Algorithm xxx : NOMAD : Nonlinear Optimization with the MADS algorithm

NOMAD is software that implements the Mesh Adaptive Direct Search (MADS) algorithm for blackbox optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and aims for the best possible solution with a small number of evaluations. The objective of this article is to describe the underlying algorithm, the software’s functionalities, and its implementation.

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

[2]  Tamara G. Kolda,et al.  Algorithm 856: APPSPACK 4.0: asynchronous parallel pattern search for derivative-free optimization , 2006, TOMS.

[3]  Jennie Malboeuf Algorithm , 1994, Neurology.

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

[5]  William C. Davidon,et al.  Variable Metric Method for Minimization , 1959, SIAM J. Optim..

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

[7]  Luís N. Vicente,et al.  Analysis of direct searches for discontinuous functions , 2012, Math. Program..

[8]  O. SIAMJ.,et al.  ON THE CONVERGENCE OF PATTERN SEARCH ALGORITHMS , 1997 .

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

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

[11]  H. Aoudjit Planification de la maintenance d'un parc de turbines-alternateurs par programmation mathématique , 2010 .

[12]  Charles Audet,et al.  Pattern Search Algorithms for Mixed Variable Programming , 2000, SIAM J. Optim..

[13]  Pierre Hansen,et al.  A note on diameters of point sets , 2009, Optim. Lett..

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

[15]  Masao Fukushima,et al.  Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization , 2006, J. Glob. Optim..

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

[17]  Charles Audet,et al.  Analysis of Generalized Pattern Searches , 2000, SIAM J. Optim..

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

[19]  Charles Audet,et al.  Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems , 2008 .

[20]  Ken Naono,et al.  Software Automatic Tuning : From Concepts to State-of-the-Art Results , 2010 .

[21]  Charles Audet Convergence Results for Generalized Pattern Search Algorithms are Tight , 2004 .

[22]  J. Dennis,et al.  Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems , 2004 .

[23]  M. Abramson Mixed Variable Optimization of a Load-Bearing Thermal Insulation System Using a Filter Pattern Search Algorithm , 2004 .

[24]  Charles Audet,et al.  Mesh adaptive direct search algorithms for mixed variable optimization , 2007, Optim. Lett..

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

[26]  Charles Audet,et al.  The mesh adaptive direct search algorithm for periodic variables , 2009 .

[27]  Nikolaos V. Sahinidis,et al.  Derivative-free optimization: a review of algorithms and comparison of software implementations , 2013, J. Glob. Optim..

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

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

[30]  L. N. Vicente,et al.  Using simplex gradients of nonsmooth functions in direct search methods , 2008 .

[31]  J. Dennis,et al.  Mixed Variable Optimization of the Number and Composition of Heat Intercepts in a Thermal Insulation System , 2001 .

[32]  Charles Audet,et al.  Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points , 2006, SIAM J. Optim..

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

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

[35]  Charles Audet,et al.  Convergence Results for Pattern Search Algorithms are Tight , 2002 .

[36]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[37]  Virginia Torczon,et al.  On the Convergence of Pattern Search Algorithms , 1997, SIAM J. Optim..

[38]  Charles Audet,et al.  Parallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm , 2007, SIAM J. Optim..

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

[40]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[41]  Luís N. Vicente,et al.  Using Sampling and Simplex Derivatives in Pattern Search Methods , 2007, SIAM J. Optim..

[42]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[43]  Jack Dongarra,et al.  MPI: The Complete Reference , 1996 .

[44]  Nicholas I. M. Gould,et al.  CUTEr and SifDec: A constrained and unconstrained testing environment, revisited , 2003, TOMS.