## 1 Introduction  
The impellent need to decrease greenhouse gases (GHGs) emissions is driving car manufacturers towards different propulsion systems. In the last decade, the internal combustion engine (ICE) has often been coupled with electrical components in order to reduce its fuel consumption and, consequently, its pollution. In this context, hybrid electric vehicles (HEVs) are being developed by most car manufacturers owing to their interesting trade-off between fuel efficiency, drivability, and CO2 emissions [1]. Nevertheless, the presence of different power sources along with the additional components for implementing the electric drive do impact the design process of HEVs. To find a globally optimal and universally accepted development method still represents an open question [2]. A lot of research has recently been conducted worldwide to address this problem. Fuel economy (FE) variability (i.e., the variation in fuel economy due to different driving styles, traffic conditions, and so on) has been studied and addressed in [3], hence providing a design method capable of reducing the variability in FE by up to 34% with respect to a standard process. A clutch-less multimode parallel HEV (CMP-HEV) has been firstly introduced in [4] and then its design parameters have been studied in [5], providing interesting FE and acceleration performance analyses. The battery degradation and its effect on fuel economy and total cost of ownership (TCO) have been considered in [6] for the design methodology of a heavy-duty HEV. Evolutionary algorithms (EAs) have been exploited for sizing HEVs thanks to their capability of thoroughly exploring the design space. As an example, a heavy-duty series HEV is sized using chaos-enhanced accelerated particle swarm optimization (CA PSO) in [7], outperforming the standard PSO and providing an interesting design method. In [8], a light-duty parallel HEV is designed using three different derivative-free optimization algorithms (i.e., divided rectangles, simulated annealing, and genetic algorithm) and a hybrid method, obtaining improvements in fuel consumption when comparing the results with the initial HEV layout. Nevertheless, to the best of the authors' knowledge, the previous works in the literature have not always completely assessed the light-duty HEV design problem. Indeed, they often focused specifically on achieving high fuel economy without accurately addressing the production costs and/or they did not exhaustively explore the whole design space. Moreover, not many studies take into account a lower number of gears than the standard (i.e., five or six gears for passenger cars). In a recent study of the authors [9], a comparison of different numbers of gears in a parallel HEV has been brought up, based upon economic considerations taking into account both the lifetime operative cost and transmission cost. The cooperation of the electric machine (EM) with the ICE was demonstrated to be capable of balancing a lower number of gears compared with a conventional vehicle (i.e., propelled by the ICE alone) while assessing the fuel economy. Starting from the reviewed studies, the objective here is to provide an exhaustive methodology to assess the performances of an HEV by means of various analyses. Evaluation metrics include not only vehicle performance such as acceleration capability and estimated fuel consumption, but also the production cost of chassis, battery, ICE, EM, and transmission, thus addressing the optimal HEV powertrain design problem considering different targets. To this end, a multi-objective PSO algorithm is used at the vehicle design level for efficiently sizing the different components in the HEV powertrain architecture. Then, dynamic programming (DP) is used at the powertrain control level for the optimal choice of driving mode, gear selection, and power split between ICE and EM, retaining both a standard drive cycle and different real-world driving missions.