A concurrent implementation of the surrogate management framework with application to cardiovascular shape optimization
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A concurrent implementation of the surrogate management framework with application to cardiovascular shape optimization Aekaansh Verma1 · Kwai Wong2 · Alison L. Marsden3,4,5 Received: 25 February 2019 / Revised: 8 January 2020 / Accepted: 8 January 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The surrogate management framework (SMF) is an effective approach for derivative-free optimization of expensive objective functions. The SMF is typically comprised of surrogate-based infill methods (SEARCH step) coupled to pattern search optimization (POLL step). Although the latter is easy to parallelize, parallelization of the SEARCH step requires surrogate-based strategies that generate multiple candidates at each iteration. The impact of such SEARCH methods on SMF performance remains poorly explored. In this paper, we extend the SMF to incorporate concurrent evaluations at the SEARCH step by comparing two different infill approaches: single search multiple error sampling and expected improvement constant liar approaches. These variants are generalized to address non-linearly constrained problems by the filter method. The proposed methods are benchmarked for different infill sizes, while accounting for the variability in initialization. We then demonstrate the proposed methods on two shape optimization problems motivated by hemodynamically-driven surgical design. Surrogate-based multiple-infill strategies outperform their single-infill counterparts for a fixed computational time budget on bound constrained problems. Insights drawn from this study have implications not only on future instances of the SMF, but also for other surrogate-based and hybrid parallel infill methods for derivative-free optimization. Keywords Surrogate management framework · Derivative free optimization · Parallel optimization
* Aekaansh Verma [email protected] Extended author information available on the last page of the article
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1 Introduction Surgeries performed to treat cardiovascular disease are becoming increasingly personalized and precise, moving away from one-size-fits all treatment plans. This has led to the need for methods that assess the likelihood of adverse postsurgical outcomes, including tools that predict blood flow patterns and distributions for a variety of cardiovascular diseases. Realistic hemodynamic simulation techniques have emerged as an accurate method to obtain patient-specific blood flow patterns. Advances in high performance computing (HPC) have recently enabled coupling these methods to optimization techniques to design cardiovascular surgeries and medical devices. This combination represents a paradigm shift in medical treatment planning and device design towards extensive computational prototyping, followed by targeted in-vitro or in-vivo testing. Several prior studies couple optimization methodology with cardiovascular modeling frameworks towards design and development of surgical geometries (Abraham et al. 2005; Verma et al. 2018
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