Modified particle swarm optimization with chaotic attraction strategy for modular design of hybrid powertrains

This paper proposes a new modular design method for hybrid powertrains using a modified accelerated particle swarm optimization (MAPSO) algorithm. The method determines the optimal combination of component specifications and control parameters, where the component specifications include integer variables (e.g. the number of battery modules). A unified chaotic attraction strategy for MAPSO is developed based on a logistic map to improve the probability of achieving the global optimal result. Pareto analysis is carried out to identify the weighting value for the trade-off in modular design. The Comprehensive Reputation Score (CRS), considering both Monte Carlo results and the probability of achieving global optima, is employed to evaluate the advantageous of the MAPSO compared to conventional PSO and four other PSO variants. The MAPSO is verified as the best because it has the highest CRS. Both two-level and simultaneous methods for modular design are developed with the MAPSO, where the former firstly operates component sizing at the level-1 and then conducts control optimization at the level-2, the later optimizes the size and control simultaneously. Compared to the two-level method, the simultaneous method achieves 7% higher cost function value and saves 50% time.