BFO, A Trainable Derivative-free Brute Force Optimizer for Nonlinear Bound-constrained Optimization and Equilibrium Computations with Continuous and Discrete Variables

A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favorably with that of NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search), a well-known derivative-free optimization package. It is also applicable to multilevel equilibrium- or constrained-type problems. Its easy-to-use interface provides a number of user-oriented features, such as checkpointing and restart, variable scaling, and early termination tools.

[1]  Serge Gratton,et al.  Direct Search Based on Probabilistic Descent , 2015, SIAM J. Optim..

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

[3]  Patrice Marcotte,et al.  An overview of bilevel optimization , 2007, Ann. Oper. Res..

[4]  Christopher M. Siefert,et al.  Model-Assisted Pattern Search Methods for Optimizing Expensive Computer Simulations , 2002 .

[5]  Stephan Dempe,et al.  Foundations of Bilevel Programming , 2002 .

[6]  L. N. Vicente,et al.  Discrete linear bilevel programming problem , 1996 .

[7]  G. Box,et al.  On the Experimental Attainment of Optimum Conditions , 1951 .

[8]  Sébastien Le Digabel,et al.  Algorithm xxx : NOMAD : Nonlinear Optimization with the MADS algorithm , 2010 .

[9]  Charles Audet,et al.  Optimization of algorithms with OPAL , 2012, Math. Program. Comput..

[10]  Stefano Lucidi,et al.  Derivative-free methods for bound constrained mixed-integer optimization , 2011, Computational Optimization and Applications.

[11]  R. Oeuvray,et al.  A New Derivative-Free Algorithm for the Medical Image Registration Problem , 2007 .

[12]  Christodoulos A. Floudas,et al.  Global optimization of mixed-integer bilevel programming problems , 2005, Comput. Manag. Sci..

[13]  Matteo Leonetti,et al.  Combining Local and Global Direct Derivative-Free Optimization for Reinforcement Learning , 2012 .

[14]  D. Shanno Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[15]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[16]  C. G. Broyden The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[17]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[18]  Humberto Rocha,et al.  Incorporating minimum Frobenius norm models in direct search , 2010, Comput. Optim. Appl..

[19]  C. J. Price,et al.  On the Convergence of Grid-Based Methods for Unconstrained Optimization , 2000, SIAM J. Optim..

[20]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[21]  Andrew R. Conn,et al.  Bilevel derivative-free optimization and its application to robust optimization , 2012, Optim. Methods Softw..

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

[23]  Katya Scheinberg,et al.  A derivative free optimization algorithm in practice , 1998 .

[24]  Nicholas I. M. Gould,et al.  CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization , 2013, Computational Optimization and Applications.

[25]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[26]  Jonathan F. Bard,et al.  Practical Bilevel Optimization , 1998 .

[27]  CHARLES AUDET,et al.  Finding Optimal Algorithmic Parameters Using Derivative-Free Optimization , 2006, SIAM J. Optim..

[28]  L. Grippo,et al.  A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations , 2015, Comput. Optim. Appl..

[29]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications) , 2006 .

[30]  D. Goldfarb A family of variable-metric methods derived by variational means , 1970 .

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

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

[33]  Charles Audet,et al.  Algorithmic Parameter Optimization of the DFO Method with the OPAL Framework , 2010, Software Automatic Tuning, From Concepts to State-of-the-Art Results.

[34]  Stefano Lucidi,et al.  Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems , 2015, J. Optim. Theory Appl..

[35]  Stefan M. Wild,et al.  Benchmarking Derivative-Free Optimization Algorithms , 2009, SIAM J. Optim..

[36]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .

[37]  Marco Sciandrone,et al.  An Algorithm Model for Mixed Variable Programming , 2005, SIAM J. Optim..

[38]  Tamara G. Kolda,et al.  HOPSPACK: Hybrid Optimization Parallel Search Package. , 2008 .

[39]  Jonathan Cole Smith,et al.  A class of algorithms for mixed-integer bilevel min–max optimization , 2015, Journal of Global Optimization.