## 2 State of the Art
### Focus on Satellite Module Layout Problems  
The application case considered in this paper is the Satellite Module Layout Problem (SMLP) [19; 21; 112]. The SMLP has been studied for the past 20 years and is considered as a representative optimal layout problem for the aerospace industry. Mainly, metaheuristic techniques have been developed in order to deal with this benchmark, sometimes assisted by other methods.  
[PERSON] et al. [113] adopted a Pareto genetic algorithm for optimizing the compactness, assembly and maintenance of a small SMLP composed of seven components and a single-container. [PERSON] et al. [114] proposed a hybrid algorithm combining a genetic algorithm and sequential quadratic programming (SQP) to solve the layout of spacecraft propellant systems comprising six components.  
Those studies involved less than a dozen components. With the increase in the number of components, objective functions and constraints, cooperative co-evolutionary and hybrid algorithms were developed in order to deal with up to 60 components. [PERSON] et al. developed a dual-system cooperative co-evolutionary algorithm (named Oboe-CCEA) forthe SMLP based on both the cooperative co-evolutionary framework and the variable-grain model [20]. [PERSON] et al. proposed a hybrid multi-mechanism optimization approach (HMMOA) for the satellite layout optimization problem [115]. [PERSON] et al. developed a new dual-system cooperative co-evolutionary algorithm for the SMLP based on the cooperative co-evolutionary framework [112].  
The previous studies dealt with multi-container configurations of the SMLP, as described in Figure 1. However, the assignment of the components to the containers was fixed and determined thanks to human expert knowledge. The mentioned methods only focused on solving the layout of the components in the four containers. Some recent studies optimized the assignment of the components in addition to their layout. [PERSON] et al. proposed an integrated assignment and layout method for an SMLP [116]. This approach adopts Tabu Search and Differential Evolution to solve the component assignment and layout optimization problems. However, the number of components was limited to 19. [PERSON] et al. proposed a two-stage algorithm called Dynamic FS to solve both assignment and layout tasks of the multi-container SMLP [19]. Heuristic rules are used to assign the components. They are mathematically translated into a multi-objective optimization problem and an NSGA-II algorithm is employed to optimize it. The assignment list is then determined using a fuzzy decision-making method. The layout task is performed using the NDCCDE/DPSO algorithm from [112], which corresponds to a dual-system cooperative co-evolutionary algorithm.  
Most of the previous methods used to tackle optimal layout problems and, more particularly, Satellite Module Layout Problems rely on metaheuristic frameworks. Metaheuristic algorithms provide various frameworks that can be easily adapted to the problems at hand and benefit from a large number of references in the literature. However, it has been highlighted in [62; 63; 64] that pure metaheuristic techniques may present some weaknesses for solving problems with complex combinatorial spaces or a large number of constraints. Moreover, a small number of studies tackle both assignment and layout tasks of the considered SMLP benchmark [19].  
Consequently, in this paper, a two-stage algorithm combining the Genetic Algorithm for optimizing the assignment and a quasi-physical approach for optimizing the layout of multi-container optimal layout problems is proposed. It is applied to the SMLP as a benchmark.