Orienting people-centred disaster shelter planning based on risk assessing with semi-supervised learning

Abstract

Climate-related disasters have been escalating worldwide, incurring major losses. Landslides have become one of the most destructive disasters, especially in China's mountainous areas. To address this, constructing emergency shelters and designing evacuation routes are critical to ensure public safety and minimize impacts on affected residents. This study proposes a novel two-phase, people-centric approach. The first phase applies stakeholder theory and risk economics to develop a landslide hazard assessment model considering vulnerable populations. The model effectively classified 28 landslide points in Bazhou Town, with 35.71 % deemed high-risk and low-risk 64.29 %, reflecting the model's comprehensive risk differentiation capability. The second phase utilizes public choice theory to construct a bi-level multiple objective programming (BLMOP) model addressing conflicting government and resident goals. The algorithm produced 4 Pareto-optimal shelter plans for each village assessed, results demonstrate the proposed approach generates shelter plans meeting government aims while maximizing resident satisfaction, accounting for local conditions. Grounded in field data and a people-focused lens, this two-stage methodology provides a multiple objective optimization framework balancing stakeholder need. A case study of Bazhou Town validates the method's effectiveness.

1. Introduction

Natural and human-induced disasters have escalated worldwide, incurring major losses [1]. With its vast and diverse geography, China frequently faces geological disasters like landslides and mudflows, resulting in substantial casualties and economic damage profoundly impacting local residents (Fig. 1). Constructing emergency shelters and evacuation routes in hazard-prone areas are critical to ensure timely safety and minimize harm [2,3]

Fig. 1.

Risk assessment map of landslide and debris flow in China. *China geological survey.

Emergency shelters serve as crucial temporary shelters offering protection during calamitous events [2]. In their planning, it is imperative that government bodies factor in public feedback and satisfaction [4]. Yet, the status quo of shelter planning and site selection presents glaring deficiencies—misplacement and flawed design contribute to resource misallocation and a mismatch in supply and demand [5]. One such study revealed that, due to suboptimal shelter locations during a specific disaster episode, up to 40 % of the affected population did not receive shelter within the crucial 72-h post-disaster window [6], highlighting inefficiencies in disaster response and decreasing the chances of survival for many.

Effective emergency shelter planning should aim to fulfill two fundamental objectives: ensuring rapid and safe accessibility for evacuees and minimizing the number of casualties and scale of economic loss resulting from disasters. Given the often-sudden onset of climate-related disasters such as landslides, optimizing Shelter Location and Site Planning (SLSP) is of paramount importance in reducing the detrimental effects of such incidents [7]. Amidst physical, environmental, and resource constraints, there is an urgent necessity for emergency management to incorporate rational SLSP that integrates public preferences as a priority in disaster risk reduction efforts [8].

Further investigations underscore that issues stemming from inadequate site selection and planning affect not only the efficiency of evacuations but also impinge upon evacuee safety and satisfaction, reflecting a frequent misalignment between the realized outcomes of shelter planning and the initial protective intent [9]. Although the intent to provide a safe haven during disasters is clear, the challenge remains to balance the exigencies of rapid accessibility with effective resource allocation and the varying needs of the disaster-affected population. Hence, this study focuses on developing a robust and more efficient SLSP model by considering a fusion of geographic information, demographic data, and socio-economic factors, intending to elevate shelter planning to new heights in safeguarding human life against future disasters.

As transitional facilities, shelters should account for displaced resident needs [10]. Selecting sites rationally enhances evacuation and resettlement efficiency after landslides, minimizing harm [10]. However, problematic SLSP causes misused resources and supply-demand imbalance [11], so addressing this is critical for efficient services. Yet SLSP has conflicting goals [12]. The shortest evacuation may not guarantee lowest cost and highest satisfaction [13]. Costs also vary based on location and fluctuating capacity needs [14]. Thus, optimizing site and size leads to trade-offs [15]. Hence, conflicting objectives and constraints must be addressed urgently. We formulate SLSP as a bi-level multiple objective programming (BLMOP) model with upper and lower-level programs optimizing multiple goals. In BLMOP, two decision makers (DMs), as leader and follower controlling separate variables and objectives [16], pursue their own interests but are affected by the other and upper-lower factors, achieving satisfactory bi-level multiple objective solutions.

As discussed by Eiselt and Marianov (2011) [17], the multiple objective nature of Shelter Location Selection Problems enhances the complexity of Bi-Level Multi-Objective Optimization Problems (BLMOP). Due to their complex nature, these problems are categorized as NP-hard. An NP-hard problem is one that is as complex as the most difficult problems that can be verified in nondeterministic polynomial time (NP); there is currently no known algorithm that can solve these problems quickly and efficiently in all cases. Hence, because of their complexity and the large solution space they occupy, NP-hard problems are often solved by approximate or heuristic methods rather than exact algorithms. Therefore, to address these complex and computationally challenging problems, an enhanced particle swarm optimization (PSO) algorithm, known as Multiple Objective Particle Swarm Optimization (MOPSO), is introduced, which aims to find satisfactory solutions within a reasonable time frame despite the NP-hard nature of the problem [18].

This research adopts a bi-level perspective on real-world landslide frequency and losses. One aim assists government in reducing shelter costs and concentrating construction. Another balances SLSP trade-offs with resident satisfaction for better comfort. Major contributions are:

Research Gap: Despite advancements in shelter planning and site selection research, there remains a significant gap in integrating geographic information, demographic data, and socio-economic factors comprehensively, as well as in optimizing site selection to meet the diverse needs of different disaster-affected populations. Furthermore, existing studies often overlook the complexity of achieving rapid and safe access to shelters in emergencies and balancing effective resource allocation with the varied needs of the disaster-affected population.

Objective: This study aims to develop a robust and more efficient SLSP model that incorporates a blend of geographic information, demographic data, and socio-economic factors to improve the quality of shelter planning, ensuring the protection of human life against future disasters.

• 1.Assess landslide hazard points using the Adam-SSL semi-supervised algorithm for enhanced precision and reliability in disaster evaluation.
• 2.Under the guidance of stakeholder theory and risk economics, establish a unique human-oriented landslide evaluation system.

• 3.Make trade-offs between SLSP and socio-economic impacts from both governmental and resident perspectives to improve living conditions and satisfaction.

• 4.Modify and optimize the Multiple Objective Particle Swarm Optimization (MOPSO) algorithm to address the Bi-Level Multi-Objective Optimization Problem (BLMOP), enhancing the efficiency of solving NP-hard problems.

Novelty: The novelty of this study lies in the development of a solution based on a multi-theoretical approach, combining human-centric principles and decision management to optimize the site selection and planning of emergency shelters. In terms of algorithms, the introduction of advanced semi-supervised learning algorithms and improved particle swarm optimization algorithms not only enhances the precision and efficiency of disaster assessments but also better balances resource allocation and the needs of the affected population during the planning process of emergency shelters. Overall, this achieves a more equitable and effective disaster response strategy, offering new perspectives and methodologies for the future of disaster management.

2. Literature review

Landslides are an extremely serious climate-related disaster. Evaluating the hazard level of landslide sites while considering the needs of disaster victims to optimize the location selection has become a hot topic of research among scholars. The scientific and effective optimization of the selection and placement of emergency shelters is now a priority.

2.1. Risk avoidance and stakeholder theory in landslide shelter planning

Risk aversion is a strategic approach to protecting lives and property by preventing or eliminating risks, which is crucial for effectively planning shelters and identifying hazards [19]. Stakeholder theory emphasizes the importance of considering the interests of various stakeholders, including the government, residents, developers, and environmental organizations, in risk management. Their concerns and needs should be incorporated into landslide indicators to achieve people-oriented decision-making [20]. The theory advocates that managers should pay attention to the interests of all relevant parties, not just those of the government, acknowledging the influence and rights of various stakeholders in the decision-making process [[21], [22], [23]]. Incorporating risk aversion is critical to developing a robust SLSP framework. By identifying and avoiding high-risk locations, we improve the safety of shelter residents and simplify emergency evacuation.

Accurate assessment of landslide risk and optimization of shelter placement are crucial for emergency planning [10]. Eliminating low-benefit, high-risk locations reduces government resource waste and allows for focus on priority areas [24]. With the development of machine learning, particularly semi-supervised learning algorithms like Adam-ssl, the ability to predict landslide risk has been enhanced by optimizing networks through the integration of labeled and unlabeled data [25,26]. Jihyeon Lee et al. [27] utilized satellite imagery and semi-supervised learning to assess post-disaster damage, improving accuracy with unlabeled data. Similarly, Iustin Sirbu et al. [28] investigated disaster-related tweet classification using unlabeled social media data, significantly improving performance through semi-supervised learning.

Furthermore, The Adam-SSL algorithm has been widely applied in landslide research. Yao et al. [29] combined deep learning and semi-supervised learning with Adam-SSL to improve the efficiency and accuracy of landslide susceptibility assessment in China. Dalan Xie [30] proposed semi-supervised learning for landslide identification without extensive labeled data. This method overcomes the need for extensive labeled datasets and offers a viable solution for landslide assessment.

Combining Adam-SSL with multidimensional site assessment, including physical, environmental, and infrastructure data, enhances the robustness and accuracy of potential landslide risk assessment. A risk assessment model, constructed by integrating various factors such as socioeconomic status [31], geographical location [32], and historical landslide events, can effectively identify regions in greatest need of protective measures [26]. This model supports strategic planning and fortification of shelters, aiding in the formulation of effective disaster prevention measures. Overall, Adam-SSL improves the accuracy and efficiency of landslide risk assessment, providing a solid scientific basis for disaster shelter planning and demonstrating the significant potential of semi-supervised learning in this field.

2.2. Bi-level multiple objective programming and public choice theory in emergency shelter planning

Public choice theory, an economic framework, examines individual decision-making in collective processes, assuming people act rationally to maximize self-interest, underpinning political and economic outcomes [33,34]. Peter Nijkamp and Piet Rietveld [35] examined coordination challenges in multiple level models related to multiple objective decision-making for regional and environmental planning in the Netherlands. This paper applies public choice theory by establishing a two-tier model to address the necessities and trade-offs of decision-makers at both levels.

SLSP is a multiple objective development of the semi-bilevel optimization model.

Bonnel and Morgan [36] pioneered semi-bilevel programming. Jamali et al. [37] presented a stochastic multiple objective model for seismic Shelter Location Networks (SLNs). Bi-level multiple objective programming can effectively address conflicting stakeholder interests, while the multiple objective approach offers practical solutions. Trivedi et al. [38] developed a hybrid multiple objective model using AHP for location-relocation projects. Praneetpholkrang et al. [39] proposed a multiple objective optimization for shelter location-allocation in humanitarian logistics. Ma et al. [12] introduced a multi-criteria optimization model for earthquake shelters. Rizk-Allah and Abo-Sinna [40,41] integrated reference point Kuhn–Tucker conditions and neural network approach for multi-objective and multi-level programming problems. Garg and Rizk-Allah [42] developed a unique approach for rough multi-objective transportation problems, incorporating rough set theory into decision-making under uncertainty, presenting versatile compromise solutions. Rizk-Allah [43] proposed a quantum-based sine cosine algorithm for nonlinear equations, enhancing diversity and convergence. Garg et al. [44] introduced a VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje”) approach to address bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems, advancing our capability to solve these NP-hard challenges by converting multi-dimensional objective spaces into a more manageable form and interlinking decision variables across levels with fuzzy logic. These case studies, spanning from earthquake shelter placement to the allocation of humanitarian refuge sites, showcase the application and progress of bi-level optimization models and multi-objective planning in addressing complex issues. They highlight the practical value of these models in making complex decisions where multiple objectives need to be balanced.

These studies address various SLSP facets and enhance solutions.

Scholars have determined shelter placements by considering practical needs and social, economic, and environmental factors. While aligning location and sizing can improve public systems, the spectrum of alternatives from bi-level planning provides more options to address optimization challenges. Consequently, bi-level models and multiple objective programming are combined.

The bi-level multiple objective model yields multiple optimal solutions catering to different level decision-makers, enabled by Pareto optimality. Zheng and Wan [45] resolved semi-vector bi-level challenges using distinct penalty functions. Khanchehzarrin et al. [46] proposed a bi-level location method accounting for various transportation factors. In summary, by adeptly coordinating decision-makers and optimizing the system, the bi-level multiple objective model ensures equitable and practical location decisions.

To solve the SLSP, an appropriate swarm intelligence algorithm is applied alongside model identification. Laporte et al. [47] introduced the SLSP model, which minimizes shelter-evacuation distance and belongs to the multiple objective p-median model. In 1995s, Kennedy and Eberhart [48] originally proposed PSO, which is extensively employed in multiple objective optimization. Enhancements have been made to its parameters, learning strategies, topologies, and hybridization. Ye et al. [49] enhanced the topology and learning strategy, while the inertia weight and acceleration coefficient for exploration were adjusted by Tripathi et al. [50], in 2007. Z Wang et al. [51] presents PESSA (PSO and an enhanced sparrow search algorithm work in parallel), a potent hybrid of PSO and enhanced sparrow search, that excels in Unmanned Aerial Vehicle (UAV) path planning, surpassing other algorithms in effectiveness. This study adopts a holistic approach synthesizing socioeconomic and environmental factors to produce practical shelter strategies. The improved algorithm effectively solves the computational complexity. Consequently, this framework provides valuable guidance for shelter planning in landslide zones, ultimately reducing risks to lives and property. The framework is shown in Fig. 2:

Fig. 2.

Framework of two-stage method.

Research Gaps and Current Study's Focus: Research reveals three key unresolved issues despite extensive studies on emergency shelter planning for landslides:

• (1)Practical application of stakeholder theory in risk assessment, particularly the lack of involvement of local communities in decision-making practices.
• (2)Insufficient exploration of the integration of semi-supervised learning, such as Adam-SSL, with comprehensive site assessment and real-time operational decision-making.
• (3)Although multi-objective programming shows potential in reconciling conflicting objectives, its specific implementation in shelter planning and integration with public choice theory still require development [52].

3. Method

3.1. Phase 1: Landslide hazard assessment

Based on historical landslide data and anticipated regional scenarios, we have developed a geological landslide hazard assessment framework tailored for the Southwestern mountainous regions of China. In collaboration with local authorities, we are utilizing relevant disaster data (Comprehensive Hazard Points Management Information Table, not publicly permitted for release. For full information on data sources see data availability statement.) to optimize resource allocation and strengthen preventative measures against potential landslide events in these areas.

3.1.1. Evaluation framework establishment

Stakeholder theory recognizes the diverse stakeholders involved in organizational management and business ethics [21]. For landslide hazard assessment, it considers the participation of government, residents, and other interested groups. The framework focuses on four key aspects:

• (1)Location: Identifies priority areas for mitigation based on field studies and government data.
• (2)Loss: Evaluates potential damage to infrastructure, property, environment, and lives to help stakeholders allocate resources and minimize impacts.
• (3)Impact: Assesses the social, economic, and environmental consequences on stakeholders and communities.
• (4)Threat: Evaluates the probability, frequency, and vulnerability of landslides to enable proactive preparedness and risk reduction.

Applying stakeholder theory promotes inclusivity and participation in the evaluation framework, ensuring all perspectives are considered for better decisions and effective landslide hazard mitigation.

3.1.2. Evaluation indicators construction

To rigorously construct a set of landslide risk assessment indicators sensitive to the interaction between socioeconomic factors and landslide physical characteristics, our approach is systematic and iterative. Firstly, we conducted a literature review to identify the main domains influencing landslides and summarized their impacts on communities and the environment to guide indicator classification. Next, in collaboration with experts, disaster management personnel, and officials involved in land planning and emergency response, we fine-tuned the indicators to comprehensively reflect landslide dynamics and their socioeconomic impacts. Socioeconomic indicators primarily consider potential casualties, economic losses, and impacts on community resilience, taking into account population density, economic value of at-risk infrastructure, recovery costs and duration, with particular attention to vulnerable groups.

The indicators were empirically derived and selected by using records of resident feedback available on official government websites and interviews with local government leaders to ensure a degree of relevance and inclusion. They not only cover all aspects of landslide risk, but also advocate a stakeholder-centred approach to disaster management and preparedness. The process of the methods used in data collection for this study is described in Section 3.8 (Table 1).

Table 1.

The evaluation indicators for landslide hazard assessment.

Category	Indicator	Description
Geographical Location Evaluation	Proximity	Proximity to populated clusters
	Accessibility	Distance from critical transport arteries
Economic Loss Evaluation	Direct Losses	Direct economic losses
	Indirect Losses	Indirect economic losses
	Economic Recovery Time	Time for economic recovery
Impact Assessment	Human Safety	Human life safety
	Infrastructure	Buildings, roads, infrastructure
	Agriculture & Production	Agriculture, water, production
	Ecological Environment	Ecological environment
	Public Services	Public facilities and services
Threat Assessment	Affected Individuals	Number of affected individuals
	Disaster Scale	Disaster scale
	Hazard Severity	Hazard severity

3.1.3. Adam semi-supervised learning algorithm

The Adam algorithm, combining stochastic gradient descent with adaptive learning rates, is utilized for landslide hazard assessment to effectively leverage available data. By using labeled and unlabeled data, it improves the accuracy and robustness of the assessment model [53]. Integrating the Adam algorithm within a framework guided by stakeholder theory and relevant indicators establishes a robust foundation for the Phase 1 hazard assessment, enabling more efficient and reliable evaluation. This lays the groundwork for subsequent research stages, allowing comprehensive and precise landslide hazard analysis.(Fig. 3)

Fig. 3.

Diagram of the semi-supervised learning program.

3.2. Phase 2: Bi-level multiple objective shelter site planning

The bi-level multiple objective model addresses the complexity of mountainous terrain and transportation networks, enhancing the accessibility of shelters in high-risk landslide areas. The upper level model optimizes evacuation times, ensures route safety, considers damage to mountain roads, and provides safe and efficient evacuation paths. Simultaneously, it considers cost-effectiveness to ensure the cost-benefit ratio of shelter construction. The lower level model emphasizes resident shelter utility and service efficiency, supporting optimal evacuation strategies during disasters. In this context, public choice theory provides a good framework for analyzing the relationship between decision-making processes and resident preferences.

Government's Perspective: The government's objectives typically focus on minimizing overall risks, allocating resources efficiently, ensuring public safety, and maintaining economic stability. It may prioritize larger-scale strategic initiatives that align with these goals.

Residents' Perspective: Residents may prioritize more personal concerns such as property rights, individual freedoms, and specific community needs, which may not always align with the government's broader objectives.

BLMOP Model Application: The application of the BLMOP model introduces a structured approach, distinguishing between government and resident objectives to ensure that the needs of both parties are considered. The model, at the upper level, focuses on modeling government objectives, formulating risk mitigation plans, optimizing resources, and enhancing public safety. At the lower level, the model addresses resident objectives, aiming to minimize inconvenience and safeguard individual interests.

Resolving Conflicts: The BLMOP model iteratively seeks solutions that are satisfactory for both levels. This iterative process fosters a participatory decision-making environment where compromise between conflicting goals can be systematically explored. Through this bi-level optimization, the model identifies policy and operative measures that achieve a balance, incorporating the government's strategic risk perspectives while respecting the residents' individual preferences.

Significance: The significance of the BLMOP model within our study lies in its ability to formalize and quantify the trade-offs between different stakeholder objectives. This approach can elucidate potential areas of consensus and disagreement, providing a transparent and replicable method for mediating between the collective needs of a community and the personal preferences of its members.

In conclusion, by integrating the BLMOP model into the landslide risk management framework, our study leverages public choice theory to address the divergent, and often competing, goals between the government and local residents. This bi-level approach allows for a more democratic, equitable, and thus sustainable decision-making process in the face of complex socio-environmental challenges.

3.2.1. Bi-level multiple objective model

Public choice theory is applied in the shelter site model to address diverse stakeholder interests. Both levels are influenced by their own objectives and others' preferences. Upper-level goals include minimizing evacuation time, ensuring site safety, enhancing path security, and cost planning. Lower-level objectives focus on resident utility and service efficiency. By integrating public choice theory, the model recognizes non-unique optimal solutions and considers factors beyond distance like facility quality and availability. This inclusive approach promotes transparency, equity, and resilience in site planning.

In the context of academic discourse, we provide a numerical example to elucidate the interplay and solution derivation of the dual-objective, bi-level optimization model presented in Section 3.2.2, “Numerical Example for Bi-level Optimization Model.” Note that the ensuing figures and the narrative are for illustrative purposes only and are not drawn from empirical data.

3.2.2. Numerical example for bi-level optimization model

Consider a hypothetical scenario wherein a municipality is evaluating the strategic deployment of emergency shelters within a mountainous locale. The area under consideration is prone to potential disaster stimuli at two distinct nodes (E1 and E2), and it encompasses a trio of viable sites for erecting emergency shelters (S1, S2, S3), in conjunction with two residential clusters (R1 and R2).

Objectives at the Upper Level (Governmental Decision-Making Sphere):

• 1.To minimize the cumulative evacuation time.
• 2.To maximize the safety indices of the selected shelter locales.
• 3.To preclude the budgetary allotment from surpassing the threshold of one million yuan.

Formalization of the Upper Level Paradigm:

$$\min \sum _{i=1}^2\sum _{j=1}^3{t}_{ij}·x_{ij}$$

$$\text{Subject}\text{to}:\sum _{j=1}^3{x}_{ij}=1,{\forall }_i\in \left\{1,2\right\}$$

$$\sum _{i=1}^2{x}_{ij}<B_j,{\forall }_j\in \left\{1,2,3\right\}$$

$$C\left(S1,S2,S3\right)\le 1,000,000$$

$$x_{ij}\in \left\{0,1\right\}$$

here, $x_{ij}$ denotes the binary assignment variable for evacuee node i to safe haven j, $t_{ij}$ signifies the temporal metric for evacuating from node i to safe haven j, $B_j$ delineates the capacity constraints of shelter j, and $C(·)$ symbolizes the cumulative fiscal outlay for shelters.

3.2.2.1. Objectives at the lower level (residential cohort's disposition)

• 1.To maximize the residents' utility derived from their selected refuge.
• 2.To escalate the service efficiency proffered by the shelters.

Codification of the Lower Level Schema:

$$\mathit{max}\sum _{j=1}^3{U}_j·y_j$$

$$\text{Subject}\text{to}:\sum _{j=1}^3{y}_j=1$$

$$E\left(S1,S2,S3\right)\le 1,000,000$$

$$y_j\in \left\{0,1\right\}$$

In this instance, $U_j$ quantifies the utility index of shelter j from the residents' standpoint, $y_j$ is the binary selection variable indicating the preference of the residents for shelter j, and $E(·)$ encapsulates the efficiency metrics of the shelters.

Elucidation of Solution:

Postulation of rationalized computation and iterative methods yields the following plausible solutions:

Optimal Design at the Upper Level:

• -Shelter S1 with an occupancy of fifty people, incurring an expense of 300,000 yuan.
• -Shelter S2 is excluded from the developmental blueprint.
• -Shelter S3 with an occupancy of one hundred people, incurring an expense of 600,000 yuan.

Optimal Preference at the Lower Level:

• -The residential sectors R1 and R2 optimally adjudge S1 and S3 as their preferred sanctuaries.

The governmental strategy orchestrates the budgetary provisions and safety exigencies at the preliminary phase, advocating the establishment of shelters S1 and S3. Conversely, the residential population predicates their choices predicated upon the derived utility and efficiency criteria, designating S1 and S3 as the prime shelters.

This numerical example is presented to illuminate the practical applicability and the inherent complexities of a bi-level planning framework. It exemplifies a methodical approach to harmonize the divergent goals of distinct stakeholder groups via an integrated algorithmic process. Consequently, it establishes a theoretical underpinning for understanding the dynamic interplay present within bi-level multi-objective optimization problems.

3.2.3. Upper-level programming: objective functions

Emergency shelters located near urban areas provide shelter and assistance during emergencies like disasters and attacks [54]. To balance social, economic, and security factors, the upper-level model has four objectives: (1) minimizing evacuation time; (2) maximizing site safety; (3) maximizing path safety; and (4) minimizing placement cost. These guide decision-making (Y) for shelter location distribution.

Objective1: Evacuation time. The objective is to minimize the total time taken for evacuation from the disaster site to an emergency shelter. This aims to reduce the risk of fatalities and optimize the evacuation process for improved efficiency.

$$f_1:\mathit{min}\sum _{i=1}^I\sum _{j=1}^J{w}_{ij}\overline{{\mathit{t}}_{\mathit{i}\mathit{j}}}{x}_{ij}$$ (1)

where $\overline{{\mathit{t}}_{\mathit{i}\mathit{j}}}=\left\{\overline{{\mathit{t}}_{\mathbf{11}}},\overline{{\mathit{t}}_{\mathbf{12}}},\dots \overline{{\mathit{t}}_{\mathbf{1}\mathit{j}}},\dots \overline{{\mathit{t}}_{\mathbf{21}}},\overline{{\mathit{t}}_{\mathbf{31}}},\dots ,\overline{{\mathit{t}}_{\mathit{i}\mathbf{1}}},\dots \overline{{\mathit{t}}_{\mathit{i}\mathit{j}}}\right\}$ is the evacuation time from residence assembly i to shelter j, $w_{ij}$ are the crowding effect weights, $i=1,\dots ,I$。 $j=1,\dots ,J$.

Objective2: Objective2: Safety of site selection. Locating emergency shelters in safe areas reduces the risk of casualties and minimizes economic losses, leading to cost savings.

$$f_2:\max \sum _{\mathrm{e}=1}^{\mathrm{e}}\sum _{\mathrm{j}=1}^{\mathrm{J}}\Vert {\mathrm{X}}_{\mathrm{j}}-{\mathrm{X}}_{\mathrm{e}}\Vert {\mathrm{X}}_{\text{ej}}$$ (2)

where ${\mathrm{X}}_{\mathrm{j}}=\left\{{\mathrm{x}}_1,{\mathrm{x}}_2,\dots {\mathrm{x}}_{\mathrm{J}}\right\}$ is the location of the shelter, ${\mathrm{X}}_{\mathrm{e}}=\left\{{\mathrm{x}}_1,{\mathrm{x}}_2,\dots {\mathrm{x}}_{\mathrm{E}}\right\}$ is the location of landslide disaster site; and $\Vert X_j-X_e\Vert$ are the Euclidean distance between the site of shelter and the site of landslide disaster.

Objective3: Path security. Ensuring secure evacuation paths to emergency shelters reduces casualties and enhances the reliability of shelter locations.

$$f_3:\mathit{max}\sum _{i=1}^I\sum _{e=1}^e\sum _{j=1}^J\overline{d\left(X_e,l_{ij}\right)}$$ (3)

Objective4: Cost planning. This study considers shelter construction costs, living material expenses, and post-disaster facility maintenance costs as key factors in cost planning. The objective is to minimize the total cost, which includes per capita construction costs $f_j$ and maintenance costs $h_j$.

$$f_4:\mathit{min}\sum _{j=1}^J\left(f_j{K}_j+h_j\right)y_j$$ (4)

In this context, $K_j=\left\{k_1,k_2,\dots k_e\right\}$ represents the shelter-sized collection, which also serve as the lower-level decision variables. The constant costs are directly linked to the shelter size in the lower-level model.

3.2.4. Upper-level programming: constraints

Firstly, the needs of all disaster sites must be met (constraints (5), (6)).

$$\sum _{j=1}^J{x}_{ij}=1;\forall i\in I$$ (5)

$$x_{ij}\in \left\{0,1\right\};\forall i\in I;\forall j\in J$$ (6)

Secondly, all shelter sites must be secured (Constraints (7), (8)).

$$\sum _{e=1}^E{x}_{ej}=1;\forall j\in J$$ (7)

$$x_{ej}\in \left\{0,1\right\};\forall e\in E\text{;}$$ (8)

Thirdly, considering the family attributes of residents, evacuation speeds of residents should be differentiated. The speeds of different age groups are shown in Table D1.

$$t_{ij}=S_{ij}/v_{ij}^p$$ (9)

$$S_{ij}\le S$$ (10)

where $\mathrm{S}$ is the evacuation distance control index, ${\mathrm{v}}_{\text{ij}}^{\mathrm{p}}$ is the rate of movement per household, and p is the different types of household movement speed. But the size of the movement speed depends on the property of the family. When the family members include individuals requiring additional support, such as people with disabilities, older adults, young children, pregnant women, and so on, they can opt for a priority-time scheme for shelter.

Fourthly, the location of the shelter should meet the safety distance limit (constraint condition (11))

$$l_{ej}\ge R_e$$ (11)

Fifthly, shelter construction should meet financial constraints (constraint condition (12)).

$$f_4\le \mathrm{\varphi }$$ (12)

where $\mathrm{\varphi }$ is the financial expenditure budget of Sichuan Province.

3.2.5. Lower-level programming: objective functions

This paper focuses on maximizing the effectiveness of emergency shelters for residents. To achieve this, a two-part objective function is proposed: one part relates to service efficiency, and the other part pertains to residents' shelter utility,in the lower-level model.

Objective 1: Resident shelter utility. In emergency management, residents' choice of shelters competes for limited resources. During disasters, residents prioritize shelters that are most effective for them [16]. The attenuation function $f\left(d\right)=e^{-\lambda l_{ij}}$ is used to calculate the distance (d) between shelters and residents, where λ is the attenuation coefficient. However, shelter preferences are influenced by various factors, not just distance. Thus, the utility function is modified to incorporate multiple shelter factors, improving the selection process for residents.

$$g_1:\mathit{max}{A}_{ij}{e}^{-\lambda l_{ij}}$$ (13)

The definition is as follows:

$$A_{ij}=\frac{{f_{1}f}_2{K}_j{g}_2}{N_j}$$ (14)

Objective2: Service Efficiency. A bigger shelter enables the provision of more emergency services. Service efficiency is defined as follows:

$$g_2:\mathit{max}\sum _{j=1}^J\sum _{i=1}^I\frac{K_j}{l_{ij}}$$ (15)

3.2.6. Lower-level programming: constraints

Firstly, the area of human settlements should meet the minimum limits.

$$\frac{K_j}{N_j}\ge \rho$$ (16)

where $\rho$ is the minimum per capita shelter area, ${\mathrm{K}}_{\mathrm{j}}$ is the capacity of the jth emergency shelter, and ${\mathrm{N}}_{\mathrm{j}}$ is the number of residents the j-emergency shelter can hold.

Secondly, the shelter capacity should be at a minimum.

$$\sum _{j=1}^J{K}_j\ge \sigma ,\forall j\in J$$ (17)

where $\sigma$ is the total number of residents.

To sum up, the entire mathematical model involves four upper-level objectives and two lower-level objectives. The entire mathematical model is shown below.

$$f_1:\mathit{min}\sum _{i=1}^I\sum _{j=1}^J{w}_i{\overline{{\mathit{t}}_{\mathit{i}\mathit{j}}}x}_{ij}$$

$$f_2:\max \sum _{\mathrm{e}=1}^{\mathrm{e}}\sum _{\mathrm{j}=1}^{\mathrm{J}}\Vert {\mathrm{X}}_{\mathrm{j}}-{\mathrm{X}}_{\mathrm{e}}\Vert {\mathrm{X}}_{\text{ej}}$$

$$f_3:\mathit{max}\sum _{i=1}^I\sum _{e=1}^e\sum _{j=1}^J\overline{d\left(X_e,l_{ij}\right)}$$

$$f_4:\mathit{min}\sum _{j=1}^J\left(f_j{K}_j+h_j\right)y_j$$

$$s.t.\{\begin{array}{c}\sum _{j=1}^J{x}_{ij}=1;\forall i\in I;x_{ij}\in \left\{0,1\right\};\forall j\in J\\ \sum _{e=1}^E{x}_{ej}=1;\forall j\in J;x_{ej}\in \left\{0,1\right\}；\forall e\in E;\\ t_{ij}=S_{ij}/v_{ij}^p\\ S_{ij}\le S\\ l_{ej}\ge R_e\\ f_4\le \mathrm{\varphi }\\ g_1:\mathit{max}{A}_{ij}{e}^{-\lambda d_{ij}}\\ g_2:\mathit{max}\sum _{j=1}^J\sum _{i=1}^I\frac{K_j}{l_{ij}}\\ s.t.\{\begin{array}{c}\sum _{j=1}^J{K}_j\ge \sigma ,\forall j\in J\\ \frac{K_j}{N_j}\ge \rho \end{array}\end{array}$$

3.3. Adam-SSL

The validation and assessment phase of the study saw the implementation of the Adam semi-supervised learning (Adam-SSL) algorithm, with a focus on evaluating its efficacy in the context of landslide susceptibility modelling. The data encompassed information on geographical location, economic loss, impact assessment, and threat assessment associated with 100 landslide events and 300 non-landslide locations in the southwestern region. Key indicators across these categories included proximity to populated clusters, accessibility to critical transport arteries, direct and indirect economic losses, time required for economic recovery, human life safety, the integrities of buildings, roads, and other infrastructures, agricultural viability, water resources, production capabilities, ecological preservation, public facility and service integrity, the number of individuals affected, the overall scale of disaster, and the severity of the hazard.

The results demonstrate a significant improvement in the performance measures of landslide risk assessment when using the Adam-SSL algorithm, even with limited labeled data, by leveraging the structure within unlabeled data. These findings underscore the advantages of integrating semi-supervised learning algorithms during the model training phase, particularly in the context of geospatial datasets where labeled examples are scarce.(Table 2)

Table 2.

The performance measures of landslide risk assessment.

Evaluation Metric	Adam-SSL Model	Fully Supervised Model
Accuracy (%)	92.1325	87.0023
Recall (%)	89.8564	82.5624
Precision (%)	90.3158	85.7953
F1 Score	0.8911	0.8335
ROC Curve AUC	0.9533	0.8826

3.4. MOPSO

The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm distinguishes itself from a plethora of optimization techniques due to its unique advantages. It is celebrated for its straightforward implementation, exceptional multi-objective problem-solving efficiency, robust global search capability, adaptability to a wide range of issues, and its ability to maintain a diverse set of non-dominated solutions. Significantly, MOPSO demonstrates commendable adaptability and competence in tackling NP-hard problems. Its collective intelligence and information-sharing mechanism among particles afford effective approximate solutions to computationally intensive challenges, making it an ideal tool for addressing complex optimization problems with multiple objectives The following comparison table further underscores the stark differences between MOPSO's approach and that of other traditional algorithms, illuminating the myriad ways in which MOPSO excels.(Table 3)

Table 3.

Advantages of MOPSO compared to other algorithms.

Indicator	MOPSO	Other Algorithms
Finding Multi-objective Solutions	MOPSO is capable of finding multiple Pareto optimal solutions in a single run, ensuring the richness of the solution pool.	Other algorithms, such as genetic algorithms (GA) and multi-objective genetic algorithms (MOGA) often require multiple runs to form an adequate Pareto front.
Computational Efficiency	MOPSO shows high computational efficiency.	Traditional algorithms like GA are computationally expensive.
Implementation Simplicity	Due to fewer control parameters, MOPSO implementation is more straightforward.	Some algorithms, such as the Multi-Objective Genetic Algorithm (MOGA), require numerous control parameters, increasing the complexity of their implementation.
Solution Diversity	MOPSO maintains the diversity of solutions without explicit diversity preservation mechanisms.	Many algorithms need explicit diversity mechanisms and may experience premature convergence to sub-optimal solutions.
Adaptability	MOPSO is self-adaptive, benefiting from changing environments.	Not all algorithms are inherently adaptive. Some require operator selection, which may amplify the noise.

MOPSO solves the multiple objective optimization problem by adjusting the parameters, learning structure and topology of the PSO. To prevent premature convergence, we introduce an improved MOPSO algorithm that combines a changing grouping approach, a multivariable velocity update approach, and a particle replacement approach [55]. Maintain diversity and prevent premature convergence by replacing particles with randomly generated ones with similar fitness values. The parameters employed in the algorithm design are detailed in Table B1. The experimental results establish that the proposed algorithm surpasses other contemporary algorithms on benchmark problems, underscoring its efficacy in addressing multiple objective optimization challenges.

Particles and neighbourhoods are given in Eqs. (20), (21):

$$v_s^{\tau +1}=\omega v_s^{\tau }+c_p{r}_1\left(pbes{t}_s^{\tau }-{\theta }_s^{\tau }\right)+c_g{r}_2\left(gbes{t}^{\tau }-{\theta }_s^{\tau }\right)+c_l{r}_3\left(lbes{t}_g^{\tau }-{\theta }_s^{\tau }\right)$$ (20)

$$v_g^{\tau +1}=\omega v_g^{\tau }+c_p{r}_1\left(pbes{t}_s^{\tau }-{\theta }_s^{\tau }\right)+c_g{r}_2\left(gbes{t}^{\tau }-{\theta }_s^{\tau }\right)$$ (21)

where $v_s^{\tau +1}$ and $v_g^{\tau +1}$ are the velocities of regular particles and neighboring entities, $lbes{t}_s^{\tau }$ denotes the optimal local position of the particle. s, nbestτ g is the best position within the neighbourhood of group g, $c_l$ and $c_n$ refer to the acceleration coefficients., $r_3$ and $r_4$ represent random numbers uniformly distributed within the specified range [0, 1].

Then, the positions of each particle are given in Eq. (22)

$${\theta }_s^{\tau +1}={\theta }_s^{\tau }+v_s^{\tau +1}$$ (22)

If ${\theta }_{s,g}^{\tau +1}>{\theta }_{s,g}^{\mathit{max}}$,then set ${\theta }_{s,g}^{\tau +1}={\theta }_{s,g}^{\mathit{max}}$ and $v_{s,g}^{\tau +1}=0\text{.}$ If ${\theta }_{s,g}^{\tau +1}<{\theta }_{s,g}^{\mathit{min}}$,then set ${\theta }_{s,g}^{\tau +1}={\theta }_{s,g}^{\mathit{min}}$ and $v_{s,g}^{\tau +1}=0$. Where ${\theta }_s^{\tau +1}$ and ${\theta }_g^{\tau +1}$ represent the positional coordinates of both regular particles and neighboring entities.

The acceleration coefficients $c_p$ and $c_g$ play a crucial role in facilitating information exchange among particles, thereby influencing the collective velocity of the entire population [56].

A broader exploration of the search space is facilitated by a large value of $c_p$, while a high $c_g$ value guides particles towards converging to a local optimum. To achieve a better balance between exploration and exploitation, time-varying acceleration coefficients, as described in Ref. [50], are utilized.

$$c_p=c_p^{\mathit{min}}+\frac{\left(c_p^{\mathit{max}}-c_p^{\mathit{min}}\right)\bullet \left(T-\tau \right)}{T}$$ (23)

$$c_g=c_g^{\mathit{min}}+\frac{\left(c_g^{\mathit{max}}-c_g^{\mathit{min}}\right)\bullet \tau }{T}$$ (24)

The goal of this algorithm is to identify the optimal solution from a set of multiple objectives. During each iteration, particles explore the solution space by adjusting their velocities and positions. The personal best and global best solutions are continually updated according to their fitness values. Over several iterations, the algorithm converges towards a collection of optimal or near-optimal solutions that strike a balance across multiple objectives.

During the iteration period, the searching efficiency of bad particles is far less than others. These worst particles will increase the computational burden and hence should be exchanged. As a result, the worst particle g ${\text{lworst}}_g^{\mathrm{\tau }}$ will be replaced with a ${\text{lbest}}_g^{\mathrm{\tau }}$ before regrouping. Overall, the calculation processes of the proposed algorithm including 11 steps is described in Fig. 4

• Step 1.

  Initialize the parameters in the upper-level model: s, g, τ, ω, $c_p$,and $c_g$, Then, initialize the $v_s$ and ${\theta }_s$ of the particle-represented solutions.

• Step 2.

  Calculate the fitness values for each particle's four objectives. Specifically, the fitness value for the fourth objective (total cost) requires the use of the optimal solution k from the lower-level model. In the first iteration, initialize and update the personal best solution ${\text{pbest}}_{\mathrm{s}}^{\mathrm{\tau }}$ and the global best solution ${\mathrm{g}\text{best}}_{\mathrm{s}}^{\mathrm{\tau }}$.

• Step 3.

  Update the particle velocities, applying limitations. Then update the particle positions, also applying limitations. Return to step 2.

• Step 4.

  When the maximum iteration limit is reached, filter the upper-level solutions.

• Step 5.

  Initialize the parameters with the same steps as in the upper-level model.

• Step 6.

  Calculate the fitness values for two objectives, requiring the use of the optimal solution $X_j$ from the upper-level model.

• Step 7.

  Perform multi-objective optimization for the two objectives at the lower level, calculating the fitness values for each particle's two objectives at the upper level. Initialize and update the ${\text{pbest}}_{\mathrm{s}}^{\mathrm{\tau }}$ and the ${\mathrm{g}\text{best}}_{\mathrm{s}}^{\mathrm{\tau }}$ in the first iteration. Update ${\text{pbest}}_{\mathrm{s}}^{\mathrm{\tau }}$ and ${\mathrm{g}\text{best}}_{\mathrm{s}}^{\mathrm{\tau }}$.

• Step 8.

  Update the particle velocities and positions, applying limitations. Return to step 7.

• Step 9.

  Check the termination condition for the lower-level model: if the best result is achieved, end the process. Otherwise, proceed to step 6.

Fig. 4.

The flow framework of Adam-SSL algorithm.

The objective of this algorithm is to find the optimal solution among multiple objectives. In each iteration, particles search the solution space by updating their velocities and positions. The personal best solution and global best solution are updated based on fitness values. Through multiple iterations, the algorithm converges to a set of optimal or near-optimal solutions that balance multiple objectives.

3.5. Implications

The construction of robust evaluation indicators for landslide hazard assessment is significant for both theoretical advancements and practical applications. Integrating socioeconomic factors with landslide characteristics emphasizes the need for a comprehensive approach to hazard evaluation, which could improve how communities and local authorities prepare for and understand landslide risks. From a theoretical perspective, this stakeholder-centric approach fosters a deeper understanding of the interaction between human systems and climate-related disasters. It supports interdisciplinary research that connects geosciences and social sciences in disaster risk reduction. In practical terms, these indicators help authorities to create more effective and equitable responses. Accounting for both direct and indirect economic influences aids in optimizing mitigation resources, and community involvement ensures assessments are relevant and effective. This framework also informs policymaking, promoting proactive risk management in landslide-prone areas.

Overall, the indicators and framework proposed in this study encourage joint efforts in disaster risk prevention and help protect communities against the impact of landslides, enhancing their overall resilience (see Fig. 5).

Fig. 5.

The flow framework of MOPSO algorithm.

3.6. Methodology of data collection and participant recruitment process

This section elaborates in detail on the method of data collection and its implementation process for the research.

3.6.1. Data acquisition

This study adhered to rigorous data collection procedures, complying with ethical standards and confidentiality agreements. The collected data originated from official public records and local governmental departments in Sichuan Province, including but not limited to the Sichuan Provincial Bureau of Statistics (http://tjj.sc.gov.cn/), the Wenchuan County Statistical Yearbook (https://dfzb.abazhou.gov.cn/abzdfsbgs/zxnj/common_list.shtml), the Wenchuan County Bureau of Natural Resources (http://www.wenchuan.gov.cn/wcxrmzf/c100053/202404/68d44de60a374de196bf791792554aa6.shtml), and the Bazhou Town Land Bureau. Additional data were acquired through the research team's visits to local potential disaster risk points. The primary data encompass geographic locations and demographic statistics, such as maps of shelters and residential areas, along with environmental and demographic information about Wenchuan County. By signing confidentiality agreements, we also gained support from local administrative agencies such as the Bureau of Statistics, the Bureau of Education, and the Bureau of Land and Resources Planning, supplementing some missing data.

3.6.2. Consent procedures

This study did not directly recruit individuals as participants. Our data collection was based on information obtained from public channels or through confidentiality agreements with governmental departments. All relevant representatives, representatives, and institutions were clearly informed and verbally consented to the use of their information for the purposes of this research.

3.6.3. Aggregpation and anonymization of participant Information

Given that the study focused on geographic information and demographic data, all data related to individuals or groups were aggregated and anonymized. The demographic data primarily came from the “Wenchuan County Statistical Yearbook” and relevant government databases. The research did not involve direct surveys of frontline personnel, thus there was no need to impose an age restriction of 18 years or older on participants. Our handling of data sources and disclosures strictly followed confidentiality agreements, avoiding the revelation of any information that could potentially harm national interests or sensitivity.

3.6.4. Data collection methods and tools

We utilized databases from government departments such as the Bureau of Statistics, the Bureau of Education, and the Bureau of Land and Resources Planning. Data were also obtained through field research, which included consulting local government officials and reviewing official yearbooks. Furthermore, we applied the Analytic Hierarchy Process (AHP) to assess the environmental impact weights of street congestion in the area. Related research findings and data are detailed in Appendix Table C1.

4. Application

4.1. Study area

Located 15 km north of Wenchuan County in southwest China's Aba Prefecture, Bazhou Town (31°29′- 31°43′N, 103°28′- 103°37′E) is situated. Its special geography with frequent geological disasters includes undulating terrain, steep hills, and narrow valleys ranging 1500–2780 m. Despite rich mineral, wildlife, and tourism resources, the topography makes geological hazards like landslides extremely dangerous. Thus, disaster prevention and shelter planning are critical in this region to protect resident lives and property.(Fig. 6)

Fig. 6.

Thermal distribution map of landslide disaster in Bazhou town.

4.2. Parameters

4.2.1. Adam- SSL

• Step 1Adjust the parameters of the Adam algorithm, such as weight decay, learning rate, and momentum, by incrementally increasing the learning rate and experimenting with various ranges and step sizes.
• Step 2Construct a neural network model for semi-supervised learning with an input layer, two hidden layers (16 units in the first layer and 32 units in the second layer), and an output layer (1 unit).
• Step 3Apply the ReLU activation function to the output of the first and second hidden layers to introduce non-linearity and capture complex patterns.
• Step 4Insert two Dropout layers with a dropout probability of 0.2 between the hidden layers to mitigate overfitting and enhance the model's robustness.
• Step 5As the objective function for the model, employ the mean squared error (MSE) loss function to minimize the disparity between predicted and actual values.
• Step 6Choose the Adam optimizer with a learning rate of 0.01 for parameter optimization. Adam adapts the learning rate dynamically during training, helping with convergence and sparse gradients.
• Step 7Train the model for a specified number of iterations (e.g., 8500) using backpropagation and parameter updates to improve its performance and optimize the model's predictions.

4.2.2. MOPSO

According to findings by Piotrowski [57] and colleagues in 2020, populations between 70 and 500 particles give the finest performance, however each added 10 particles increases iterations 100-fold, substantially increasing computation time. Therefore, Kennedy and Eberhart [48] put forward the primary people amount of 20 that we keep. To adjust parameters [48], we examined inertia weight (ω) from 0.5 to 3, and acceleration coefficients (c1, c2) from 0.1 to 1.0. Varying ω from 0.5 to 3 produced similar fitness trends, but ω = 2.3 gave the smoothest curve. For $c_p$ and $c_g$, fitness improved when values were <0.39 or >0.65, indicating further optimization potential. The algorithm was less sensitive to c1 and c2 changes, though overall fitness rose.

Therefore, the following parameter settings have been chosen:

• -Particle dimension: 2
• -X-coordinate range: 31.508551588212462 to 31.559481711692426
• -Y-coordinate range: 103.50085948144827 to 103.53050470342116
• -Particle velocity range: -0.00008 to 0.00008
• -Inertia weight for velocity update: 2.3
• -Number of iterations: 600
• -Individual update weight ($c_p$) and group update weight ($c_g$): both set to 0.5
• -The number of particles in one group (g) is equal to the amount of Pareto best solutions.

These parameter settings define the operational characteristics of the algorithm for the given problem.(Fig. 7)

Fig. 7.

(a) The fitness values change plot after modifying the parameters; (b) The objective function values of three villages.

4.2.3. Metrics of performance on MOPSO performance

To evaluate the influence of velocity parameters on the convergence and stability of the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm, a series of controlled experiments were conducted. The results are summarized in Table 4, which presents the observed performance metrics under varying velocity constraints.

Table 4.

Performance metrics of MOPSO with varying velocity constraints.

Velocity Range	Convergence Time (sec)	Standard Deviation	Stability Score (1–5)
[0.2, 0.4]	9.8	0.008	4.8
[0.5, 0.7]	12.0+	0.015	3.5
[0.0, 0.1]	12.0+	0.020	3.0

*Note: Convergence time is the average time to reach an acceptable solution. The stability score represents the robustness of the optimization process, with higher scores indicating greater stability of the solution sets Pareto frontier. A '+' indicates the algorithm exceeded the specified maximum time frame for convergence. *.

As delineated in Table 4, imposing a velocity constraint within the interval [0.2, 0.4] significantly augmented the MOPSO algorithm's performance, yielding an average convergence time of 98 s and the lowest recorded standard deviation of 0.008. Moreover, this parameter setting achieved the highest stability score on the Pareto frontier, rated at 4.8 out of a possible five points. In contrast, velocity ranges [0.5, 0.7] and [0.0, 0.1] respectively contributed to longer convergence times, where certain trials did not converge within the pre-set maximum duration of 120 s. This is also reflected in the increased standard deviations and diminished stability scores, indicating a compromise in solution reliability and robustness.

The empirical data thus emphasizes the significance of selecting an optimal velocity range for enhancing the efficiency and effectiveness of the MOPSO algorithm. Ensuring stable convergence within a reasonable timespan is critical for practical applications, where the algorithm performance can substantively impact the quality of the derived solution set for complex multi-objective optimization problems.

4.3. Results

4.3.1. Adam- SSL for assessment of landslide

The Adam semi-supervised algorithm was implemented in PyTorch 1.7 on a P4000 GPU, with gradients updated 3*16*32*8500 times over 8500 iterations. The MSE loss approached 0.04. Evaluation for the three villages completed within 5 min.

The known landslide points in Bazhou Town, Wenchuan County, Sichuan were used. Semi-supervised learning was implemented in Python using PyTorch with torch. optim tools like SGD and Adam. The data was split 80/20 for train/test. The 16 feature inputs for each point generated landslide probabilities, which were rounded and ranked to select points.

28 landslide points in Bazhou Town were assessed for risk levels (Table 5). 10 were high-risk, while 18 were low risk. High-risk accounted for 35.71 %, low-risk 64.29 %. Fig. 8 maps the distribution of high-risk points (see Fig. 9) (see Table 6).

Table 5.

Hazard assessment results of landslide points.

Landslide point distribution
Xiazhuang Village	Risk score	Aer Village	Risk score	Keku Village	Risk score
19	52.4	28	93.6	11	94.3
18	50.1	15	92.8	23	93.7
17	84.2	29	86.3	7	84.6
8	94.2	30	88.3	13	80.1
5	95.1	42	64.8	20	76.8
4	96.2	14	59.6	6	61.3
3	94.5			21	85.0
1	84.3			22	92.5
16	86.4			10	62.7
12	84.2			39	69.3
2	81.5
9	65.3

Note: The bold part is a high risk landslide point.

Fig. 8.

(a) Distribution map of landslide points in Bazhou Town; (b) High-risk landslide points in Bazhou Town. *The data of all pictures are from Wenchuan County Land Bureau.

Fig. 9.

Map of the affected area *Google Earth.

Table 6.

Disaster points data.

Affected area	Number of victim/person
AER VILLAGE	758
XIAZHUANG VILLAGE	878
KEKU VILLAGE	711

Fig. 8(a) shows the locations of the disaster sites, and Fig. 8(b) displays the locations of landslide points in three villages impacted by major landslides in Bazhou Town after filtering. To provide a detailed representation of the distribution of landslide points, a 2D projection map was employed [52]. Population data is obtained through field visits to local governments in order to obtain accurate census data (for full information on data sources, see the Data Availability Statement). The specific number of affected individuals at each disaster site is derived from the quantity of residential structures; the population condition is provided in Table 5.

4.3.2. MOPSO for shelter location planning

The MOPSO algorithm was implemented using Matlab r2022a on an Intel Core i9-12900H processor with 16 GB of memory. In the computational simulations, individual population size is 20, the algorithm executed for a sum of 600 iterations. For the scatter plot visualization, the two minimum objective functions (or the two maximum objective functions) were chosen as the x and y axes.(Fig. 10)

Fig. 10.

Effect of parameter settings and number of iterations on the objective function value.

After 600 iterations, 20 sets of non-dominated solutions were generated for each village using shelters as particles. Four aspects of the objective solutions were analyzed: economic, safety, time, and comprehensive. The economic-oriented approach aims to maximize economic benefits and cost-effectiveness. The safety-oriented approach focuses on ensuring people's safety and managing risks. The time-oriented approach aims to minimize evacuation time through efficient planning and execution. The comprehensive-oriented approach considers multiple objectives, including economic, safety, and time goals, to achieve a balanced solution and enhance the overall performance of the shelter system.

In each village, the final Pareto optimal solution set comprises four schemes. For specific details, please refer to Fig. 11, Fig. 12, Fig. 13. Each row represents a scheme, where shelter allocation schemes denote the assignment of hazard points to shelter numbers. Objective function values are arranged in the order specified by the multi-objective model. For instance, in Fig. 13, under the consideration of economic factors, hazard points III, V, and part of IV are reallocated to shelter number 15, while hazard points VII and the remainder of IV are reallocated to shelter number 11.

Fig. 11.

(a) Three oriented shelter location solutions in Xiazhuang Village; (b) Comprehensive-oriented shelter location solutions in Xiazhuang Village.

Fig. 12.

(a) Three oriented shelter location solutions in Aer Village; (b) Comprehensive-oriented shelter location solutions in Aer Village.

Fig. 13.

(a) Three oriented shelter location solutions in Keku Village; (b) Comprehensive-oriented shelter location solutions in Keku Village.

5. Discussion and conclusion

This study presents a comprehensive approach to optimizing emergency shelter planning in Bazhou Town, incorporating varying goals of government authorities and local residents, which reflects a novel adaptation of Bi-Level Multi-Objective Optimization Problems (BLMOP) in the context of disaster management.

5.1. Discussion

The research's use of a two-phase method is significant because it goes beyond traditional singular objective approaches, incorporating a breadth of stakeholder preferences that adhere to theories from multiple disciplines. While previous studies may have overlooked the complex interplay of stakeholder desires, our model facilitates a more nuanced understanding and negotiation of these preferences, capitalizing on stakeholder theory, risk economics, and public choice theory.

Our research aligns with the growing demand for sophisticated disaster management planning tools and introduces a unique contribution distinct from existing literature. We employed a semi-supervised Adam-SSL algorithm for risk assessment and used an enhanced MOPSO algorithm for optimization, improving the efficiency of emergency shelter planning. Compared to the methods and results summarized in Table 7, our approach provides a more diversified optimization of shelter siting to accommodate different risk areas and stakeholder objectives.

Table 7.

Comparative analysis of disaster management studies.

Study Title	Selection Method	Optimization Method	Unique Contributions
Evaluating the efficiency of relief centers in disaster and epidemic conditions using multi-criteria decision-making methods and GIS: A case study [58]	Multi-Criteria Decision-Making Methods, GIS	PROMETHEE Method	Efficiency assessment of relief centers under disaster and epidemic conditions.
A New Multiechelon Mathematical Modeling for Pre- and Postdisaster Blood Supply Chain: Robust Optimization Approach [59]	Multiechelon Mathematical Modeling	Robust Optimization Approach	Blood supply chain management modeling for pre- and post-disaster scenarios.
Efficient Crisis Management by Selection and Analysis of Relief Centers in Disaster Integrating GIS and Multicriteria Decision Methods: A Case Study of Tehran [60]	GIS, Multicriteria Decision Methods	PROMETHEE Method, Entropy, MOORA	Integrated methodology for the site selection and analysis of relief centers in disaster scenarios.
Estimation of relief supplies demands through fuzzy inference system in earthquake condition [61]	Fuzzy Inference System	–	Demand estimation for relief supplies in earthquake conditions using fuzzy logic.
A GIS-based crisis management using fuzzy cognitive mapping: PROMETHEE approach (a potential earthquake in Tehran) [62]	GIS, Fuzzy Cognitive Mapping	PROMETHEE Method	Innovative use of fuzzy cognitive mapping to determine the weight of criteria for the selection and ranking of relief centers considering an earthquake scenario.
Orienting people-centred disaster shelter planning based on risk assessing with semi-supervised learning	Semi-Supervised Learning (Adam-SSL algorithm), Risk Assessment	Bi-Level Multiple Objective Programming (BLMOP), Enhanced MOPSO Algorithm	People-focused landslide risk mitigation and shelter planning with a dual-phase methodology balancing government and resident objectives.

Following rigorous investigation and comprehensive analysis, a systematic assessment of the potential landslide risk in Bazhou Town has been conducted. This section will elaborate on the critical discoveries, evidence of validity, and the tangible impact of the work conducted.

Key Findings: In the first risk assessment phase, the landslide hazard assessment framework and Adam-SSL algorithm identified 28 potential landslide risk points. Using the Adam semi-supervised learning algorithm to assess the risks associated with these points, the results indicated that 10 points were classified as high risk and 18 points as low risk. High-risk points not only signify a high probability of occurrence but also carry the potential for extensive losses, underscoring the urgency and importance of emergency shelter planning in Bazhou Town.

In the second phase of shelter planning, our research found that a bi-level multi-objective emergency shelter planning model, guided by public choice theory and tailored to the region's layout, yielded four scenario directions for three villages, which completely addressed all needs. Even the slowest scenario direction maintained an average evacuation time under 3 min per person, and the total construction cost for the shelters did not exceed 400,000 yuan for the entire village.

This shelter planning model, which takes into account both safety and cost-effectiveness, provides an optimized solution for disaster risk management and truly meets the needs of the region.

Evidence of Effectiveness: The cross-validation results indicate that the Adam-SSL model outperforms the fully supervised model across all key performance metrics, including higher accuracy, recall, precision, and F1 score, as well as a notably better ROC AUC value. These outcomes suggest that the Adam-SSL model is more effective in landslide risk assessment.

Shelter Location Planning Effectiveness: The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm was utilized to derive optimized locations for shelters, producing a set of Pareto solutions that effectively balance cost, safety, and evacuation efficiency. Selected solutions were subjected to evacuation simulation drills, and when compared with pre-existing shelter sites, these simulations suggested a reduction in evacuation time by an average of 20 % and an increase in cost-efficiency for the optimized locations.

5.2. Conclusion

This study adopted a two-phase, people-centric approach to optimize emergency shelter planning in Bazhou Town, balancing government and resident perspectives.

Phase 1 involved landslide risk assessment integrating stakeholder theory and risk economics to model spatial hazards. The Adam-SSL algorithm conducted the calculations.

Phase 2 formulated a multiple objective bi-level model based on public choice theory to manage conflicting risk preferences of government and residents. An enhanced MOPSO algorithm addressed the trade-offs through modified parameters and learning strategies.

Through a rural case study, the proposed approach generated shelter plans satisfying government aims while maximizing resident satisfaction. By incorporating stakeholder goals, it provided effective optimization balancing supply and demand.

Recommendations include extending the model's applicability to other domains like facility planning. This research establishes a foundation and methodology to address similar multi-stakeholder problems across regions and hazards. By successfully integrating multiple theories, it presents a comprehensive data-driven solution for the Bazhou Town case, offering valuable insights for future research and planning.

5.3. Suggestions

This section provides targeted suggestions derived from the study's findings. These recommendations are designed to guide strategic intervention and protection efforts with an emphasis on prioritizing human life, maintaining infrastructure, and conserving the environmental integrity of Bazhou Town.

Human Life Safeguarding: Integrate risk scores from Adam-SSL into emergency planning and resource allocation to ensure high-risk locations are granted prioritized intervention.

Infrastructure Protection: Use risk assessment outcomes to inform infrastructure development, steering construction away from high-risk areas. Advocate for upgrading existing infrastructure to withstand potential landslide impacts guided by the identified risk levels.

Environmental Conservation: Implement land-use strategies that consider environmental impact assessments, guided by the risk evaluation indicators from Adam-SSL. Develop green infrastructure solutions within shelters as part of ecological preservation amidst disaster response.

Comprehensive Approach to Prioritization: Utilize a multi-criteria decision-making framework that accounts for economic, safety, and time-efficiency factors to establish a comprehensive risk management strategy. Align the MOPSO-derived shelter planning with sustainable development goals, ensuring that interventions contribute to long-term resilience.

Iterative Improvement: Encourage ongoing data collection and risk factor analysis to refine and update the Adam-SSL model, thus improving its predictive accuracy. Regularly reassess the effectiveness of the intervention strategies post-implementation and adjust planning processes based on lessons learned.

In conclusion, this paper proposes a novel framework for intervention prioritization in disaster management that is robust and comprehensive. The suggestions outlined emphasize a balance between protecting human life, infrastructure, and the environment, reflecting a holistic view of resilience and sustainability. Adopting these recommendations promises to strengthen Bazhou Town's preparedness and response strategies, ultimately leading to a safer and more secure future for its inhabitants. The continuous adaptation and improvement of these measures will be crucial in meeting the complex challenges posed by climate-related disasters.

5.4. Limitations

Although this study has offered new insights into the landslide risk assessment in Bazhou Town, it is important to articulate the limitations involved. Firstly, while the collaboration with local agencies has ensured the comprehensiveness and relevance of our data, confidentiality agreements restrict data sharing which may affect the transparency of the research and pose challenges for reproducibility studies. Furthermore, despite meticulous data preprocessing to ensure its accuracy, the origin and process of managing the dataset could result in limited generalizability of our model.

Secondly, Bazhou Town was selected for our study because it is located in the Longmen Mountain fault zone, a region that was significantly affected by the 2008 Wenchuan earthquake, thus providing a vital dataset for our risk assessment model due to its specific seismic-geological conditions and representative seismic landslide phenomena. Based on our research, Bazhou Town is among the most meaningful and representative regions affected by the Wenchuan earthquake, and theoretically, our findings could be extended to the entire Wenchuan region and other similar geographic regions in Northwestern Sichuan Basin. However, the complexity of geological structures and terrain variations in the Northwestern Sichuan Plateau necessitates further study and validation before our model can be widely applied.

Lastly, in the algorithm design and parameter tuning phase, although the semi-supervised learning algorithms demonstrated potential in risk assessment, parameter optimization remains crucial for improving model accuracy and generalizability. Future work will focus on validating these parameters through broader methods to enhance model performance.

In conclusion, the current study has uncovered the potential for assessing seismic landslide risks in Bazhou Town, while recognizing limitations concerning data acquisition, model generalization, and the selection of geographic regions. These limitations not only draw attention to areas that warrant caution in research but also indicate directions for improvement and in-depth exploration in future work. Succeeding studies will aim to address these limitations in detail and will attempt to expand to different geological backgrounds, thereby strengthening the robustness and applicability of the assessment model.

5.5. Future recommendations

While the two-phase methodology has been meticulously developed, its practical application in the field is planned for a forthcoming stage. We intend to collaborate with local authorities in Chinese mountainous regions to implement our model, particularly in Sichuan Province, known for its susceptibility to landslides. The future application will involve a series of systematic steps: starting with the identification of potential high-risk landslide zones using our Phase 1 framework, followed by the application of our Phase 2 planning model to determine optimal shelter locations that will be evaluated against real-world emergency scenarios. The outcomes from these future deployments are anticipated to provide invaluable data that will validate and refine our approach, with a long-term goal of bolstering resilience and minimizing the impact of landslides in vulnerable mountainous landscapes. To advance the field of landslide risk assessment, the following detailed recommendations are made for future research:

5.5.1. Improving landslide data

• F095Future research should seek to procure more comprehensive and diverse landslide datasets. This may necessitate forming partnerships with a variety of geological institutions to access a broader range of data.

• F095The employment of advanced data collection technologies, such as LiDAR, UAV photogrammetry, and satellite imagery, is suggested to improve the detail and accuracy of topographical data.

• F095The adoption of open data practices is recommended to facilitate greater transparency and allow for the validation and replication of research findings across the scientific community.

5.5.2. Optimizing algorithm parameters

• F095Rigorous parameter optimization techniques, including cross-validation and grid search, should be employed to identify the most effective parameters for the specific models in use.

• F095Future studies are encouraged to explore a wider range of computational algorithms, potentially including novel machine learning and deep learning methods, to improve the precision of landslide risk prediction.

• F095Incorporating geotechnical and environmental factors into algorithm development can offer additional insights and enhance the accuracy of risk assessments.

5.5.3. Extending model applicability

Validation of the landslide risk assessment model across different regions with similar seismic and geological settings is crucial to ascertain the model's generalizability and identify transferable predictive features.

• F095Research should be undertaken to adapt the model for application in varied geological contexts, using techniques such as transfer learning, to ensure the model's utility in a vast array of environments.

• F095It is important to evaluate the model under an assortment of climactic and geographic conditions to fine-tune its performance and dependability in predicting landslide occurrences.

Financial support

We gratefully acknowledge the financial backing received for this work from the National Natural Science Foundation of China (NO. 72104165), the Sichuan Philosophy and Social Science Foundation (NO. SCJJ23ND206), the Foundation of Sichuan Province Cyclic Economy Research Center (NO. XHJJ-2105), the National Innovation and Entrepreneurship training program for college student (NO. 202210626006).

Ethics declarations

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

For ethics approval

This study did not involve human or animal subjects in a conventional manner. The data collection process involved direct members of our research team, as well as officials and experts from government departments. The information collected was neither sensitive nor identifiable. All data was aggregated and anonymized before access. Given the professional nature of the participation and the lack of direct research interventions with human or animal subjects, the authors determined that the study did not require ethics approval, based on the non-sensitive nature of the data and the absence of personally identifiable information at the time of access.

For consent

All individuals who provided information for this study were members of our research team or officials and experts from government departments. As such, all contributors were informed and verbally consented to the use of their information for research and publication purposes. Consent for the publication of the anonymized information provided was obtained.

This consent statement aligns with our understanding of current ethical standards in research. No private or sensitive data from vulnerable populations were obtained, and traditional ethical concerns related to participants' rights and protections were not directly pertinent to this study. The study did not involve any minors or individuals under the age of 18.

Consent statement

Informed consent was appropriately obtained verbally from all participants, given the professional nature of the data collection. This method of consent was deemed sufficient for the type of data collected and the context in which the study was conducted.

This ethics and consent statement aligns with our understanding of the current ethical standards in research and is based on the nature of our study. All participants were informed and provided their consent. No private or sensitive data from vulnerable populations were obtained, and therefore, traditional ethical concerns related to participants' rights and protections were not directly pertinent to this study.

Data availability statement

The authors do not have permission to share data, due to the signing of confidentiality agreements for this article and requires the consent of the relevant personnel. The data sources used are mainly from Sichuan Provincial Bureau of Statistics, Wenchuan County Statistical Yearbook, Wenchuan County Bureau of Natural Resources and Bazhou Town Land Bureau. The absent data were obtained from the field visit and signing a confidentiality agreement with the local administration, and by accessing the databases of the local Bureau of Statistics, the Bureau of Education, and the Bureau of Land Resources Planning. The shelter sites, residential areas and other map data were obtained from Wenchuan County Natural Resources Bureau and Bazhou Town Land Bureau (see Table 4). The crowding effect environmental weights of local streets were acquired by local professional advisors according to the Analytic Hierarchy Process [63] (refer to Table C1).

CRediT authorship contribution statement

Yucheng Zhu: Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Data curation. Lu Gan: Validation, Supervision, Resources, Methodology, Investigation, Funding acquisition, Conceptualization. Xianglong Li: Visualization, Software, Investigation, Formal analysis, Data curation. Yufei Zuo: Visualization, Software. Jiaxin Liu: Writing – original draft. Benjamin Lev: Writing – review & editing, Writing – original draft, Supervision.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:Lu Gan reports financial support was provided by National Natural Science Foundation of China (NO. 72104165). Lu Gan reports financial support was provided by Sichuan Philosophy and Social Science Foundation (NO. SCJJ23ND206). Yucheng Zhu reports financial support was provided by National Innovation and Entrepreneurship training program for college student (NO. 202210626006). Lu Gan reports a relationship with Land and Resources Bureau in Wenchuan County that includes: consulting or advisory, non-financial support, and paid expert testimony. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix.

Table A1.

Definition of variables.

Variables	Description
Indexes and collections
i $/\mathrm{I}$	domicile locations/the set of domicile locations
j $/\mathrm{J}$	shelter locations/the set of shelter locations
e $/\mathrm{E}$	landslide disaster sites/the set of landslide disaster sites
Parameters
${\mathrm{w}}_{\mathrm{i}}$	Crowding effect weights
${\mathrm{t}}_{\text{ij}}$	Time required for the i-resident to walk from home to the j-shelter
${\mathrm{X}}_{\mathrm{e}}$	Location of landslide disaster site
${\mathrm{t}}_{\text{ij}}$	Safety planning distance between disaster site and disaster site
${\mathrm{v}}_{\text{ij}}^{\mathrm{p}}$	The rate of movement per household
${\mathrm{A}}_{\text{ij}}$	The appeal of the shelter to the residents of the community
$l_{ij}$	The A European distance between i and j
$y_j$	1 if the shelter will be relocated; 0 otherwise
${\mathrm{K}}_{\mathrm{j}}$	Capacity of the jth emergency shelter
${\mathrm{N}}_{\mathrm{j}}$	Number of residents the J-emergency shelter can hold
Upper-level decision variables
${\mathrm{X}}_{\mathrm{j}}$	The location of the shelter
Lower-level decision variables
$K_j$	The size of the shelter

Table B1.

Parameters in MOPSO.

Parameters	Description	Scope
τ	Iteration	$\mathrm{\tau }=1,2,\dots ,\mathrm{T}$
s	Swarm size	$\mathrm{s}=1,2,\dots ,$ S
g	Swarm group	$\mathrm{g}=1,2,\dots ,\mathrm{G}$
ω	Inertia weight	$\left[{\omega }^{\mathit{min}},{\omega }^{\mathit{max}}\right]$
${\mathrm{v}}_{\mathrm{s}}^{\mathrm{\tau }}$	velocity of $\mathrm{s}$ in $\mathrm{\tau }$ th iteration	$\left[v^{\mathit{min}},v^{\mathit{max}}\right]$
ɒ	The mean velocity of all particles.	–
${{\mathrm{\theta }}_{\mathrm{x}}}^{\mathrm{\tau }}$	Location of particle $\mathrm{s}$ in $\mathrm{\tau }$ iteration	$\left[{\theta }^{\mathit{min}},{\theta }^{\mathit{max}}\right]$
${\text{pbest}}_s^{\mathrm{\tau }}$	Particle $\mathrm{s}$ individual optimal position.	–
${\text{gbest}}_s^{\mathrm{\tau }}$	The collective optimal position among all particles.	–
${\mathrm{c}}_{\mathrm{p}}$	Coefficient of acceleration for the individual best position.	$\left[c_p^{\mathit{min}},c_p^{\mathit{max}}\right]$
${\mathrm{c}}_{\mathrm{g}}$	Coefficient of acceleration for the global best position.	–

Table C1.

Weights in the proposed model.

Crowding effect weights
n ≤ 50	50 < n ≤ 100	100 < n ≤ 150	n ≥ 200
0.98	0.75	0.56	0.38
Cost and Finance
$f_{c1}$	$f_{c2}$	$f_{c3}$	$f_{c4}$	$f_{c5}$	$f_{c6}$	$f_{c7}$	$f_{c8}$	$f_{c9}$
300	300	300	260	260	350	300	260	350
$h_{c1}$	$h_{c2}$	$h_{c3}$	$h_{c4}$	$h_{c5}$	$h_{c6}$	$h_{c7}$	$h_{c8}$	$h_{c9}$
23000	18000	21000	15000	13000	30000	28000	18000	30000

Table D1.

The regression model for average travel speed values [64,65].

	Age/A	Speed
Male	2–5	0.16A + 0.3
	5–12.5	0.06 A + 0.8
	12.5–18.8	0.008 A + 1.45
	18.8–39.2	−0.01 A + 1.78
	39.2–70	−0.009 A + 1.75
Female	2–8.3	0.06 A + 0.5
	8.3–13.3	0.04 A + 0.67
	13.3–22.25	0.02 A + 0.94
	22.25–37.5	−0.018 A + 1.78
	37.5–70	−0.01 A + 1.45