Comparison of the genetic algorithm and incremental optimisation routines for a Bayesian inverse modelling based network design

The design of an optimal network of atmospheric monitoring stations for the observation of carbon dioxide (CO₂) concentrations can be obtained by applying an optimisation algorithm to a cost function based on minimising posterior uncertainty in the CO₂ fluxes obtained from a Bayesian inverse modelling solution. Two candidate optimisation methods assessed were the evolutionary algorithm: the genetic algorithm (GA), and the deterministic algorithm: the incremental optimisation (IO) routine. This paper assessed the ability of the IO routine in comparison to the more computationally demanding GA routine to optimise the placement of a five-member network of CO₂ monitoring sites located in South Africa. The comparison considered the reduction in uncertainty of the overall flux estimate, the spatial similarity of solutions, and computational requirements. Although the IO routine failed to find the solution with the global maximum uncertainty reduction, the resulting solution had only fractionally lower uncertainty reduction compared with the GA, and at only a quarter of the computational resources used by the lowest specified GA algorithm. The GA solution set showed more inconsistency if the number of iterations or population size was small, and more so for a complex prior flux covariance matrix. If the GA completed with a sub-optimal solution, these solutions were similar in fitness to the best available solution. Two additional scenarios were considered, with the objective of creating circumstances where the GA may outperform the IO. The first scenario considered an established network, where the optimisation was required to add an additional five stations to an existing five-member network. In the second scenario the optimisation was based only on the uncertainty reduction within a subregion of the domain. The GA was able to find a better solution than the IO under both scenarios, but with only a marginal improvement in the uncertainty reduction. These results suggest that the best use of resources for the network design problem would be spent in improvement of the prior estimates of the flux uncertainties rather than investing these resources in running a complex evolutionary optimisation algorithm. The authors recommend that, if time and computational resources allow, that multiple optimisation techniques should be used as a part of a comprehensive suite of sensitivity tests when performing such an optimisation exercise. This will provide a selection of best solutions which could be ranked based on their utility and practicality.