# A Facility Layout Algorithm for Logistics Scenarios Driven by Transport Lines
###### Abstract
The simulated annealing algorithm can escape local optima during the search for feasible solutions, and its execution is related to the immediate temperature, with strong search capability and robustness for facility layout problems [24; 25; 26]. The layout algorithm requires solving a mathematical model based on mixed integer programming [27] or linear programming [28] methods. Acceptance criteria for multi-objective simulated annealing algorithms are typically designed using two main approaches. The first approach involves calculating acceptance criteria for multiple objective functions in the problem modeling using weighted summation [29; 30], and the second approach involves designing the acceptance probability based on the Pareto dominance relation [31; 32]. The facility layout problem is similar to the layout problem of the graph structure. Both problems involve placing layout elements within a specified area while satisfying specific constraints; there is a direct correlation between certain layout elements, and the corresponding objectives need to be optimized in the layout problem. The force-directed algorithm is effective for layout problems with a graph structure and is commonly used in the field of visual layout [33; 34; 35] as it applies forces to each element, promoting the clustering or movement of these elements. The facility layout problem can be approached through optimization strategies for layout algorithms and the design of new facility layout models that consider specific assumptions and constraints. [PERSON] et al. [36] introduced a dynamic facility layout problem that incorporates material entrances and exits within the facility. The positioning of material entrances and exits is determined by the actual location and orientation of the facility within the workshop, which is obtained by transforming the layout according to the facility center coordinates. [PERSON] [37] proposed the T-row facility layout problem, which involves a set of facilities and two orthogonal rows, optimizing the layout scheme by determining the vertical entrance points between the orthogonal rows and the arranging the facilities within the interior. [PERSON] et al. [38; 39] addressed the facility layout problem in two ways: by considering obstacles and by extending it to 3D space. Obtaining the shortest path between facilities according to the A* algorithm is more practically valuable than the cost calculation in terms of Euclidean distance or Manhattan distance. There are three main aspects of the logistics facility layout problem: the working facility layout, the layout constraint processing, and the transport line routing. The existing method involves arranging the working facilities initially, followed by placing the transportation lines. The orientation of the transportation routes in a logistics scenario becomes excessively reliant on the layout of the facilities. Indeed, the cost of operating a workshop is primarily determined by the transportation cost associated with each segment of the transport line. Therefore, in logistics planning, the route of the transport line holds greater significance than the layout of the facility. Moreover, in the actual industrial logistics workshop design, the transport line is firstly considered according to the material transport scheme; then, the location of the facilities within the scheme is determined by the preestablished route, and the strategy of designing facility layout around the transport line is adopted, which is quite different from the existing methods. To overcome the limitations of existing methods in solving logistics facility layout problems, this paper proposes a multi-objective facility layout model that integrates industrial logistics characteristics. The key contributions of this model are as follows:  
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