diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 8c53f62..9eb2132 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -1826,12 +1826,12 @@ we will set the number_of_parallel_points parameter to 12, and also limit oursel Level lines of the objective function, built with the parameter kernel='rbf' During the experiment an optimal quality metric value of -0.9469 was obtained with the following combination -of parameters: :math:`C = 1.6474∙10^5` `C = 1.6474 \dot 10^5`, gamma = 0.0767, kernel = 'rbf'. +of parameters: :math:`C = 1.6474∙10^5, C = 1.6474 \dot 10^5`, gamma = 0.0767, kernel = 'rbf'. Example of solving a multi-criteria optimization problem -____________________________________________________________________________________ +________________________________________________________ If optimization is performed using several criteria, then the solution to the problem becomes more complicated. @@ -1839,3 +1839,22 @@ The problem is that the criteria are usually contradictory: decreasing the value to an increase in the values of others. Let's consider the work of the iOpt framework when solving a multi-criteria problem. To do this, we modify the problem statement in Section Tuning support vector machine hyperparameters for a classification problem in machine learning. +Dataset used +~~~~~~~~~~~~ + +We will use the `breast cancer_` dataset. The dataset includes 569 examples, each with 30 +numerical characteristics. Characteristics are calculated from a digitized fine needle aspiration +(FNA) image of the breast mass. They describe the characteristics of the nuclei of the cells present +in the image. The distribution by class is as follows: 212 malignant, 357 benign tumors. + +.. _`breast cancer`: https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+(Diagnostic) + + +Finding optimal parameters using the iOpt framework +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Let's launch the iOpt framework to construct the Pareto set. +We consider two continuous parameters: +#. regularization parameter **C**: [10\ :sup:`1`, 10\ :sup:`6`]; +#. kernel coefficient **gamma**: [10\ :sup:`-7`, 10\ :sup:`-3`]. +First, we need to formulate the basic problem as a class inherited from Problem.