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This paper presents an optimal control co-design framework of a parallel electric-hydraulic hybrid powertrain specifically tailored for heavy-duty vehicles. A pure electric powertrain, comprising a rechargeable lithium-ion battery, a highly efficient electric motor, and a single or double-speed gearbox, has garnered significant attention in the automotive sector due to the increasing demand for clean and efficient mobility. However, the state-of-the-art has demonstrated limited capabilities and has struggled to meet the design requirements of heavy-duty vehicles with high power demands, such as a class 8 semi-trailer truck. This is especially evident in terms of a driving range on one battery charge, battery charging time, and load-carrying capacity. These challenges primarily stem from the low power density of lithium-ion batteries and the low energy conversion efficiency of electric motors at low speeds.