1. Introduction
The cruise industry has experienced continuous expansion in recent years, with global passenger volumes reaching tens of millions annually. In 2023, the number of cruise passengers reached 31.7 million, representing 107% of the 2019 level and reflecting a net increase of nearly 2 million compared to 2019 [
1]. Simultaneously, demographic shifts are reshaping the demand for cruise tourism. Global population aging has become a growing concern in many developed and developing countries. In China, for instance, the number of individuals aged 60 and above reached 297 million by the end of 2023 [
2], and this number is projected to exceed 400 million by 2035, accounting for approximately 30% of the national population [
3]. This aging trend presents challenges and opportunities, positioning older adults as a key consumer segment in the cruise market.
Modern cruise ships are enclosed, multifunctional environments that integrate hospitality, entertainment, and transport functions, where limited evacuation alternatives amplify the critical importance of efficient and comprehensive emergency planning. Ensuring the safety of all passengers, particularly during emergencies, is paramount, and is complicated by the asymmetrical characteristics of the onboard population. Passengers differ in mobility, perceptual abilities, walking speeds, and cognitive response, all of which influence evacuation performance. The spatial environment of cruise ships, however, is often symmetrical by design, especially in public spaces such as theaters and atria, highlighting the tension between environmental symmetry and passenger heterogeneity. Bridging this asymmetry-symmetry gap is a fundamental challenge in evacuation planning.
Evacuation simulation has emerged as a widely adopted tool for assessing emergency response in complex environments such as buildings, airports, and ships. With advances in computational technologies, evacuation analysis has evolved from retrospective investigations to predictive modeling. In the maritime domain, simulation evacuation models are recognized by the International Maritime Organization (IMO) as effective tools for analyzing passenger movement and developing improved evacuation strategies.
Evacuation modeling methods are typically categorized into two types: macroscopic models and microscopic models. Macroscopic models treat crowd movement as continuous fluid-like flows, offering computational efficiency but lacking the capacity to account for individual behavioral variability [
4,
5,
6]. Microscopic models, on the other hand, consider each passenger as an autonomous agent with specific attributes, enabling a more accurate representation of decision-making and interactions in evacuation scenarios [
7,
8,
9].
Within the category of microscopic models, cellular automata (CA) models [
10] and social force models [
11,
12] are widely adopted. While the social force model captures human dynamics through continuous force interactions, CA models discretize time, space, and movement states, offering higher computational efficiency and scalability for large-crowd simulations [
13,
14]. To enhance the simulation of passenger behavior in confined spaces, numerous extensions of cellular automata (CA) have been proposed over time, including multi-grid, fine mesh, floor field, and lattice gas models [
15,
16,
17,
18].
In ship evacuation research, environmental variables and passenger characteristics have been given attention. For example, fire-related factors (such as carbon monoxide concentration, temperature, and visibility [
19,
20]) have been incorporated into CA models to simulate fire evacuation more accurately [
21]. Other studies have addressed congestion caused by reverse movement in narrow corridors [
22], rapid smoke spread in flat, large spaces [
23], and the influence of ship motion, including list and trim [
24,
25,
26]. Furthermore, agent-based models have also been utilized to examine how ship swaying influences passenger movement [
27].
While prior studies have incorporated certain environmental and behavioral aspects, many still treat passengers as homogeneous entities, neglecting the influence of individual differences on evacuation outcomes. In the real evacuation process, factors such as age, gender, mobility, and cognitive ability can substantially affect evacuation performance. Capturing these heterogeneities is essential for reliable evacuation modeling.
To address this need, the IMO’s Maritime Safety Committee issued guidelines recommending both simple and advanced evacuation analyses [
23]. The former assumes identical characteristics for all passengers, while the latter accounts for individual variability, producing more realistic but also more complex and stochastic results. In addition, the IMO further issued MSC.1/Circ1533 [
28], which outlines key personal attributes—such as age, gender, reaction time, and walking speed—necessary for simulating evacuation on passenger ships. Building on these frameworks, recent research has introduced behavior-based models that distinguish passengers by type [
29], simulate collaborative search behavior [
30], incorporate interaction effects such as friction and repulsion [
31], and further extend to heterogeneous populations characterized by multi-type mobility speed and avoidance strategies [
32].
Despite these advances, limited research has focused on the role of evacuation signage, especially within the context of cruise ships. Most studies emphasize architectural elements, focusing on stair design [
33], evacuation route planning [
34], or the timing of evacuation orders [
35], while signage layout optimization has often been overlooked. Signage serves as a primary guidance system in maritime environments, where the unfamiliarity of layouts and the absence of alternative escape routes make effective signage layout strategies critical for passenger safety during emergencies. A few efforts have modeled signage placement as a maximum coverage location problem [
36], incorporating occlusion effects and assuming a fixed number of signs. These studies, applied in single-floor supermarkets, demonstrated improvements in evacuation efficiency using CA model validation. Others have developed multi-objective signage models that jointly optimize economic costs and visibility coverage [
37], validated in exhibition halls using AnyLogic simulations with gender-specific speed parameters. However, most of these approaches employ a two-stage framework—signage layout optimization followed by separate evacuation validation—and often neglect dynamic passenger-signage interactions or comprehensive cost-performance integration.
To overcome these limitations, this study proposes a bi-objective signage optimization model that simultaneously considers cost and visibility coverage across heterogeneous age groups. A cellular automata-based evacuation simulation is developed to capture dynamic interactions between passengers and signage, with a specific emphasis on visibility reductions under smoke-filled conditions. Through this integrated framework, the study explores how the asymmetry of passenger behavior interacts with the symmetry of cruise ship layouts to affect evacuation outcomes.
The remainder of the paper proceeds as follows:
Section 2 introduces the cellular automata modeling framework, including static potential field construction, signage attraction mechanisms, and evacuation rules.
Section 3 presents an improved signage layout optimization model, which integrates heterogeneous passenger features to identify the respective optimal results.
Section 4 describes the simulation experiments designed to assess evacuation performance under various scenarios. Finally,
Section 5 presents a summary of the key results, discusses the study’s limitations, and suggests directions for future research.
5. Conclusions
This study proposes a cellular automata model that incorporates the age structure of passengers to simulate evacuation dynamics in enclosed ship environments. The model accounts for variations in passengers’ visual field ranges and signage influence zones across different age groups. It quantitatively integrates the static potential field, signage attraction field, and direction guidance factor to reflect realistic evacuation behavior. An optimal signage layout strategy is explored to achieve a balance between economic cost and evacuation effectiveness. The model further investigates the influence of passenger age composition and smoke concentration on evacuation performance. A simulation experiment is conducted using the main theater of the Adora Magic City cruise ship as a case scenario, incorporating varying proportions of age groups and smoke visibility conditions. The proposed model provides a practical decision-support tool for onboard signage layout by incorporating passenger mobility and visual asymmetries. This approach offers valuable guidance for improving signage design and enhancing evacuation efficiency in ship environments, thus supporting safety managers’ decision-making.
Based on the simulation results, the following conclusions can be drawn:
(1) A cellular automata model considering the age structure of passengers is successfully constructed. Passengers are categorized into three age-based groups, each defined by distinct movement speeds and visual field ranges. The model integrates static terrain features, signage attraction, and directional guidance, enabling the quantification of signage effectiveness across different passenger types. This enhances the model’s capacity to represent asymmetrical evacuation behavior in a symmetrical spatial environment.
(2) The study incorporates the light occlusion effect on signage visibility and formulates an optimization model aimed at maximizing guidance effectiveness while minimizing signage costs. Differences in signage recognition across age groups are embedded in the model, and the optimal signage layout is obtained using a genetic algorithm. The validity of this strategy is demonstrated through simulation.
(3) Evacuation experiments based on the cruise ship theater show that, under a constant age distribution, evacuation efficiency decreases as smoke concentration increases. At the same smoke level, scenarios with a higher proportion of elderly passengers exhibit lower evacuation efficiency, whereas scenarios dominated by younger passengers perform better. The proposed model effectively captures how differences in movement speed, visual range, and signage response across age groups influence evacuation outcomes. It is particularly applicable for evaluating emergency evacuation capacity in complex, smoke-filled environments such as cruise ships and terminals.
Although the simulation results validate the effectiveness of the proposed framework, several limitations remain, which provide avenues for future development. The current model focuses on a single-level theater and does not incorporate vertical evacuation routes or multi-deck configurations commonly found on cruise ships. Psychological and behavioral aspects, such as panic, stress, cognitive hesitation, or gender-based responses, are also not explicitly modeled, despite their potential influence during emergencies. Environmental dynamics, including fire spread, heat, toxic gases, ship motion, turbulence, and evolving smoke conditions, are simplified through static assumptions, limiting the model’s ability to reflect real-time degradation of visibility. Although signage occlusion by static obstacles is considered, the model does not yet simulate dynamic line-of-sight disruptions caused by moving crowds or physical interactions. Moreover, signage is assumed to be perfectly visible and interpretable whenever within a passenger’s field of vision, without accounting for recognition errors or guidance failures under stress. The cost model also adopts a simplified proxy, using the total number of signs as a stand-in for real-world economic factors such as installation, maintenance, and operational overhead. These simplifications may limit the model’s applicability in real-world scenarios.
Future work will aim to incorporate multi-deck layouts and vertical circulation, integrate cognitive behavior modeling, and adopt dynamic fire-smoke simulations to improve realism. Further, more detailed economic assessments and empirical validation, potentially through virtual reality-based human experiments, will be conducted to support the development of robust and adaptive signage layout strategies. Such improvements will support a more comprehensive assessment of evacuation efficiency in complex maritime environments.