.9 -1.6 0.36 -1.2 -0.16 -0.46 0.34 -0.35 4.9e+03 0.023 8.8 0.91 ++ 5 -0.21 -1.1 1.9 -1.7 0.34 -1.1 1.6 -0.43 0.41 -1.3 4.9e+03 0.0036 8.8 0.82 + 6 -0.22 -1.2 2 -1.7 0.33 -1.1 1.2 -0.42 0.41 -1.2 4.9e+03 0.00065 88 1.2 ++ 7 -0.22 -1.2 2 -1.7 0.33 -1.1 0.98 -0.42 0.41 -1.1 4.9e+03 0.00011 8.8e+02 1.1 ++ 8 -0.22 -1.2 2 -1.7 0.33 -1.1 0.98 -0.42 0.41 -1.1 4.9e+03 5.3e-06 8.8e+02 1 ++ Model 16/36 Biogeme parameters read from biogeme.toml. Model with 9 unknown parameters [max: 50] *** Estimate b21_multiple_models_000017 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.46 -0.64 0.57 -0.92 1.9 -1 -0.45 -0.25 -0.24 5.5e+03 0.087 1 0.73 + 1 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 10 1.2 ++ 2 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 1.6 -11 - 3 -0.56 -1.1 1.6 -1 1.2 -0.95 -0.47 0.12 -0.36 5e+03 0.019 0.8 -0.46 - 4 -0.55 -1.2 1.9 -1.5 0.42 -1.1 -0.48 0.3 -0.4 4.9e+03 0.017 8 0.99 ++ 5 -0.21 -1.1 1.9 -1.7 0.33 -1.1 -0.42 0.41 -0.45 4.9e+03 0.00079 80 0.98 ++ 6 -0.21 -1.1 1.9 -1.7 0.33 -1.1 -0.42 0.41 -0.45 4.9e+03 3.4e-06 80 1 ++ Model 17/36 Biogeme parameters read from biogeme.toml. Model with 5 unknown parameters [max: 50] *** Estimate b21_multiple_models_000018 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost_ref b_cost_diff_GA asc_car Function Relgrad Radius Rho 0 -0.92 -0.67 -0.9 0.097 -0.5 5.4e+03 0.041 10 1.1 ++ 1 -0.71 -1.2 -0.98 -0.74 -0.13 5.3e+03 0.0075 1e+02 1.1 ++ 2 -0.68 -1.3 -1 -1 -0.097 5.3e+03 0.0002 1e+03 1 ++ 3 -0.68 -1.3 -1 -1 -0.097 5.3e+03 1.2e-06 1e+03 1 ++ Model 18/36 Biogeme parameters read from biogeme.toml. Model with 6 unknown parameters [max: 50] *** Estimate b21_multiple_models_000019 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time lambda_time b_cost_ref b_cost_diff_GA asc_car Function Relgrad Radius Rho 0 -0.71 -1 1.7 -0.82 -0.17 -0.5 5.6e+03 0.059 1 0.77 + 1 -0.78 -1.6 0.69 -1.3 -0.38 -0.33 5.4e+03 0.049 10 1 ++ 2 -0.44 -1.7 0.53 -0.96 -1.2 0.085 5.3e+03 0.002 1e+02 0.96 ++ 3 -0.46 -1.7 0.51 -1 -1.1 0.06 5.3e+03 1e-05 1e+03 1 ++ 4 -0.46 -1.7 0.51 -1 -1.1 0.06 5.3e+03 7.2e-10 1e+03 1 ++ Model 19/36 Biogeme parameters read from biogeme.toml. Model with 7 unknown parameters [max: 50] *** Estimate b21_multiple_models_000020 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.33 -0.81 -0.63 -0.91 0.11 -0.52 -0.04 5.3e+03 0.043 10 1.1 ++ 1 0.052 -1.1 -1.2 -0.98 -0.72 -0.42 0.29 5.2e+03 0.0097 1e+02 1.1 ++ 2 0.11 -1.2 -1.3 -1 -1 -0.41 0.31 5.2e+03 0.00036 1e+03 1 ++ 3 0.11 -1.2 -1.3 -1 -1 -0.41 0.31 5.2e+03 9.1e-07 1e+03 1 ++ Model 20/36 Biogeme parameters read from biogeme.toml. Model with 8 unknown parameters [max: 50] *** Estimate b21_multiple_models_000021 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car Function Relgrad Radius Rho 0 -0.92 -0.66 -1 0.026 -0.0026 0.2 0.21 -0.49 5.4e+03 0.041 10 1.1 ++ 1 -0.74 -1.2 -1.4 -0.53 0.22 0.52 0.69 -0.17 5.3e+03 0.0075 1e+02 1.1 ++ 2 -0.71 -1.3 -1.5 -0.66 0.24 0.56 0.75 -0.15 5.3e+03 0.0002 1e+03 1 ++ 3 -0.71 -1.3 -1.5 -0.66 0.24 0.56 0.75 -0.15 5.3e+03 1.5e-07 1e+03 1 ++ Model 21/36 Biogeme parameters read from biogeme.toml. Model with 12 unknown parameters [max: 50] *** Estimate b21_multiple_models_000022 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.51 -0.82 1 -0.59 -0.69 -0.094 -0.32 -0.15 -0.041 -0.47 -0.15 -0.21 5.1e+03 0.045 10 1.1 ++ 1 -0.57 -0.94 1.8 -1.1 -1.4 -0.37 0.15 0.51 0.71 -0.62 0.38 -0.29 4.9e+03 0.012 1e+02 1.1 ++ 2 -0.58 -1.1 1.9 -1.2 -1.5 -0.6 0.17 0.56 0.75 -0.65 0.44 -0.33 4.9e+03 0.00078 1e+03 1 ++ 3 -0.58 -1.1 1.9 -1.2 -1.5 -0.6 0.17 0.56 0.75 -0.65 0.44 -0.33 4.9e+03 4.5e-06 1e+03 1 ++ Model 22/36 Biogeme parameters read from biogeme.toml. Model with 10 unknown parameters [max: 50] *** Estimate b21_multiple_models_000023 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.37 -0.6 -1 -0.72 -0.082 -0.27 -0.28 -0.045 -0.32 -0.13 5.3e+03 0.036 10 1 ++ 1 0.38 -1.3 -1.6 -1.4 -0.22 0.22 0.56 0.76 -0.22 0.24 5.2e+03 0.0092 1e+02 1 ++ 2 0.38 -1.3 -1.7 -1.5 -0.36 0.23 0.6 0.81 -0.25 0.27 5.2e+03 0.00022 1e+03 1 ++ 3 0.38 -1.3 -1.7 -1.5 -0.36 0.23 0.6 0.81 -0.25 0.27 5.2e+03 2.4e-07 1e+03 1 ++ Model 23/36 Biogeme parameters read from biogeme.toml. Model with 9 unknown parameters [max: 50] *** Estimate b21_multiple_models_000024 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.43 -0.59 0.47 -1 -0.76 -0.12 -0.34 -0.16 -0.18 5.2e+03 0.042 10 1 ++ 1 -0.21 -1 2 -1.6 -1 0.89 -0.36 0.33 -0.91 4.9e+03 0.018 1e+02 1 ++ 2 -0.2 -1.2 2 -1.7 -1.1 0.91 -0.39 0.37 -0.99 4.9e+03 0.0011 1e+03 1 ++ 3 -0.2 -1.2 2 -1.7 -1.1 0.91 -0.39 0.38 -0.99 4.9e+03 8.4e-06 1e+04 1 ++ 4 -0.2 -1.2 2 -1.7 -1.1 0.91 -0.39 0.38 -0.99 4.9e+03 5.4e-10 1e+04 1 ++ Model 24/36 Biogeme parameters read from biogeme.toml. Model with 10 unknown parameters [max: 50] *** Estimate b21_multiple_models_000025 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -1 0.85 -0.7 -0.75 -0.11 -0.31 -0.21 -0.052 -0.41 -0.23 5.2e+03 0.049 10 1.1 ++ 1 -1.2 1.9 -1.1 -1.5 -0.54 0.19 0.54 0.71 -0.28 -0.19 5e+03 0.012 1e+02 1.1 ++ 2 -1.3 2 -1.2 -1.6 -0.78 0.23 0.59 0.78 -0.26 -0.21 5e+03 0.0006 1e+03 1 ++ 3 -1.3 2 -1.2 -1.6 -0.78 0.23 0.59 0.78 -0.26 -0.21 5e+03 1.8e-06 1e+03 1 ++ Model 25/36 Biogeme parameters read from biogeme.toml. Model with 6 unknown parameters [max: 50] *** Estimate b21_multiple_models_000026 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.88 0.66 -0.79 -1 -0.36 -0.25 5.2e+03 0.047 10 1.1 ++ 1 -1.2 1.9 -1.1 -1.1 -0.28 -0.28 5.1e+03 0.014 1e+02 1.1 ++ 2 -1.3 2 -1.2 -1.1 -0.25 -0.3 5.1e+03 0.0007 1e+03 1 ++ 3 -1.3 2 -1.2 -1.1 -0.25 -0.3 5.1e+03 2.4e-06 1e+03 1 ++ Model 26/36 Biogeme parameters read from biogeme.toml. Model with 8 unknown parameters [max: 50] *** Estimate b21_multiple_models_000027 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma asc_car_diff_GA Function Relgrad Radius Rho 0 -0.44 -0.59 0.47 -1 -0.76 -0.34 -0.17 -0.18 5.2e+03 0.044 10 1 ++ 1 -0.21 -1 2 -1.6 -1 -0.36 0.33 -0.35 4.9e+03 0.018 1e+02 1 ++ 2 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.37 -0.42 4.9e+03 0.0011 1e+03 1 ++ 3 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.38 -0.42 4.9e+03 8.5e-06 1e+04 1 ++ 4 -0.2 -1.2 2 -1.7 -1.1 -0.39 0.38 -0.42 4.9e+03 5.5e-10 1e+04 1 ++ Model 27/36 Biogeme parameters read from biogeme.toml. Model with 7 unknown parameters [max: 50] *** Estimate b21_multiple_models_000028 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.73 0.39 -1 1.6 -0.73 -0.45 -0.21 5.5e+03 0.049 1 0.83 + 1 -1.1 1.4 -1.3 0.9 -1.1 -0.2 -0.35 5.1e+03 0.022 10 1.1 ++ 2 -0.87 2 -1.9 0.26 -1.1 0.037 -0.36 5e+03 0.012 10 0.82 + 3 -1 2 -1.7 0.36 -1.1 -0.061 -0.31 5e+03 0.0012 1e+02 1 ++ 4 -1 2 -1.7 0.38 -1.1 -0.064 -0.31 5e+03 3.1e-05 1e+03 1 ++ 5 -1 2 -1.7 0.38 -1.1 -0.064 -0.31 5e+03 3.6e-09 1e+03 1 ++ Model 28/36 Biogeme parameters read from biogeme.toml. Model with 7 unknown parameters [max: 50] *** Estimate b21_multiple_models_000029 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.76 0.19 -1 -0.36 -0.089 -0.27 -0.12 5.4e+03 0.044 10 1 ++ 1 -0.98 2.4 -1.6 -0.98 0.71 -0.08 -0.61 5e+03 0.027 1e+02 0.93 ++ 2 -1.1 2.1 -1.7 -1.1 0.92 -0.071 -0.87 5e+03 0.00067 1e+03 1 ++ 3 -1.1 2.1 -1.7 -1.1 0.92 -0.071 -0.87 5e+03 2e-06 1e+03 1 ++ Model 29/36 Biogeme parameters read from biogeme.toml. Model with 9 unknown parameters [max: 50] *** Estimate b21_multiple_models_000030 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time lambda_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car Function Relgrad Radius Rho 0 -0.72 -1 1.6 -0.74 -0.092 -0.26 -0.31 -0.047 -0.48 5.6e+03 0.044 1 0.81 + 1 -0.64 -1.6 0.65 -0.91 -0.36 -0.47 0.12 -0.013 -0.22 5.3e+03 0.038 10 1 ++ 2 -0.49 -1.7 0.51 -1.5 -0.59 0.27 0.6 0.8 0.012 5.3e+03 0.00074 1e+02 1 ++ 3 -0.49 -1.7 0.5 -1.6 -0.65 0.28 0.62 0.81 0.0042 5.3e+03 7e-06 1e+03 1 ++ 4 -0.49 -1.7 0.5 -1.6 -0.65 0.28 0.62 0.81 0.0042 5.3e+03 1.3e-09 1e+03 1 ++ Model 30/36 Biogeme parameters read from biogeme.toml. Model with 6 unknown parameters [max: 50] *** Estimate b21_multiple_models_000031 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost asc_car_ref asc_car_diff_ma Function Relgrad Radius Rho 0 -0.37 -0.59 -1 -0.89 -0.33 -0.13 5.3e+03 0.036 10 1 ++ 1 0.4 -1.3 -1.6 -1 -0.22 0.22 5.2e+03 0.0091 1e+02 1 ++ 2 0.4 -1.3 -1.7 -1 -0.24 0.25 5.2e+03 0.00022 1e+03 1 ++ 3 0.4 -1.3 -1.7 -1 -0.24 0.25 5.2e+03 2.4e-07 1e+03 1 ++ Model 31/36 Biogeme parameters read from biogeme.toml. Model with 7 unknown parameters [max: 50] *** Estimate b21_multiple_models_000032 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -1 0.9 -0.7 -0.93 -0.072 -0.43 -0.22 5.2e+03 0.046 10 1.1 ++ 1 -1.2 1.9 -1.1 -1.1 0.98 -0.28 -0.87 5.1e+03 0.011 1e+02 1.1 ++ 2 -1.3 2 -1.2 -1.1 0.89 -0.25 -0.87 5e+03 0.00055 1e+03 1 ++ 3 -1.3 2 -1.2 -1.1 0.89 -0.25 -0.87 5e+03 1.5e-06 1e+03 1 ++ Model 32/36 Model 33/36 Biogeme parameters read from biogeme.toml. Model with 8 unknown parameters [max: 50] *** Estimate b21_multiple_models_000033 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train_ref asc_train_diff_ b_time lambda_time b_cost_ref b_cost_diff_GA asc_car_ref asc_car_diff_GA Function Relgrad Radius Rho 0 -0.73 0.39 -1 1.6 -0.73 -0.15 -0.45 -0.2 5.5e+03 0.05 1 0.83 + 1 -1.1 1.4 -1.3 0.91 -1.1 -0.2 -0.19 -0.33 5.1e+03 0.021 10 1.1 ++ 2 -0.87 2 -1.9 0.26 -1.1 1.3 0.034 -1.1 5e+03 0.013 10 0.81 + 3 -1 2 -1.7 0.36 -1.1 1 -0.066 -0.95 5e+03 0.0012 1e+02 1 ++ 4 -1 2 -1.7 0.38 -1.1 0.92 -0.068 -0.89 5e+03 3.3e-05 1e+03 1 ++ 5 -1 2 -1.7 0.38 -1.1 0.92 -0.068 -0.89 5e+03 8.2e-08 1e+03 1 ++ Model 34/36 Biogeme parameters read from biogeme.toml. Model with 8 unknown parameters [max: 50] *** Estimate b21_multiple_models_000034 As the model is not too complex, we activate the calculation of second derivatives. To change this behavior, modify the algorithm to "simple_bounds" in the TOML file. Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] ** Optimization: Newton with trust region for simple bounds Iter. asc_train b_time b_cost_ref b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc b_cost_diff_inc asc_car Function Relgrad Radius Rho 0 -0.75 -1 -0.36 -0.045 -0.13 -0.14 -0.023 -0.29 5.5e+03 0.035 10 1 ++ 1 -0.54 -1.6 -1.4 -0.17 0.37 0.6 0.73 0.0049 5.3e+03 0.0064 1e+02 1.1 ++ 2 -0.51 -1.7 -1.5 -0.64 0.28 0.63 0.75 0.011 5.3e+03 0.00037 1e+03 1 ++ 3 -0.51 -1.7 -1.5 -0.64 0.28 0.63 0.75 0.011 5.3e+03 2.2e-06 1e+03 1 ++ Model 35/36 Biogeme parameters read from biogeme.toml. Model with 6 unknown parameters [max: 50] *** Estimate b21_multiple_models_000035 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 ++ 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: {} 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: 1.059559503933971e-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: 0:00:00.293176 Calculate second derivatives and BHHH File b21_multiple_models_000000.html has been generated. File b21_multiple_models_000000.yaml has been generated. 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: {} 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: 3.608609121164929e-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: 0:00:00.986043 Calculate second derivatives and BHHH File b21_multiple_models_000001.html has been generated. File b21_multiple_models_000001.yaml has been generated. 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: {} 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: 5.482789752269039e-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: 0:00:00.429961 Calculate second derivatives and BHHH File b21_multiple_models_000002.html has been generated. File b21_multiple_models_000002.yaml has been generated. 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: {} 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: 2.0806244410800506e-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: 0:00:00.360752 Calculate second derivatives and BHHH File b21_multiple_models_000003.html has been generated. File b21_multiple_models_000003.yaml has been generated. 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: {} 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 9.9e-05 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 9.3e-08 1.2e+02 1 ++ Optimization algorithm has converged. Relative gradient: 9.314421529692506e-08 Cause of termination: Relative gradient = 9.3e-08 <= 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: 0:00:01.265093 Calculate second derivatives and BHHH File b21_multiple_models_000004.html has been generated. File b21_multiple_models_000004.yaml has been generated. 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: {} 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: 1.7992210209022422e-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: 0:00:00.859131 Calculate second derivatives and BHHH File b21_multiple_models_000005.html has been generated. File b21_multiple_models_000005.yaml has been generated. 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: {} 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: 3.374132016569103e-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: 0:00:01.353647 Calculate second derivatives and BHHH File b21_multiple_models_000006.html has been generated. File b21_multiple_models_000006.yaml has been generated. 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: {} 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: 5.317220515909392e-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: 0:00:01.081416 Calculate second derivatives and BHHH File b21_multiple_models_000007.html has been generated. File b21_multiple_models_000007.yaml has been generated. Pareto: 8 Considered: 36 Removed: 10 .. GENERATED FROM PYTHON SOURCE LINES 49-54 .. code-block:: Python summary, description = compile_estimation_results( non_dominated_models, use_short_names=True ) print(summary) .. rst-class:: sphx-glr-script-out .. code-block:: none Model_000000 ... Model_000007 Number of estimated parameters 4 ... 10 Sample size 6768 ... 6768 Final log likelihood -5331.252 ... -4879.461 Akaike Information Criterion 10670.5 ... 9778.922 Bayesian Information Criterion 10697.78 ... 9847.122 asc_train (t-test) -0.701 (-8.49) ... b_time (t-test) -1.28 (-12.3) ... -1.7 (-21.3) b_cost (t-test) -1.08 (-15.9) ... asc_car (t-test) -0.155 (-2.66) ... asc_train_ref (t-test) ... -0.22 (-2.44) asc_train_diff_GA (t-test) ... 1.96 (21.2) lambda_time (t-test) ... 0.334 (4.55) asc_car_ref (t-test) ... -0.422 (-4.29) asc_car_diff_GA (t-test) ... -1.03 (-2.57) asc_train_diff_male (t-test) ... -1.15 (-13.4) asc_car_diff_male (t-test) ... 0.413 (3.95) b_cost_ref (t-test) ... -1.1 (-15.1) 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) ... 0.918 (1.87) [22 rows x 8 columns] .. GENERATED FROM PYTHON SOURCE LINES 55-56 Explanation of the short names of the model. .. GENERATED FROM PYTHON SOURCE LINES 56-59 .. code-block:: Python for k, v in description.items(): if k != v: print(f'{k}: {v} AIC={summary.at["Akaike Information Criterion", k]}') .. rst-class:: sphx-glr-script-out .. code-block:: none Model_000000: asc:no_seg;b_cost:no_seg;train_tt:linear AIC=10670.5 Model_000001: asc:GA;b_cost:no_seg;train_tt:boxcox AIC=10005.51 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:MALE-GA;b_cost:INCOME;train_tt:boxcox AIC=9750.73 Model_000005: asc:no_seg;b_cost:no_seg;train_tt:boxcox AIC=10594.19 Model_000006: asc:MALE-GA;b_cost:no_seg;train_tt:boxcox AIC=9781.834 Model_000007: asc:MALE-GA;b_cost:GA;train_tt:boxcox AIC=9778.922 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 44.363 seconds) .. _sphx_glr_download_auto_examples_swissmetro_plot_b21a_multiple_models.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_b21a_multiple_models.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_b21a_multiple_models.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_b21a_multiple_models.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_