Parallel Surrogate-assisted Optimization Using Mesh Adaptive Direct Search

We consider computationally expensive blackbox optimization problems and present a method that employs surrogate models and concurrent computing at the search step of the mesh adaptive direct search (MADS) algorithm. Specifically, we solve a surrogate optimization problem using locally weighted scatterplot smoothing (LOWESS) models to find promising candidate points to be evaluated by the blackboxes. We consider several methods for selecting promising points from a large number of points. We conduct numerical experiments to assess the performance of the modified MADS algorithm with respect to available CPU resources by means of five engineering design problems.

[1]  Oliver Kramer,et al.  Derivative-Free Optimization , 2011, Computational Optimization, Methods and Algorithms.

[2]  Mathieu Lemyre Garneau.  Modelling of a Solar Thermal Power Plant for BenchmarkingBlackbox Optimization Solvers , 2015 .

[3]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[4]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[5]  Jorge J. Moré,et al.  Benchmarking optimization software with performance profiles , 2001, Math. Program..

[6]  Jonathan F. Bard,et al.  Engineering Optimization: Theory and Practice, Third Edition , 1997 .

[7]  W. Cleveland,et al.  Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting , 1988 .

[8]  W. Cleveland.  LOWESS: A Program for Smoothing Scatterplots by Robust Locally Weighted Regression , 1981 .

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

[10]  Andrew W. Moore,et al.  Locally Weighted Learning , 1997, Artificial Intelligence Review.

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

[12]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[13]  Charles Audet,et al.  Order-based error for managing ensembles of surrogates in derivative-free optimization , 2016 .

[14]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[15]  Anirban Chaudhuri,et al.  Parallel surrogate-assisted global optimization with expensive functions – a survey , 2016 .

[16]  Wagdi G. Habashi,et al.  Constrained problem formulations for power optimization of aircraft electro-thermal anti-icing systems , 2015 .

[17]  Enrique Alba,et al.  Parallel metaheuristics: recent advances and new trends , 2012, Int. Trans. Oper. Res..

[18]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[19]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[20]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[21]  W. Cleveland,et al.  Regression by local fitting: Methods, properties, and computational algorithms , 1988 .

[22]  Sébastien Le Digabel,et al.  Statistical Surrogate Formulations for Simulation-Based Design Optimization , 2015 .

[23]  C. Murray Woodside,et al.  Evaluating the scalability of distributed systems , 1998, Proceedings of the Thirty-First Hawaii International Conference on System Sciences.

[24]  Harish Garg.  Solving structural engineering design optimization problems using an artificial bee colony algorithm , 2013 .

[25]  Charles Audet,et al.  Locally weighted regression models for surrogate-assisted design optimization , 2016 .

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

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

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

[29]  Farrokh Mistree,et al.  Managing computational complexity using surrogate models: a critical review , 2020, Research in Engineering Design.