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Algorithm Selection for Black-Box Continuous Optimization Problems: a Survey on Methods and Challenges
Accepted Manuscript Algorithm selection for black-box continuous optimization problems: a survey on methods and challenges Mario A. Muñoz, Yuan Sun, Michael Kirley, Saman K. Halgamuge PII: S0020-0255(15)00368-0 DOI: http://dx.doi.org/10.1016/j.ins.2015.05.010 Reference: INS 11563 To appear in: Information Sciences Received Date: 18 November 2014 Revised Date: 17 March 2015 Accepted Date: 1 May 2015 Please cite this article as: M.A. Muñoz, Y. Sun, M. Kirley, S.K. Halgamuge, Algorithm selection for black-box continuous optimization problems: a survey on methods and challenges, Information Sciences (2015), doi: http:// dx.doi.org/10.1016/j.ins.2015.05.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Algorithm selection for black-box continuous optimization problems: a survey on methods and challenges Mario A. Munoz˜ a,b,∗, Yuan Sunb, Michael Kirleyc, Saman K. Halgamugeb aSchool of Mathematical Sciences, Monash University, Clayton, Victoria 3800 Australia bDepartment of Mechanical Engineering, The University of Melbourne, Parkville, Victoria 3010 Australia cDepartment of Computer and Information Systems, The University of Melbourne, Parkville, Victoria 3010 Australia Abstract Selecting the most appropriate algorithm to use when attempting to solve a black-box continuous optimization problem is a challenging task. -
A Survey of Random Methods for Parameter Optimization
A survey of random methods for parameter optimization Citation for published version (APA): White, R. C. (1970). A survey of random methods for parameter optimization. (EUT report. E, Fac. of Electrical Engineering; Vol. 70-E-16). Technische Hogeschool Eindhoven. Document status and date: Published: 01/01/1970 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. -
Solution of Stochastic Quadratic Programming with Imperfect Probability Distribution Using Nelder-Mead Simplex Method
Journal of Applied Mathematics and Physics, 2018, 6, 1111-1119 http://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 Solution of Stochastic Quadratic Programming with Imperfect Probability Distribution Using Nelder-Mead Simplex Method Xinshun Ma*, Xin Liu Department of Mathematics and Physics, North China Electric Power University, Baoding, China How to cite this paper: Ma, X.S. and Liu, Abstract X. (2018) Solution of Stochastic Quadratic Programming with Imperfect Probability Stochastic quadratic programming with recourse is one of the most important Distribution Using Nelder-Mead Simplex topics in the field of optimization. It is usually assumed that the probability Method. Journal of Applied Mathematics distribution of random variables has complete information, but only part of and Physics, 6, 1111-1119. https://doi.org/10.4236/jamp.2018.65095 the information can be obtained in practical situation. In this paper, we pro- pose a stochastic quadratic programming with imperfect probability distribu- Received: April 16, 2018 tion based on the linear partial information (LPI) theory. A direct optimizing Accepted: May 28, 2018 Published: May 31, 2018 algorithm based on Nelder-Mead simplex method is proposed for solving the problem. Finally, a numerical example is given to demonstrate the efficiency Copyright © 2018 by authors and of the algorithm. Scientific Research Publishing Inc. This work is licensed under the Creative Keywords Commons Attribution International License (CC BY 4.0). Stochastic Quadratic Programming, LPI, Nelder-Mead http://creativecommons.org/licenses/by/4.0/ Open Access 1. Introduction Stochastic programming is an important method to solve decision problems in random environment. -
On Sample Size Control in Sample Average Approximations for Solving Smooth Stochastic Programs
1 On Sample Size Control in Sample Average Approximations for Solving Smooth Stochastic Programs Johannes O. Royset Operations Research Department, Naval Postgraduate School Monterey, California, USA May 29, 2012 Abstract. We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on variable sample av- erage approximations (VSAA). The control problem aims to minimize the expected computational cost to obtain a near-optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal-control problem depends on unknown parameters such as rate of convergence, computational cost per iteration, and sampling error. Hence, we implement the approach within a receding-horizon framework where parameters are estimated and the optimal- control problem is solved repeatedly during the calculations of a VSAA algorithm. The resulting sample-size selection policy consistently produces near-optimal solutions in short computing times as compared to other plausible policies in several numerical examples. 1 Introduction Stochastic programs that aim to minimize the expectations of random functions are rarely solv- able by direct application of standard optimization algorithms. The sample average approximation (SAA) approach is a well-known framework for solving such difficult problems where a standard op- timization algorithm is applied to an approximation of the stochastic program obtained by replacing the expectation by its sample average. The SAA approach is intuitive, simple, and has a strong theoretical foundation; see [2] and Chapter 5 of [46] for a summary of results, and [24, 50, 23, 1] for examples of applications. However, the framework suffers from a main difficulty: what is an appropriate sample size? A large sample size provides good accuracy in SAA, but results in a high computational cost.