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Global optimization using the asymptotically independent Markov sampling method

Zuev, Konstantin M. and Beck, James L. (2013) Global optimization using the asymptotically independent Markov sampling method. Computers and Structures, 126 . pp. 107-119. ISSN 0045-7949. doi:10.1016/j.compstruc.2013.04.005.

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In this paper, we introduce a new efficient stochastic simulation method, AIMS-OPT, for approximating the set of globally optimal solutions when solving optimization problems such as optimal performance-based design problems. This method is based on Asymptotically Independent Markov Sampling (AIMS), a recently developed advanced simulation scheme originally proposed for Bayesian inference. This scheme combines importance sampling, Markov chain Monte Carlo simulation and annealing for efficient sampling from an arbitrary target distribution over a multi-dimensional space. Instead of a single approximation of the optimal solution, AIMS-OPT produces a set of nearly optimal solutions where the accuracy of the near-optimality is controlled by the user. Having a set of nearly optimal system designs, for example, can be advantageous in many practical cases such as when there exists a whole set of optimal designs or in multi-objective optimization where there is a Pareto optimal set. AIMS-OPT is also useful for efficient exploration of the global sensitivity of the objective function to the design parameters. The efficiency of AIMS-OPT is demonstrated with several examples which have different topologies of the optimal solution sets. Comparison is made with the results of applying Simulated Annealing, a well-known stochastic optimization algorithm, to the three two-dimensional problems.

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Additional Information:© 2013 Elsevier Ltd. Received 23 August 2012; Accepted 1 April 2013; Available online 29 April 2013. This paper is devoted to the memory of Professor Gerhart I. Schuëller, a great scientist and colleague who is sadly missed. This work was supported by the National Science Foundation under award number EAR-0941374 to the California Institute of Technology. This support is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect those of the National Science Foundation. The authors thank Professor S.K. Au for supplying the structural model for example in Section 5.4. The authors also thank anonymous reviewers of the manuscript for their valuable suggestions and comments that improved the quality of the paper.
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Subject Keywords:Global optimization; Advanced simulation techniques; Markov chain Monte Carlo; Importance sampling; Simulated annealing
Record Number:CaltechAUTHORS:20130806-152109681
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Official Citation:Konstantin M. Zuev, James L. Beck, Global optimization using the asymptotically independent Markov sampling method, Computers & Structures, Volume 126, 15 September 2013, Pages 107-119, ISSN 0045-7949, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39793
Deposited By: Kristin Buxton
Deposited On:06 Aug 2013 22:28
Last Modified:09 Nov 2021 23:47

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