Comparison of bi-level optimization frameworks for sizing and control of a hybrid electric vehicle

This paper discusses the integrated design problem related to determining the power specifications of the main subsystems (sizing) and the supervisory control (energy management). Different bi-level optimization methods, with the outer loop using algorithms as Genetic Algorithms, Sequential Quadratic Programming, Particle Swarm Optimization or Pattern Search (DIRECT) and the inner loop using Dynamic Programming, are benchmarked to optimally size a parallel topology of a heavy duty vehicle. Since the sizing and control of a hybrid vehicle is inherently a mixed-integer multi-objective optimization problem, the Pareto analyses are also addressed. The results shows significant fuel reduction by hybridization and engine downsizing and offer insights in the usability of these nested optimization approaches