## 1 Introduction
More precisely, the simplified model of the telecommunication satellite INTELSAT-III is employed [19; 20; 21]. This application case has been widely studied in the literature and constitutes a representative optimal layout problem. Figure 1 shows different views of the satellite module. The layout problem is mostly referred to as a Satellite Module Layout Problem (SMLP) in the literature. This involves determining the optimal assignment scheme for components within the module's containers as well as identifying the optimal positions and orientations of these components within the container. The objective is to minimize the overall inertia of the system. The following geometrical constraints have to be satisfied: non-overlapping constraint, balancing constraints and angle of inertia constraints. Functional constraints must also be satisfied in order to keep some components apart from a given distance (e.g., to ensure to satisfy specifications about the radiative environment). Over the past twenty years, many approaches have been developed to deal with optimal layout problems. The first range of techniques are exact methods that guarantee  
Figure 1: Views of the simplified model of the INTELSAT-III satellite module, as detailed in [20]. The redder the components, the heavier their corresponding masses. the optimality of the solution. Among them, the CPLEX solver [22], the Branch and Bound algorithm [23; 24; 25] and Dynamic Programming [26; 27; 28] have been used to solve Quadratic Assignment Problem [29] and Mixed Integer Linear Programming [30] formulations. Heuristics have then been developed in order to provide good quality results in a more reasonable computational time in comparison to exact methods. They mainly consist of construction [31; 32; 33] and improvement-based algorithms [34; 35; 36]. The most used approaches employed for optimal layout problems involve the utilization of metaheuristic algorithms. These problem-independent techniques are designed to explore the search space more comprehensively compared to previously employed heuristic methods, often yielding better solutions. Among them, Simulated Annealing [37; 38; 39; 40], Tabu Search [41; 42; 43], Genetic Algorithm [44; 45; 16; 46], Particle Swarm Optimization [47; 48; 49], Covariance Matrix Adaptation-Evolution Strategy [47; 50], etc. have been used to solve various forms of optimal layout problems. Those techniques have also been hybridized between themselves [51; 52; 53] or with heuristic methods [17; 54] in order to take advantage of the strengths of different algorithms and improve their overall computational performance. Another range of techniques are quasi-physical methods, which have their origins in both physics and mathematics and aim at mimicking the laws of physics. Most of the time, they correspond to energy [55] or force-based algorithms [3; 56; 57]. Eventually, machine learning methods have been applied to layout optimization problems, although their exploration and investigation in this domain are still relatively limited at present [58]. For instance, Bayesian Optimization [59], Neural Networks [60] or Reinforcement Learning [61] have been used to solve optimal layout problems. In the literature, mostly single-container optimal layout problems are solved. Moreover, considering the SMLP, very few studies include the optimization of the components' assignment. Most of the time, the components are allocated to the containers with an assignment scheme based on human knowledge and a method is derived to solely solve the layout of the assigned containers [20]. Finally, the existing approaches are mostly based on metaheuristic methods. However, it has been highlighted in [62; 63; 64] that metaheuristic techniques may present some weaknesses for solving problems with complex combinatorial spaces or a large number of constraints. In that respect, this paper aims to develop a two-stage algorithm combining a genetic algorithm and a quasi-physical approach for component assignment and layout optimization.