# Safe Three-Dimensional Assembly Line Design for Robots Based on Combined Multiobjective Approach
## 1 Introduction
[PERSON] [26] approached assembly line balance and resource planning problems with a mixed approach that optimized the layout of the block of work cells. However, assembly lines inside work cells have not been designed for layout. Customized indicators have been broadly researched in practical applications for improved algorithm performance. The researchers have considered robust indicators that are related to the layout design [9; 27; 28]. Safety indicators are essential for the design of facility layouts [29]. [PERSON] [30] focused on the occupational health and safety indicators of operators. [PERSON] [31] established a mathematical optimization model in order to consider compactness as an economic measure and distance as a safety indicator for achieving a safe area-matching layout that considers adjacency relationships. Notably, safety indicators can vary in different application scenarios with different research objects. Currently, few researches on safety layouts of assembly lineswith robots have been done, which not only satisfy the safety of robot's collaborative assembly, but also consider the security of the overall layout design of robots and other devices in assembly lines. The above-mentioned researches have not taken into account the safety layout of the application scenarios of the assembly line with robots, a complete layout optimization of workstations, machines, robots, and 3D layout design that highlights safety is missing. In advanced industrial automation, industrial robots must be incorporated into layout models of assembly lines. A review of the literature suggests that many studies have focused on the layout design of assembly lines. Table 1 summarizes the state-of-the-art methods for solving FLPs with assembly lines and then compares layout optimization objects, constraints, and scopes of application. The results indicate that safety has rarely been considered in assembly lines with robots. Moreover, the 3D height information of layout equipment has not been investigated so far. Therefore, this paper proposes a safety layout optimization approach, named SE-NSGA2, which considers safe 3D layout design for assembly lines with robots. This approach considers the height of equipment and determines the safety of different assembly process routes. A quantitative safety indicator is used in order to ensure a safety layout plan for the output assembly line. Subsequently, the multi-objective combination method is based on the high-quality performance of NSGA-II and it integrates the DE algorithm in order to reduce repetitive planning and effectively increase the diversity of solutions. Our experimental and statistical results of optimal layout plan for assembly lines increase by 14.5%, and our approach can generate a safety layout in order to optimize economics and safety. When compared with the original NSGA-II method, the safe layouts increase by 20.63%. This paper is structured, as follows: Section 2 establishes a safety layout model for assembly lines with robots and irregular shaped equipment, describes the assembly line layout problem, and defines the modeling rules of irregularly shaped equipment. Section 3 proposes the combined approach.