I. Introduction
Transportation sector is perceived as one of the main contributors of greenhouse gas emissions largely owing to burning fossil fuels like gasoline and diesel. In this regard, several pathways have been considered for the electrification of the conventional vehicles, such as pure electric and hybrid electric vehicles. The former has challenges for fast recharging and long-distance driving [1], and the latter is still reliant on fossil fuels. These shortfalls have led to the emergence of proton exchange membrane (PEM) fuel cells (FCs) in electrified vehicles. Fuel cell hybrid electric vehicles (FCHEVs) typically employ a PEMFC as the primary and a battery pack as the secondary power source. Since these sources have variant energetic characteristics, the use of an energy management strategy (EMS) is crucial to distribute the power flow between them [2]. The developed EMSs for FCHEVs can be divided into two main categories of rule-based and optimization-based [3]. Rule-based strategies benefit from straightforward implementation in real-time applications. However, they are sub-optimal owing to their heuristic bases. Optimization-based strategies revolve around the idea of defining a cost function (CF) and minimizing it using different algorithms. They are divided into two groups of global (optimization over a fixed driving cycle) and real-time (optimization based on instantaneous cost functions) methods. CF has a direct influence over the performance of an optimization-based EMS. It quantifies an event arising from one or more variables onto a real number (cost associated with the event). The existing CFs can be roughly divided into single-objective (best solution for a specific criterion) and multi-objective (reaching the best trade-off between two or more conflicting objectives like maximizing performance whilst minimizing fuel consumption). In [4], a single-objective CF (hydrogen consumption minimization) is solved by Pontryagin's minimum principle in a FC-battery hybrid train. In [5], a single-objective CF based on maximizing the FC efficiency is defined for a FCHEV while respecting the dynamic limitations of the system. This work uses quadratic programming (QP) to solve the optimization problem. In [6], a multi-objective CF including the hydrogen consumption and the degradation of the power sources is defined for a hybrid FC bus where the optimal policy is achieved using an offline method dynamic programing. In [7], [8], a multi-objective CF embracing the hydrogen consumption and degradation of the sources is defined and solve by genetic algorithm. In [9]–[11], a multi-objective CF is solved in real-time by means of model predictive control.