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Cited by 161Advanced Multi-Objective Optimization AlgorithmsMachine Learning in Materials ScienceSpectroscopy and Chemometric Analyses

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Chimera: enabling hierarchy based multi-objective optimization for self-driving laboratories

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Häse, Florian, Roch, Loïc M., Aspuru-Guzik, Alán·2018·Chemical Science
DOI 10.1039/c8sc02239aPMC PMC6182568

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Abstract

Chimera enables multi-target optimization for experimentation or expensive computations, where evaluations are the limiting factor.

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Fig. 1 Example for the construction of Chimera from three one-dimensional objective functions. Panel (A) Illustration of the three objective functions, f0, f1 and f2, in order of the hierarchy. For constructing Chimera, each objective is considered only in the parameter region where higher-level objectives satisfy the tolerances (dashed lines). Solid lines indicate the upper objective bound in the region of interest used as a reference for the tolerance on the considered objective. The objective functions considered in different parameter regions for this example are illustrated in A.IV. Panel (B) The construction of Chimera for the considered objective. The discrete variant of Chimera (black, panel B.II) is constructed using eqn (2), which was substituted with eqn (6) to generate smooth variants (green, panel B.III) using different smoothing parameter values, where lighter traces correspond to larger parameter values. Panel (C) Pseudo code showcasing the conceptual implementation of Chimera. Panel (D) Analytic expression for the discrete Chimera variant constructed from three objective functions.
Fig. 1 Example for the construction of Chimera from three one-dimensional objective functions. Panel (A) Illustration of the three objective functions, f0, f1 and f2, in order of the hierarchy. For constructing Chimera, each objective is considered only in the parameter region where higher-level objectives satisfy the tolerances (dashed lines). Solid lines indicate the upper objective bound in the region of interest used as a reference for the tolerance on the considered objective. The objective functions considered in different parameter regions for this example are illustrated in A.IV. Panel (B) The construction of Chimera for the considered objective. The discrete variant of Chimera (black, panel B.II) is constructed using eqn (2), which was substituted with eqn (6) to generate smooth variants (green, panel B.III) using different smoothing parameter values, where lighter traces correspond to larger parameter values. Panel (C) Pseudo code showcasing the conceptual implementation of Chimera. Panel (D) Analytic expression for the discrete Chimera variant constructed from three objective functions.CC BY · PubMed Central
Fig. 2 Average relative distance from the Pareto-optimal point determined by the applied constraints. We compare the achieved relative distances of Chimera and c-ASF. Parameter spaces were searched via a grid search (see the main text for details).
Fig. 2 Average relative distance from the Pareto-optimal point determined by the applied constraints. We compare the achieved relative distances of Chimera and c-ASF. Parameter spaces were searched via a grid search (see the main text for details).CC BY · PubMed Central
Fig. 3 Average smallest relative deviations between objectives sampled by different optimization algorithms after 100 objective function evaluations averaged over 25 different optimization runs. Panel (A) reports results on the Fonseca benchmark set, and panel (B) displays results for the Viennet variant benchmark set.
Fig. 3 Average smallest relative deviations between objectives sampled by different optimization algorithms after 100 objective function evaluations averaged over 25 different optimization runs. Panel (A) reports results on the Fonseca benchmark set, and panel (B) displays results for the Viennet variant benchmark set.CC BY · PubMed Central
Fig. 4 Optimization traces representing the smallest relative deviations between sampled objectives and Pareto optimal objectives averaged over 25 individual optimization runs on the ZDT 2 benchmark set. Panel (A) shows deviations in the main objective, and panel (B) displays deviations in the sub-objective.
Fig. 4 Optimization traces representing the smallest relative deviations between sampled objectives and Pareto optimal objectives averaged over 25 individual optimization runs on the ZDT 2 benchmark set. Panel (A) shows deviations in the main objective, and panel (B) displays deviations in the sub-objective.CC BY · PubMed Central
Fig. 5 Achieved objective function values for multi-objective optimization runs on a virtual robot model obtained with Phoenics on Chimera and c-ASF averaged over 50 individual runs. The goal of the optimization runs is to maximize the HPLC response, minimize the sample volume and minimize the execution time beyond the set bounds, indicated with black dashed lines.
Fig. 5 Achieved objective function values for multi-objective optimization runs on a virtual robot model obtained with Phoenics on Chimera and c-ASF averaged over 50 individual runs. The goal of the optimization runs is to maximize the HPLC response, minimize the sample volume and minimize the execution time beyond the set bounds, indicated with black dashed lines.CC BY · PubMed Central
Fig. 6 Objective function values sampled in optimization runs with two different hierarchies in the objective. Hierarchy order shown in green dots: (i) transfer efficiency, (ii) energy gradient, (iii) total distance. Hierarchy order shown in red triangles: (i) energy gradient, (ii) transfer efficiency, (iii) total distance. (A) Optimal points with respect to all objectives discovered during individual optimizations. Projections illustrate bootstrapped sampling paths leading to the best performing points. (B–D) Detailed illustration of projected sample traces. Arrows indicate the general paths taken by the optimization algorithm for the different hierarchy orders. More transparent points have been sampled earlier in the optimization procedure, and more opaque points have been sampled at a later stage. White regions indicate the target values for all considered objectives.
Fig. 6 Objective function values sampled in optimization runs with two different hierarchies in the objective. Hierarchy order shown in green dots: (i) transfer efficiency, (ii) energy gradient, (iii) total distance. Hierarchy order shown in red triangles: (i) energy gradient, (ii) transfer efficiency, (iii) total distance. (A) Optimal points with respect to all objectives discovered during individual optimizations. Projections illustrate bootstrapped sampling paths leading to the best performing points. (B–D) Detailed illustration of projected sample traces. Arrows indicate the general paths taken by the optimization algorithm for the different hierarchy orders. More transparent points have been sampled earlier in the optimization procedure, and more opaque points have been sampled at a later stage. White regions indicate the target values for all considered objectives.CC BY · PubMed Central
Fig. 7 Results for the inverse-design of an excitonic system with (i) a low energy gradient, (ii) high transfer efficiency and (iii) large total distance between the first and the last site. (A) Optimization traces averaged over 25 individual optimization runs, indicating the average required number of designed systems to achieve one, two or all objectives. (B) Illustrations of sampled excitonic systems achieving one, two or three objectives. Arrows represent transition dipoles with their location and orientation to the principal axis. (C) Excited state energies of the systems depicted in (B). The overall energy gradients are reported in the legends.
Fig. 7 Results for the inverse-design of an excitonic system with (i) a low energy gradient, (ii) high transfer efficiency and (iii) large total distance between the first and the last site. (A) Optimization traces averaged over 25 individual optimization runs, indicating the average required number of designed systems to achieve one, two or all objectives. (B) Illustrations of sampled excitonic systems achieving one, two or three objectives. Arrows represent transition dipoles with their location and orientation to the principal axis. (C) Excited state energies of the systems depicted in (B). The overall energy gradients are reported in the legends.CC BY · PubMed Central

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Metadata

Authors
Häse, F., Roch, L. M., & Aspuru-Guzik, A.
Affiliations
  • Harvard University (US)
  • Department of Chemistry and Chemical Biology
ORCID
Venue
Chemical Science
Publisher
Royal Society of Chemistry (RSC)
Published
2018
Volume
9
Issue
39
Pages
7642-7655
ISSN
  • 2041-6520 (ISSN-L)
  • 2041-6539
DOI
10.1039/c8sc02239a
PMC
PMC6182568
OpenAlex
W2889272453
Cited by
161
References
73
Citations by year
2026: 20 · 2025: 21 · 2024: 20 · 2023: 29 · 2022: 22 · 2021: 28 · 2020: 15 · 2019: 6
FWCI
9.06
Type
journal article
Language
en
Open access
Licence
Locations
  • Chemical Science (publishedVersion, cc-by)
  • ChemRxiv (acceptedVersion, cc-by-nc-nd)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Royal College of Surgeons in Ireland (submittedVersion, cc-by-nc-nd)
Funders
  • Harvard University
  • Tata Sons (A32391)
  • FAS Division of Science, Harvard University
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Multi-Objective Optimization Algorithms
  • Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
  • Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
Keywords
chimeras, multi-objective optimization, self-driving laboratories, automated experimentation, self-calibration, inverse design, interpretability

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