Sensitivity to Constraints in Blackbox Optimization

The paper proposes a framework for sensitivity analyses of blackbox constrained optimization problems for which Lagrange multipliers are not available. Two strategies are developed to analyze the sensitivity of the optimal objective function value to general constraints. These are a simple method which may be performed immediately after a single optimization, and a detailed method performing biobjective optimization on the minimization of the objective versus the constraint of interest. The detailed method provides points on the Pareto front of the objective versus a chosen constraint. The proposed methods are tested on an academic test case and on an engineering problem using the mesh adaptive direct search algorithm.

[1]  Sven Leyffer,et al.  Nonlinear programming without a penalty function , 2002, Math. Program..

[2]  Charles Audet,et al.  Globalization strategies for Mesh Adaptive Direct Search , 2008, Comput. Optim. Appl..

[3]  Charles Audet,et al.  OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions , 2008, SIAM J. Optim..

[4]  Charles Audet,et al.  Mesh Adaptive Direct Search Algorithms for Constrained Optimization , 2006, SIAM J. Optim..

[5]  Charles Audet,et al.  A Pattern Search Filter Method for Nonlinear Programming without Derivatives , 2001, SIAM J. Optim..

[6]  Sébastien Le Digabel.  NOMAD: Nonlinear Optimization with the MADS Algorithm , 2009 .

[7]  C. T. Kelley,et al.  Superlinear Convergence and Implicit Filtering , 1999, SIAM J. Optim..

[8]  Charles Audet,et al.  Spent potliner treatment process optimization using a MADS algorithm , 2005 .

[9]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[10]  Charles Audet,et al.  A MADS Algorithm with a Progressive Barrier for Derivative-Free Nonlinear Programming , 2007 .

[11]  John L. Nazareth,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[12]  Charles Audet,et al.  Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search , 2006, J. Glob. Optim..

[13]  Boxin Tang.  Orthogonal Array-Based Latin Hypercubes , 1993 .

[14]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[15]  Andy J. Keane,et al.  Computational Approaches for Aerospace Design: The Pursuit of Excellence , 2005 .

[16]  Charles Audet,et al.  Multiobjective Optimization Through a Series of Single-Objective Formulations , 2008, SIAM J. Optim..

[17]  Charles Audet,et al.  A mesh adaptive direct search algorithm for multiobjective optimization , 2009, Eur. J. Oper. Res..

[18]  Luís N. Vicente,et al.  Direct Multisearch for Multiobjective Optimization , 2011, SIAM J. Optim..