Summary

A novel process has been developed for reducing complexity in real-world, high dimensional,
multi-objective optimisation problems. This approach relies on being able to identify and 
exploit local harmony between objectives to reduce dimensionality.

To achieve this, a systematic and modular process has been designed to cluster the
Pareto-optimal front and apply a rule-based Principal Component Analysis including
preference articulation for potential objective reduction.

Proof-of-principle is demonstrated on a simplified, real-world, automotive diesel
engine calibration optimisation problem comprising three objectives. Some objective
reduction was achieved in one cluster, from which a selected solution performed better
when compared with the parent three-objective problem.

On a six-objective version of the diesel problem, the complexity reduction process
resulted in three and four objective sub-problems. In the former, a significant
improvement was achieved in one of the retained objectives at very little cost to the
others.

A further case study comprised a ten-objective gasoline engine cold start calibration
optimisation problem, including sensitivity objectives related to a control system
actuator, which exhibited significant variation. For brevity, efficiency and to support
future software development, a mathematical notation was developed for the clustering
and objective reduction analysis. To address the computational demands, a parallel
computing cluster was utilised and a parallel island-based optimisation algorithm was
developed. The complexity reduction process consists of four stages and progressively
reduces objective dimensionality where evidence of local objective harmony exists. It
involves the calibration engineer at various stages to advise on objective priorities and
to discard clusters containing solutions of no interest. This process culminated in two
sub-problems, one of three and one of four conflicting objectives. A comparison of the
resulting Pareto-optimal front, selected preferred solution and an independently generated,
manually tuned calibration was made for each of the two sub-problems. In both
cases, the preferred solution outperformed the independent calibration.