# Generative Artificial Intelligence-Enabled Facility Layout Design Paradigm
## 1 Introduction  
Conceptually, facility layout design (FLD) or facility layout planning (FLP) is an extensive terminology that encompasses the design of factories as well as hospitals, airports, retail stores, and other types of facilities [1]. Owing to the importance and complexity ofproduction or manufacturing systems, the vast majority of research on FLD has focused on factory layout design or shop-floor design [2]. Therefore, the terms facility layout design, factory layout planning, and shop-floor layout are often used interchangeably. Macroscopically, FLD is inherently connected to the strategic planning of production and product development, as well as the planning of processes, machines, and equipment [3]. Facility layout design is crucial for optimizing production efficiency by strategically arranging resources, workstations, and equipment to streamline material flow, minimize transportation time, and reduce costs. FLD can be further divided into concept layout and detailed layout planning. A concept layout includes a coarse spatial representation of functional units with only limited consideration of detailed influences. These details are covered by the subsequent step of detailed layout planning. Generally, there are four basic types of layout, which are fixed-position layout, process layout, cellular layout, and product layout [4]. Each kind of layout has its own distinct advantages depending on the nature of the production process, types of product, and the production volume [5]. However, for a long time, no matter in theory or in practice, the problem of FLD was notoriously difficult for its complexity, and there is no ideal formulation method so far. [PERSON] [6] argued that factory design problems inevitably face ten crucial dilemmas and corresponding deep-seated underlying paradoxes. In essence, the factory design process is essentially information-deficient and is an argumentative and dynamic process [7]. Mathematically, FLD can be modeled in discrete or continuous formulations based on spatial arrangement variables [8; 9]. In discrete FLD, space is divided into a finite set of predefined locations (grid points or nodes), with components assigned to these locations. In continuous FLD, component placement is treated as a continuous variable, offering greater flexibility in design [10]. Layout alternatives are typically deduced using mathematical optimization models: discrete quadratic programming models for equal-sized departments or continuous linear or nonlinear mixed-integer programming models for departments of varying sizes. The design space should be defined by appropriate target criteria, decision variables, and constraints to offer a well-balanced solution set; yet, currently, there are no general guidelines or theoretical studies on the optimal number of goals, variables, and boundaries to achieve a suitable balance between efficiency and complexity [11]. According to computational complexity theory, FLD is a non-deterministic polynomial (NP) hard problem, meaning no algorithms guarantee an optimal solution in polynomial time [12]. To efficiently generate good layouts for large-scale problems, heuristic and metaheuristic approaches [13], as well as machine learning approaches [14], have been introduced to find near-optimal solutions within a reasonable computational time [15]. For complex scenarios, such as for lean, flexible, or agile manufacturing, dynamic or stochastic production uncertainties must be considered in the design. Uncertainty affects the stability of the Pareto set and can undermine the decision-making process [16]. FLD can be categorized as static or dynamic depending on input requirements and time frame. Static facility layout problems assume constant flow between machines, product demand, and product mix, typically addressing a single time period. Dynamic facility layout problems, however, involve periodic evaluation and adjustment based on changing conditions [17].