.. _analysis_constrained_problem: ================================================================ Analysis of the Constraints Landscape ================================================================ In this tutorial we want to show how to use the lanscape anlaysis module Dr. PyGMO for the analysis of the constraint functions. Instantiate Analysis Module --------------------------- First, we need to instantiate the analysis class as follows: .. code-block:: python from PyGMO import * #We instantiate the optimization problem as usual. prob=problem.cec2006(5) #Now we instantiate the analysis class. In this case we will sample 1000 points via via latin #hypersquare sampling (lhs) and choose output to file. inspector=util.analysis(prob,1000,'lhs',output_to_file=True) Tests on constraints functions ------------------------------ Now we can start launching the tests related to the constraints functions. .. code-block:: python inspector.c_feasibility() inspector.c_linearity() inspector.c_regression(degree=[1,1,2,2],interaction=[False,True,False,True]) inspector.c_sensitivity() The output will look like this: .. code-block:: none =============================================================================== ANALYSIS =============================================================================== ------------------------------------------------------------------------------- PROBLEM PROPERTIES ------------------------------------------------------------------------------- Problem name: CEC2006 - g5 Global dimension: 4 Integer dimension: 0 Fitness dimension: 1 Constraints dimension: 5 Inequality constraints dimension: 2 Lower bounds: [0, 0, -0.55000000000000004, -0.55000000000000004] Upper bounds: [1200, 1200, 0.55000000000000004, 0.55000000000000004] Constraints tolerance: [0.0001, 0.0001, 0.0001, 0, 0] ------------------------------------------------------------------------------- SAMPLED [1000] POINTS VIA lhs METHOD FOR THE SUBSEQUENT TESTS ------------------------------------------------------------------------------- C-FEASIBILITY ------------------------------------------------------------------------------- Constraint h_1 : Effectiveness >=0 : [0.416] Effectiveness <=0 : [0.584] Number of feasible points found : [0] Constraint h_2 : Effectiveness >=0 : [0.388] Effectiveness <=0 : [0.612] Number of feasible points found : [0] Constraint h_3 : Effectiveness >=0 : [0.879] Effectiveness <=0 : [0.121] Number of feasible points found : [0] Constraint g_1 : Effectiveness >0 : [0.128] Redundancy wrt. all other ic : [0.0] Number of feasible points found : [872] Constraint g_2 : Effectiveness >0 : [0.124] Redundancy wrt. all other ic : [0.0] Number of feasible points found : [876] Pairwise redundancy (ic) : _____| g1 | g2 | g1 | 1.0 | 0.0 | g2 | 0.0 | 1.0 | ------------------------------------------------------------------------------- C-LINEARITY ------------------------------------------------------------------------------- Number of pairs of points used : [1000] CONSTRAINT PROBABILITY OF LINEARITY h_1 [0.005] h_2 [0.005] h_3 [0.003] g_1 [1.0] g_2 [1.0] ------------------------------------------------------------------------------- C-REGRESSION ------------------------------------------------------------------------------- CONSTRAINT h_1 : DEGREE F* R2 R2adj RMSE R2pred PRESS-RMSE 1 126286.466 0.999 0.999 0.006 0.999 0.006 1(i) 126286.466 0.999 0.999 0.006 0.999 0.006 2 348689.605 1.0 1.0 0.002 1.0 0.002 2(i) 348689.605 1.0 1.0 0.002 1.0 0.002 CONSTRAINT h_2 : DEGREE F* R2 R2adj RMSE R2pred PRESS-RMSE 1 47625.385 0.998 0.998 0.01 0.998 0.01 1(i) 47625.385 0.998 0.998 0.01 0.998 0.01 2 292418.74 1.0 1.0 0.002 1.0 0.002 2(i) 292418.74 1.0 1.0 0.002 1.0 0.002 CONSTRAINT h_3 : DEGREE F* R2 R2adj RMSE R2pred PRESS-RMSE 1 51587.224 0.998 0.998 0.011 0.998 0.012 1(i) 51587.224 0.998 0.998 0.011 0.998 0.012 2 223152.687 1.0 1.0 0.003 1.0 0.003 2(i) 223152.687 1.0 1.0 0.003 1.0 0.003 CONSTRAINT g_1 : DEGREE F* R2 R2adj RMSE R2pred PRESS-RMSE 1 2.6e+31 1.0 1.0 1.0e-15 1.0 1.086e-15 1(i) 2.6e+31 1.0 1.0 1.0e-15 1.0 1.086e-15 2 3.907e+30 1.0 1.0 2.581e-15 1.0 2.557e-15 2(i) 3.907e+30 1.0 1.0 2.581e-15 1.0 2.557e-15 CONSTRAINT g_2 : DEGREE F* R2 R2adj RMSE R2pred PRESS-RMSE 1 1.792e+31 1.0 1.0 1.205e-15 1.0 1.135e-15 1(i) 1.792e+31 1.0 1.0 1.205e-15 1.0 1.135e-15 2 2.322e+30 1.0 1.0 3.347e-15 1.0 3.493e-15 2(i) 2.322e+30 1.0 1.0 3.347e-15 1.0 3.493e-15 ------------------------------------------------------------------------------- C-SENSITIVITY ------------------------------------------------------------------------------- CONSTRAINT g_1 : Percentiles : | 0 | 25 | 50 | 75 | 100 | Gradient norm : | 0.608 | 0.68 | 0.702 | 0.721 | 0.731 | |dFx|_max/|dFx|_min : | inf | inf | inf | inf | inf | Gradient sparsity : [0.4] CONSTRAINT g_2 : Percentiles : | 0 | 25 | 50 | 75 | 100 | Gradient norm : | 0.477 | 0.696 | 0.751 | 0.776 | 0.793 | |dFx|_max/|dFx|_min : | inf | inf | inf | inf | inf | Gradient sparsity : [0.4] *Constraints Gradient/Jacobian sparsity plot : *Constraint Gradient/Jacobian PCP plot : *Constraint Gradient/Jacobian PCP plot (inverted) : .. image:: ../images/tutorials/analysis_cstrs.png