PPubMed7 Jun 2019Cited 19×

Accurate and reliable estimation of kinetic parameters for environmental engineering applications: A global, multi objective, Bayesian optimization approach

Derek C. Manheim, Russell L. Detwiler

Abstract

Title: Graphical abstract

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A global multi‑objective Bayesian optimization workflow yields more accurate kinetic parameters for environmental engineering models.

What’s new

i.Developed a global, multi‑objective Bayesian optimization framework for estimating parameters of unstructured kinetic models.
ii.Integrated several evolutionary algorithms (NSGA‑III, AMALGAM‑MO, RVEA) and Approximate Bayesian Computation via DREAM‑ZS to explore compromise solution space.
iii.Demonstrated the approach on microcystin biodegradation datasets, achieving faster convergence and lower objective function values compared to local methods.
iv.Provided open access dataset and MATLAB code for reproducibility.

How they did it

The workflow first applies single‑objective global optimizers (e.g., AMALGAM‑SO) with 500,000 function evaluations, then uses multi‑objective algorithms (NSGA‑III, AMALGAM‑MO, RVEA) for 20,000 generations with a population of 100. The best compromise solutions are fed into an Approximate Bayesian Computation scheme using the DREAM‑ZS sampler to obtain posterior parameter distributions. Five independent repetitions were performed for each study to assess variability.

What they found

Convergence achieved after ~150,000–200,000 generations (≈900 k total evaluations) with R‑statistics < 1.2 for all models.
Global optimization methods produced the smallest mean sum‑of‑squared‑residuals and highest log‑likelihood values (e.g., MinOF as low as 3.29 × 10⁻² for AMALGAM‑SO in Study 1).
Multi‑objective algorithms outperformed local FMINCON methods, reducing objective function values by up to an order of magnitude.
Fixed run settings: 500,000 function evaluations for single‑objective runs; 20,000 generations, population size = 100 for multi‑objective runs.

Caveats

✕Some complex models (e.g., Contois, Dabes) required more generations and showed poorer convergence.
✕Low replication in experimental datasets (≤ 3 repeats) forced use of averaged data, potentially limiting statistical robustness.
✕The Bayesian ABC step relied on predefined tolerance and summary statistics, which may affect convergence for certain kinetic structures.
✕Results are based on batch biodegradation experiments; applicability to continuous or field‑scale systems remains untested.

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