Complexity Reduction in High-Dimensional Multi-Objective Optimisation


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.