New MOGO optimisation algorithm wins at Monte Carlo

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  • Published: Apr 2, 2017
  • Author: Ryan De Vooght-Johnson
  • Channels: Laboratory Informatics / Chemometrics & Informatics
thumbnail image: New MOGO optimisation algorithm wins at Monte Carlo

Optimisation of multiple objectives is a challenge

Classical process optimisation normally looks at varying several input variables in order to optimise a single output variable or ‘objective’, such as yield or purity. However, in practice more than one objective may be important, so methods are required to simultaneously achieve optimum outcomes for these. The different objectives often conflict, for example, increasing the yield may give an unacceptable decrease in purity. Pareto optimisation is often used, in which no unique solution is found, but a ‘Pareto front’ of points on a multi-dimensional graph is produced. At the Pareto front, any change that improves the value of one objective will make the value of another objective worse, i.e. it’s as good as it gets.

Gaussian process regression models (GPM, also known as Kriging modelling) are being increasingly employed in such problems. In these models, interpolations between data points are given by appropriate Gaussian distributions, rather than simply using the curve that optimises smoothness. Various algorithms have been applied to achieve effective GPM.

Researchers from the Forschungszentrum Jülich (Jülich Research Centre) developed a novel algorithm, MOGO (multiple objective global optimisation). GPM is used to examine the relationships between variables, and the Pareto front is given by an iterative process, in which the output from successive experimental runs determines the probability of a particular next run being chosen by the Monte Carlo method used.

New optimisation MOGO algorithm tested in ion chromatography simulation

The new MOGO algorithm was tested with an in silico ion chromatogram case study, using the CADET (chromatography analysis and design toolkit) software package. The simulated task was to separate three proteins, lysozyme, cytochrome c and ribonuclease a, on the cationic ion exchanger SP Sepharose FF. The purity and yield of cytochrome c, along with the total run time, were the three output parameters (objectives) that were optimised. These objectives were conflicting, with higher purities only being achieved with lower yields or longer run times. The five input parameters were the start and finish collection times for cytochrome c (t1 and t2) and the gradient parameters determining the changes to the salt concentration in the eluent (p1, p2 and p3).

In order to provide initial data for GPM, a classical 23 full factorial design with a centre point was carried out. The CADET software was used to give output values of the yield, purity and total run time. The iterative MOGO algorithm was then applied, each experiment being chosen to maximise the ‘expected hypervolume improvement’ (EHVI), a measure of the envisaged improvement on each iteration. The actual parameters of the new run were chosen by MCMC (Markov chain Monte Carlo) sampling. The probability of any particular new run being chosen was proportional to its EHVI value. Appropriate stopping criteria were introduced to limit the number of runs. It was found that on average less than 26 iterations were needed to reach the end point. The end points effectively matched the Pareto front calculated by a brute force method. It was noted that the optimisation could be run in parallel, saving time at the cost of more experiments. In this case, the MCMC sampling was allowed to ‘draw’ more than one set of conditions, so that the parallel runs differed.

MOGO algorithm suitable for multiple objective optimisation

The MOGO algorithm successfully allowed optimisation of conflicting multiple objectives with a relatively small number of simulation runs. The method can be run either in series or parallel, depending on whether time or minimising the number of runs is the crucial factor. Algorithms such as MOGO can give superior results to conventional experimental designs, with applications well beyond chromatography. It will be interesting to see how well the algorithm performed in real life chromatographic systems, comparing it to other optimisation techniques.

Related Links

Biotechnology Journal, 2017, Early View paper. Freier et al. Multi-objective global optimization (MOGO): Algorithm and case study in gradient elution chromatography.

Wikipedia, Kriging

Wikipedia, Markov chain Monte Carlo

Wikipedia, Pareto Efficiency

Article by Ryan De Vooght-Johnson

The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.

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