## 1 Introduction  
In recent years, additive manufacturing has grown more and more as its features provide design freedom, consolidation, customization of products, manufacturing-on-demand, weight reduction, and reduced human effects. Additive manufacturing (AM) is playing a significant role in diversified sectors such as aerospace, energy, oil and gas, automotive, medical, tool and die, and consumer goods. Directed energy deposition (DED) is one of the AM technologies. The DED process is described as \"additive manufacturing process in which focused thermal energy is used to fuse materials by melting [1, 2, 3, 4]. In industries such as aerospace, defence, automotive, tooling, and conventional machining manufacturing processes are unsustainable as they generate much more scrap material. DED can reduce material waste, energy consumption, production cost, and working hours. It can be used in the production of large parts with the possibility of powder or wire feeding using both robotic and gantry systems. It offers the opportunity to create hybrid products as well. It has a broad range of applications in manufacturing free form geometries, repair applications, coating and surface modification, and the fabrication of functionally graded materials, and it is an especially significant process in the manufacture of large parts, which is not appropriate in terms of installation on powder bed fusion device tables in the aerospace industry, such as rocket cases and big structural cross brackets [5]. [PERSON] et al. [6] reviewed that hybrid AM processes could be employed for large-scale multi-materials and/or different raw materials locally for different sections of aerospace components, in order to better tailor the component to engineering requirements as a future study. Hybrid processes have been found effective at minimising or eliminating defects occurring in AM, achieving better mechanical properties and functionality of the final parts and improving the process performance as well. The recent literature has investigated whether the DED process is available for creating hybrid parts. [PERSON] et al. [7] offered a solid foundation for a wide application of hybrid DED incorporating layer-by-layer deposition and thermal milling processes to achieve complex structural parts such as closed impellers. The thermal milling process was applied after each deposition, which not only maintained the relatively high temperature of the part but also improved the surface quality with a pre-set height for the next deposition step. [PERSON] et al. [8] observed the combination of different additive manufacturing technologies on a space part which has smaller and more suitable dimensions for powder bed technologies. They investigated samples of a hybrid SLM/DED AM-processed Inconel 718 and the hybrid process created a complex and different microstructure combining two different AM processes. In order to produce small size hybrid part, SLA can create an alternative solution with a low density heat input. It is a cost-effective AM solution for small-scale components with high build speed and resolution from photo-curable resin [9]. [PERSON] et al. [10] developed a small-size hybrid component using non-metallic biobase materials such as PCM within SLA process. Compound structures filled with different typologies of PCM were realised and thermally characterised to design a modular prototype that can be used for thermal storage. It was found that the heating process is predominant within the heating system using ANoVA analysis. In the state-of-the-art, topology optimization techniques, a useful tool for weight reduction and part optimization, do not work properly for such AM processes, as all AM methods need to have their own dedicated design rules and requirements applied. Additionally, there is no widespread and extensive knowledge on topology optimization for the DED process in order to create a hybrid part production in the literature.