## 1 Introduction  
_General Context_  
The design of aerospace engineering systems (e.g., launch vehicles, aircraft and satellites) encompasses multiple stages, from initial concept development to manufacturing. Each subsequent phase is composed of numerous analyses and optimizations. This enables designers to determine the most suitable design(s) with respect to the system's objective(s) under the hypotheses of the used models. Moreover, in realistic industrial settings, complex systems are often made up of numerous couplings between the several disciplines that are required for their design [1]. For instance, in the field of aerospace engineering, the preliminary sizing frequently integrates the coupling between vast fields such as aerodynamics, propulsion, structure and/or flight mechanics. While a number of those engineering fields are often tightly integrated at the early design stage, the design of the internal layout of future systems is, however, often set aside and is rarely part of a fully integrated design process. The internal layout refers to the task of determining the most efficient and effective arrangement of internal components, structures or devices within the given designed space or system [2]. This problem seeks to optimize the spatial organization of these elements so as to achieve specific objectives, such as maximizing capacity, minimizing costs, improving accessibility or enhancing the overall system performance. In fact, internal layout problems are often solved by hand or by a set of simple heuristic rules (e.g., expert system) able to mimic the cognitive process of experts. Although this process is performed in the last steps of the design procedure, it does not guarantee that an overall optimal solution has been identified at preliminary design stages. Indeed, the arrangement of components often has a first-order impact on the performance of the system (e.g., for flying qualities of an aircraft and power efficiency of an electronic chip) and can thus be critical to the feasibility of a concept. Therefore, the primary focus revolves around the automated optimization of the internal layout of complex systems to ensure its compatibility within multidisciplinary design processes. Optimal layout problems cover a large spectrum of applications: packing [3; 4; 5], facility layout [6; 7; 8], wind farms [9; 10; 11], coverage [12; 13; 14], complex systems layout problems [15; 16; 17], etc. This paper focuses on complex aerospace systems' layout problems. In the field of complex systems design, internal optimal layout problems [15; 16; 17] consist in optimizing the arrangement of components (e.g., various equipment, structure elements and electronics) within the internal structure or physical space of a complex system. The primary goal of addressing internal layout problems is to achieve an arrangement that optimizes various criteria, such as the flying qualities, operational efficiency, accessibility and workflow. Moreover, some geometrical and functional constraints must be satisfied, such as overlapping constraints, balancing constraints or proximity and distance between some components. Most of the time, the set of components must be positioned within a single container [18]. In this case, the layout problem consists in finding the optimal positions and orientations of the components. However, layout problems can also involve positioning the set of components within several containers [19]. Consequently, the layout problem transforms into the task of assigning each component to a specific container while concurrently identifying the optimal arrangement for the assigned containers. Considering the multi-container configuration gives rise to additional challenges as it complicates the single-container optimal layout problem's design search space in terms of both dimensionality and combinatorics. Thus, this paper focuses on solving multi-container optimal layout problems. As an illustrative benchmark, the optimal layout of a multi-container satellite module is considered.