Engine design optimization ¶

Problem Description¶

Optimization of the hardware and control system for a new 1.0 litre 3-cylinder gasoline direct injection (GDI) turbocharged engine with a low-pressure exhaust gas recirculation (LP EGR) system for Ford Motor Company A multi-objective optimization problem seeking to minimize fuel consumption and NOx emissions over a two-minute dynamic duty cycle, subject to five constraints (turbine inlet temperature, number of knock occurrences, peak cylinder pressure, peak cylinder pressure rise, total work). Seven decision variables are defined: four define the hardware choices of cylinder compression ratio, turbo machinery and EGR cooler sizing; three relate to control variables that parameterise the engine control logic.

Why was tailoring needed?¶

Combination of problem features not yet addressed by an available algorithm: multi-objective, constrained, mixed-integer, expensive

Baseline algorithm¶

ParEGO (was already implemented in the Tigon library that underpins our Liger open-source MCDM workflow tool being developed in collaboration with Ford)

Tailoring process¶

The Tigon ParEGO implementation uses ACROMUSE as the internal optimizer (this is standard for Tigon but not the vanilla ParEGO)
Integrated two constraint handling alternatives: penalty function and probability of feasibility (the penalty function approach turned out to be more effective)
For the mixed integer representation, the surrogate assumed a continuous surface based on an integer coding, but ACROMUSE was fitted with existing discrete variation operators from the literature: Yu & Gen’s discrete crossover and Rudolph’s discrete mutation
For the evaluation, we collaborated with Hartree to develop an HPC plug-in for the Liger workflow software
Benchmarking (against existing Ford methods: DoE and NSGA-II) was done using the speed reducer and OSY problems (which have similar features to the real-world problem, although only the speed reducer problem has a (single) discrete decision variable)

What was tailored¶

No response

Main problem characteristics¶

Multi-objective (discovered post hoc to have a convex Pareto front - we used an infinity norm for the scalarising function but the problem would likely benefit from using the 1-norm)
Constrained (discovered post hoc that four constraints are active)
Mixed-integer (four discrete and three continuous)
Expensive (several hours to evaluate a single design over HPC; nominal budget of 500 design alternatives)
Nominal candidate design available (which turned out to be dominated)

References¶

https://doi.org/10.1016/j.ejor.2022.08.032; https://doi.org/10.1016/j.asoc.2020.106851; https://github.com/ligerdev/liger; https://www.apcuk.co.uk/impact/funded-projects/ford-motor-company-dynamo/ (note that the engine model is proprietary to Ford; the model was developed by collaborators at the University of Bath as part of the project and is implemented in Mathworks Matlab Simulink, including a physics-based co-simulation model developed in Ricardo WAVE-RT).

Contact information (optional)¶