1 Introduction

For several decades, prevention, preparation, and response to emergencies have been of great importance and concern owing to technological accident recurrence and environmental, social, and political impacts. A clear example is the Bhopal disaster described in Reference [1], which took on a high urgency and political importance owing to its magnitude and environmental consequences. The disaster occurred when more than 40 tons of methyl isocyanate gas leaked from a pesticide plant, killing at least 3,800 people and injuring many others, causing premature death for thousands of years. As many industries are in population centers, urban centers, and metropolitan areas, the population is most at risk. For instance, a massive explosion at a liquefied petroleum gas storage facility in crowded San Juanico (Mexico) killed 452, injured 4,248, and displaced 31,000 people. The blast illustrates the precarious nature of a city with various potentially dangerous installations [2].

Despite these measures, technological accidents have not stopped entirely. Indeed, the frequency of technological disasters has increased in recent years, particularly in the transport category. Figure 1 shows the annual occurrence of technological hazards, separated by sub-group, as well as the corresponding number of total deaths [3]. Technological incidents have resulted in deaths, numerous injuries, significant environmental pollution, and massive economic losses. For example, in 2021, a fire occurred at an aerospace manufacturing site during the surface treatment of materials in a warehouse. The accident resulted in extensive damage to the warehouse and its components, including machinery, equipment, and stock. The fire also caused the release of toxic fumes and smoke, leading to the evacuation of nearby residents and the closure of nearby roads. Economic losses were significant, with an estimated damage of approximately €20 million. The fire and its aftermath also caused disruptions to the company’s operations and supply chain, leading to potential delays and financial losses [4].

Fig. 1
figure 1

Time series of technological disasters reported by the Centre for Research on the Epidemiology of Disasters [3]: a occurrence and b reported deaths over-2000–2021

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Consequently, Emergency Management (EM) research is an ever-developing field of interest in science, with a growing number of publications related to EM over time. As shown in Fig. 2a, the trend of EM publications has increased, and it has been compared with the frequency pattern of disasters shown in Fig. 2b [5]. This comparison emphasizes the importance of exploring alternative emergency management methods. Conventional emergency management methods are often found to be inadequate or obsolete because most of the information available is partial, and it can be challenging to make quick and effective decisions during an emergency [6].

Fig. 2
figure 2

Pattern of the increasing number of publications and frequency of disasters [5]

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Even though researchers in the field make proposals, methodologies, and models, emergency management remains a challenge, therefore dealing with unexpected, unconventional emergencies (technological disasters, incidents, and hazards) that frequently occur worldwide. Currently, the main problems facing emergency response [6, 7] are as follows:

  1. 1.

    Unestablished rules or protocols.

  2. 2.

    Constraints in time, information, and decisions.

  3. 3.

    Intangible and conflicting criteria.

  4. 4.

    The agent’s coordination prioritizes high-priority actions based on the emergency personnel and equipment.

In today’s emergency management systems, quick and accurate decisions rely on data analysis and processing, focusing on big data. As a result, there is a pressing need to improve the computational intelligence capabilities of emergency management, such as developing scalable and real-time algorithms for time-sensitive decisions; integrating structured, unstructured, and semi-structured data; dealing with imprecise and uncertain data; extracting dynamic patterns; tracing their evolution; working in a distributed environment; and presenting multi-scale, multilevel, and multidimensional data [8]. Artificial Intelligence (AI) has been proposed to address the issues of emergency management. Computational intelligence, a sub-discipline of AI, is a “combination of intelligent tools and computational models that can directly accept raw data and process them in a distributed manner to produce periodic responses with high fault tolerance” [5]. Computational intelligence techniques have the main decision-supporting capabilities to provide tools for solving emergency management problems. Integrating computational intelligence into emergency management has attracted considerable attention in the research area, implementing methodologies and techniques to develop metrics to compare them and choose the most efficient one [8]. For instance, implementing the Petri-net model of multi-agent emergency response for technological incidents to avert domino effects in a case study of chemical industry accidents [7]. However, there is still a need to build an in-depth integration of newly emerging computational intelligence techniques to meet the requirements of evidence-based decision-making. In addition, there is a gap in metrics, standards, and protocols during the response to an emergency and in establishing a solution with scalability [6]. This investigation aimed to determine the most appropriate computational intelligence algorithms for coordinating agents during a technological emergency.

A well-designed emergency management system ensures safe work practices, protects personal safety, reduces costs for industrial areas, and promotes sustainable and secure economic growth. It also improves the quality of life of communities by protecting their lives and well-being. A well-developed emergency plan enables preventive evacuation measures to be taken to avoid endangering adjacent communities which is the purpose of this paper [9]. From a political perspective, the approach includes global strategies and objective guidelines for reducing the impact of technological emergencies. For governmental regulation, it is critical to comply with the laws created and programs that oversee the management of emergencies. The consequences of technological disasters usually have their most significant impact on the environment because they can be irreversible, contaminate water bodies, disperse noxious and dangerous gases, and impact soils. Proper management of an emergency can counteract these consequences and reduce their severity [10, 11].

The proposed approach aims to develop a computational intelligence strategy that enhances emergency response to technological disasters by implementing coordinated decision-making among the agents involved. In addition to identifying and characterizing the variables related to multi-agent coordination for emergency management, appropriate metrics are selected to evaluate the emergency response performance. The approach is evaluated using a simulation system that tested the performance of the algorithm against state-of-the-art algorithms and analyzed the metrics identified from the emergency response variables. Furthermore, the functionality of the algorithm is evaluated to ensure its effectiveness in managing technological disasters.

2 Related work

Despite considerable efforts in process safety by the industry and increased regulatory programs, accidents still occur. As a result, all communities where hazardous materials are located or through which they are transported face some residual risk. A hazard originating from technological or industrial conditions, including accidents, dangerous procedures, infrastructure failures, or specific human activities, is defined as a technological hazard that may cause loss of life, injury, illness or other health impacts, property damage, loss of livelihoods and services, social and economic disruption, or environmental damage. Examples of technological hazards include industrial pollution, nuclear radiation, toxic waste, dam failures, transport accidents, factory explosions, fires, and chemical spills.

Emergency Management is the organization and management of resources and responsibilities for addressing all aspects of emergencies, particularly preparedness, response, and initial recovery steps [12]. Emergency Response (ER) is the phase in which this research is focused. First, ER is defined as a set of specialized agencies that have specific responsibilities and objectives in serving and protecting people and property in emergency situations, such as fire brigades, hazmat teams, and law enforcement. In addition, the provision of emergency services and public assistance is part of the response, during or immediately after a disaster, to save lives, reduce health impacts, ensure public safety, and meet the basic subsistence needs of the people affected [13].

The ER phase meets several criteria during an emergency, such as mitigation assessment, recovery assessment, fast recoverability assessment, emergency service facility location, crowd evacuation in emergencies, supply allocation, and route programming [14]. The objective of this study is to develop an approach to implement the capabilities of computational intelligence to perform the above tasks. Current emergency management uses modern technologies and management methodologies to efficiently monitor, respond to, control, and process emergencies by combining multiple social resources and scientifically assessing event causes, development processes, and negative impacts. Comprehensive emergency planning, preparedness, effective response, and recovery are required for optimal emergency management. Thus, the support of technological approaches must improve and solve tasks that are complex to accomplish.

Computational intelligence technologies are well-suited to enhance emergency response systems because of their capabilities, such as self-learning, self-organization, and self-adaptation, along with simplicity and robustness [15]. This investigation aimed to determine the most appropriate computational intelligence algorithms for coordinating agents during a technological emergency.

From a broad viewpoint, computational intelligence tools primarily include approaches for intelligent computing that use neural computing, fuzzy-logic computing, and evolutionary computation. Other intelligent computing methods (such as decision trees, association rule mining, and clustering) have also been extensively utilized in emergency management [6]. These technologies can be applied to different emergency management tasks that cover the lifecycle of an emergency and its corresponding management.

For instance, effective response management is essential for mitigating the severity of an incident and its consequences during an emergency. Reference [16] proposes a Simulated Annealing (SA) algorithm for the scheduling of relief teams in natural disasters. This study proposes a mixed-integer programming model to efficiently allocate and schedule rescue teams during disaster response, particularly focusing on uncertainty, time windows for incidents, and fatigue effects. The objective is to minimize incident completion times, an aspect often overlooked in prior studies. To tackle this NP-hard problem, a heuristic-based simulated annealing algorithm was developed, and its performance was compared with that of a Genetic Algorithm, Particle Swarm Optimization Algorithm, and a Simulated algorithm. This comprehensive approach aims to enhance disaster management and minimize casualties and financial losses resulting from natural disasters.

In contrast, [17] presented research on the allocation path of emergency materials during disasters using a hybrid algorithm that combines a Hopfield neural network and simulated annealing. The aim is to find an optimal path for the distribution of emergency materials to affected areas, considering factors such as distance, available resources, and the urgency of the situation.

Reference [18] proposed a multi-objective optimization model for emergency resource allocation and path planning in natural disasters. The model aims to minimize the response time, cost, and casualties while maximizing resource utilization. The authors used a simulated annealing algorithm to solve the model and conducted experiments on real disaster scenarios in China. The results demonstrate that the proposed model and algorithm can effectively allocate emergency resources and generate optimal evacuation paths.

Decision Tree is a nonparametric learning process; therefore, its application is in a non-complex context. This technology is typically used for risk detection and prediction during emergency management. For example, the approach of a decision-tree-based data-driven diagnostic strategy for air handling units incorporates a steady-state detector and regression model to improve diagnosis [19].

Fuzzy-logic computing is a widely used technique because it handles complex decision-making problems in uncertain environments through rules. For example, this technology was used in Reference [20], where the authors proposed a fuzzy-rule-based index for assessing flood vulnerability in Melbourne, Australia. This index was developed based on a combination of three main factors: exposure, sensitivity, and adaptive capacity. The study also utilized Geographic Information System (GIS) technology to spatially represent and analyze the flood vulnerability index. The results of this study provide valuable insights for policymakers to develop effective flood-management strategies.

Reference [21] proposed a novel approach to solving the multi-objective multi-layer congested facility location-allocation problem (MMCFLAP) using Pareto-based meta-heuristics. This study suggests that traditional approaches to solving MMCFLAP are not effective in real-world scenarios and may lead to suboptimal solutions. The proposed approach aims to simultaneously optimize multiple objectives, such as minimizing facility construction costs, minimizing congestion, and maximizing accessibility. The authors utilized Pareto-based meta-heuristics to solve the problem and provided empirical results to demonstrate the effectiveness of their approach.

Genetic Algorithms (GA) innovative approaches have been made in recent years to handle emergency response objectives, these approaches aim to optimize the location of emergency facilities to minimize the response time, cost, and resource utilization while satisfying the resource constraints. For instance, in reference [22] the authors proposed a solution to the multi-facility location problem using the GA principle. The algorithm aims to minimize the total cost and maximum response time while satisfying the resource constraints by implementing the Solver add-in, which uses the evolutionary method and is available in an Excel environment. On the other hand, Reference [23] establishes an effective emergency logistics system to reduce the suffering of disaster victims. It introduces a multi-objective optimization model for location and allocation decisions in a three-level logistics network, considering deprivation costs, unsatisfied demand costs, and logistics costs. This article presents an innovative IFA-GA algorithm that combines the firefly algorithm and genetic algorithm to effectively solve this complex model.

Reference [24] also introduced a multi-objective emergency resource allocation model considering uncertainty, integrating resource allocation with path planning using the multi-objective cellular genetic algorithm (MOCGA) and an improved A* algorithm. The proposed approach optimizes timeliness, efficiency, and fairness in rescue efforts and demonstrates its effectiveness in achieving optimal solutions for regional coordination and resilient supply in disaster chains. Finally, the article [25] focuses on the complex task of efficiently allocating emergency resources to multiple concurrent incidents to minimize casualties and losses. This study introduces the concept of disaster response coalitions, presents a multiply constrained integer linear programming model, and develops a search algorithm.

Table 1 compares the algorithms used in related work to solve optimization problems in terms of accomplishing the emergency task objectives during response. Table 1 sets the reference points in decision-making by providing information on the strengths and weaknesses of the different optimization algorithms. As a result, an appropriate algorithm should be selected for a given problem based on its objective, the type of research, the available tools, and the limitations of the algorithm. Table 1 provides a comparison of the evaluation metrics used to measure the performance of the algorithms, which can aid in selecting the appropriate metrics for a specific optimization problem.

Table 1 Comparative overview of state-of-the-art optimization approaches
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3 Proposed approach

The proposed approach involves implementing computational intelligence (CI) algorithms (both the approach and those selected from related studies) in an emergency management system to evaluate their performance during an emergency. The system inputs included three classes: those related to emergency parameters, those related to service facilities, and the algorithm to be simulated. The simulation involves emulating an emergency scenario (such as a fire, explosion, or leak) based on case studies and decisions made by service facilities to attend to the emergency by applying coordination, task assignment, resource allocation, and vehicle programming to enhance the disaster response performance.

The system interface is shown in Fig. 3, which was developed using AngularJS, Typescript, HTML, CSS, and Google Maps API to provide an intuitive and interactive user experience. On the server side, the Google Shell service from Google Cloud is used to host the system, and the server is managed with Node.Js. In addition to the front-end and server technologies, the algorithms responsible for executing each emergency scenario have been developed in Python. These algorithms are seamlessly integrated into the system using Flask, a lightweight web framework for Python coding. In this system, the user enters the parameters for the emergency to be simulated, such as the type of emergency, Severity Level, number, and type of agents. As shown in Fig. 3, the emergency response of the agents was simulated based on operational plans. Additionally, the evaluation metrics for emergency performance based on the selected CI algorithm can be observed on the right-hand side. The interface has two sections, and in Fig. 4, the Results Section is shown in detail, including a radar chart (Fig. 4a) comparing the evaluation metrics for each algorithm and the plot graph (Fig. 4b) that shows the changes in these metrics over time during the emergency development, whereas the emergency state shows the severity of the emergency as it progresses. The circle indicates that the state changes in proportion if the severity increases. Figure 5 shows the labels of the icons displayed to identify the agents and tasks during an emergency.

Fig. 3
figure 3

User interface for emergency management system

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Fig. 4
figure 4

Performance metrics and Emergency state evolution comparison

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Fig. 5
figure 5

Symbol Legend for the elements implemented in the map interface during an emergency

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System outputs consist of evaluation metrics, such as Response Time, Operation Rate, Rate of Emergency Escalation, Rate of Emergency Coverage, Emergency Severity Level, and Risk Index. These same variables can be seen graphically during the emergency simulation, as they change over time. The performance metrics selected for emergency evaluation include the coordination of task allocation, vehicle-route programming, and task assignment.

  1. 1.

    Escalation Rate: This refers to the rate of increase in the probability of a domino effect, which is influenced by factors such as received overpressure and time to failure [26].

  2. 2.

    Coverage Rate: This is defined as the percentage of the environment covered within 60 s. Decision or operation cost refers to the time taken to complete emergency tasks or events [27].

  3. 3.

    Severity Level: This measures the severity of an emergency based on factors such as toxicity, inflammability, and radioactivity. The mitigation, hazard, exposure, and resistance (MHER) formula [28] was used to calculate the overall risk of an emergency (Eq. 1).

    $$\begin{aligned} {\textbf {Risk}} = \left( \textbf{1} - {\textbf {M}} \right) \times {\textbf {H}} \times {\textbf {E}} \times \left( \textbf{1} - {\textbf {R}} \right) .\ \ \left( {\textbf {MHER}}\right) . \end{aligned}$$
    (1)

    All parameters in the study were converted to a scale of 0–1. Risk severity is then classified into five categories based on the value of the risk score: "Extremely high" for a risk score of 0.7 or higher, "High" for a risk score between 0.5 and 0.7, "Moderate" for a risk score between 0.3 and 0.5, "Low" for a risk score between 0.2 and 0.3, and "Very low" for a risk score between 0.2.

  4. 4.

    Coordination Level: This is evaluated based on the standard deviation of individual cost-time for each agent involved in completing tasks to ensure that work is distributed evenly among agents [29].

  5. 5.

    Response Time: The machine time in seconds it takes for service facilities to respond to an emergency can be a key metric for measuring the effectiveness of coordination in task allocation, vehicle-route programming, and task assignment. A shorter response time typically indicates more efficient coordination [30].

  6. 6.

    Resource Allocation: The number of resources allocated to an emergency, such as personnel and vehicles, can be used to assess the effectiveness of task allocation. The appropriate allocation of resources can result in a more efficient and effective response [30].

  7. 7.

    Task Completion Rate: The percentage of tasks completed on time can be used to assess the effectiveness of task assignment. A higher completion rate indicates more effective coordination [31].

  8. 8.

    Cost Effectiveness: The cost of an emergency response can be measured against the quality of the service provided. Effective coordination for task allocation, vehicle-route programming, and task assignment should deliver high-quality services at a reasonable cost [32].

  9. 9.

    Error Rate: The number of errors or mistakes made during an emergency response by an agent. A lower Error Rate indicates a more effective emergency response [33].

  10. 10.

    Time to Completion: The time taken to complete the tasks can be used to assess the effectiveness of coordination for task allocation, vehicle route programming, and task assignment. A shorter completion time indicates more efficient coordination [27].

In terms of functionality, Fig. 6 shows the flowchart of the system in Fig. 6a, which illustrates the stages of the system used to obtain the evaluation metrics for emergency situations based on a set of input variables. The process begins with the identification of emergency-related variables and concludes with a simulation of the disaster scenario for each selected CI algorithm, which provides the metrics for evaluation. The aim of this study is to integrate task assignment, supply allocation, and vehicle routing with a coordination mechanism for agent distribution to effectively manage emergencies. As shown in Fig. 6b) The proposed approach utilizes an individual agent analysis to determine the best course of action based on the available environmental information from both the agent and its teammates. The degree of cooperation in a multi-agent system varies and can range from local to global. It focuses on achieving global cooperation by developing a coordination mechanism that maximizes the overall utility function and considers all agent actions in the system.

Fig. 6
figure 6

Multi-agent decision-making model for emergency management: proposed approach. a Functionality and workflow. b Block diagram of the process overview

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The Improved Genetic Algorithm (IGA) is our approach for emergency decision-making under resource and time constraints [34]. This approach utilizes a genetic algorithm (GA) to optimize the allocation of limited resources and time to achieve the best possible outcomes in emergency situations. The GA approach involves the selection of a set of potential solutions, or "chromosomes," which are evaluated and ranked according to their fitness to the problem at hand. The best-fit solutions are then selected for further refinement through crossover and mutation, which generates new, potentially better solutions. The IGA approach is particularly useful in emergency situations where time and resources are limited, and decisions must be made quickly and effectively. By employing a GA, the approach can effectively handle the complexity and uncertainty inherent in emergency situations and rapidly identify the best possible courses of action. The resulting decisions are informed by the data and experience gained from previous emergency situations as well as current knowledge and expertise in the field.

  1. 1.

    Fitness function: The fitness function is used to evaluate the quality of potential solutions, or "chromosomes," generated by the GA, and to determine which solutions will be selected for further refinement through crossover and mutation. In addition, the fitness function in this study is designed to consider multiple factors that are relevant to emergency decision-making under resource constraints. These factors include the severity of the emergency, availability, and quality of resources, and psychological biases that can affect decision-making under pressure. To account for the latter, the approach uses prospect theory, which models decision-making as a function of perceived gains and losses rather than absolute outcomes. The number of relief workers demanded in a place j when the emergency loss level i is denoted by \(\chi _i = \left( \underline{\chi _i}, \overline{\chi _i}\right)\) where \(\underline{\chi _i}\) is the lower bound of the demand, and \(\overline{\chi _i}\) is the upper bound of the demand. \(\chi _i\) denotes the number of rescuers scheduled to be sent [35]. The total value function for sending \(\chi _i\) relief workers to place j can be seen in Equation 2. The number of materials demanded in a certain place when the emergency loss level is i and is denoted by \(y_i = [\underline{y_i}, \overline{y_i}]\). The evaluation value equations of \(y_i\) are defined in Equation 3:

    $$\begin{aligned} {\upsilon \left( x\right) }_j= & {} \sum _{j = 1}^{n} {\upsilon \left( x_i\right) \omega _i} \qquad \end{aligned}$$
    (2)
    $$\begin{aligned} {\upsilon (y)}_j= & {} \sum _{j=1}^{n} {\upsilon (y_i)\omega _i} \end{aligned}$$
    (3)

    The objective function is a combination of Eqs. 2 and 3, as defined in Equation. 4 [34]:

    $$\begin{aligned} \textrm{max}\sum _{j=1}^{n} {[\upsilon (x)_j+\upsilon (y)_j],} \end{aligned}$$
    (4)

    The constraints that are defined for the implementation of the algorithm are defined in Eq. 5, where Sp and Sg represent the total number of rescuers and materials owned by decision makers (DMs), respectively:

    $$\begin{aligned} \sum _{j=1}^{m}{\upsilon (x)j\le Sp},\ \ \ \ \ \ \ \sum {j=1}^{m}{\upsilon (y)_j\le Sg} \end{aligned}$$
    (5)

    The objective function can be defined as a weighted sum of four subfunctions, with each subfunction representing a different factor or constraint. The four sub-functions are response time, resource allocation, psychological bias, and severity functions. Each sub-function is designed to capture a specific aspect of the problem, and its weight is assigned to reflect its relative importance [36]. The proposed algorithm can be summarized as follows:

    1. (a)

      Step 1: Initialize the population and set the number of iterations for the population.

    2. (b)

      Step 2: Calculate the fitness function of the population using Equations (2) and (5):

    3. (c)

      Step 3: Select excellent individuals using the roulette method [37]. Through crossover and mutation, new populations are formed.

    4. (d)

      Step 4: Repeat Steps 3 and 4 and iterate according to the number of iterations to make the data converge as much as possible to find the best value.

    5. (e)

      Step 5: After the iteration is completed, stop the calculation, and output the optimal value.

  2. 2.

    Crossover: The crossover function is a two-point crossover method. In this method, two parents’ solutions are selected, and two random points are chosen in their representations. The sub-sequences between these two points are swapped to create two new offspring solutions. This helps explore different combinations of relief workers and materials, potentially leading to better solutions [38].

  3. 3.

    Mutation: The mutation function considers the bounds of demand for agents and resources. If a value falls below the lower bound, it indicates that the number of rescuers or materials does not meet the minimum standard for that emergency loss level, resulting in a negative psychological expectation for the decision-maker (DM). If it falls within the bounds, it is considered in line with expectations. If it exceeds the upper bound, it implies an excess of resources, which also doesn’t increase psychological expectations [39]. The objective function (Equation 4) aims to maximize the comprehensive evaluation value of the decision, considering both the number of relief workers and materials allocated to different places. Constraints (Equation 5) ensure that the total number of allocated resources does not exceed the total resources available to decision-makers.

In summary, the algorithm begins by initializing a population of potential solutions and setting the number of iterations for the population. The fitness function is then calculated for each member of the population, and the individuals with the best fitness scores are selected for further refinement through crossover and mutation. This process was repeated for multiple iterations until the data converged to the best possible solution. Finally, the optimal value was the output.

The improvements or proposals added to the state-of-the-art approach are as follows:

  1. 1.

    Considering multiple objectives: In real-world emergency situations, there may be multiple objectives to consider, such as minimizing casualties, property damage, and response time. Therefore, the genetic algorithm is modified to consider multiple objectives simultaneously and generate a set of optimal solutions (Pareto front).

  2. 2.

    Incorporating human decision-making: Although genetic algorithms are useful for finding optimal solutions, human decision-making is still important in emergency situations. Therefore, the incorporation of decision-making models, such as behavioral economics, is implemented to consider how humans make decisions under stress and uncertainty.

  3. 3.

    Resource allocation constraints: In emergency situations, resources such as personnel, equipment, and supplies are often limited. Therefore, the genetic algorithm considers resource allocation constraints and optimizes the resource allocation for maximum effectiveness.

  4. 4.

    Integration of coordination mechanism: The coordination mechanism is implemented in the fitness function used in the genetic algorithm. The fitness function is designed to reward individuals or groups that cooperate and effectively coordinate their actions. This is achieved by adding a term that penalizes solutions leading to conflicts or duplication of efforts among different responders.

4 Experiments

A systematic approach for planning and conducting experiments with the aim of optimizing and improving processes or products is known as the Design of Experiments (DOE). In emergency situations, DOE can aid in identifying the most efficient and effective ways to respond to emergencies, while minimizing risks and maximizing results. This section explains the step-by-step implementation of the DOE approach [40].

  1. 1.

    Definition of the problem statement and objectives: minimizing the response times, reducing the initial severity of the emergency, and optimizing the distribution of tasks and supply allocation by the coordination of the service facilities to improve the efficiency and effectiveness of the emergency response.

  2. 2.

    Identification of the relevant factors and levels that affect the response of emergency services to each scenario, such as:

    • Type of emergency (e.g., explosion, fire, leak).

    • Severity of emergency (e.g., extremely high, high, moderate, low, very low).

    • Location of emergency (e.g., chemical plant, oil refinery, seaport).

    • Number and type of response forces (e.g., firefighters, emergency response teams, first aid forces, police, coast guard, cleaning personnel).

    • Time to respond (e.g., immediate, 5 min, 10 min)

    According to [8], a statistical analysis of many fire records shows that the times of emergency response actions and firefighting follow lognormal distributions. Thus, the time required for each task follows a lognormal distribution. As shown in Fig. 7, these factors were the input variables for the system.

  3. 3.

    The matrix of experiments includes a random combination of the factors and levels identified in Step 2 is shown in Table 2.

  4. 4.

    By conducting the experiments according to the matrix and recording the evaluation performance variables mentioned in Sect. 3, the metrics are characterized as follows:

    • Metrics related to the level of risk: Risk Index, Escalation Rate, and Severity Level.

    • Metrics related to task efficiency: Coverage Rate and Time-to-completion Rate.

    • Metrics related to coordination and task quality: Coordination Level, Error Rate, and Task Completion Rate.

    • Metrics related to resources and costs: Resource Allocation and Cost Effectiveness.

    • Metric related to emergency Response Time: The time it takes for agents to respond to an emergency and begin executing appropriate actions.

    • Metric related to the level of operation: Operation Rate.

    The Emergency Management System (Sect. 3) runs the following algorithms:

    • The random task assignment algorithm (RTA) is a type of algorithm that assigns tasks to agents in a random manner [41]. The objective of the RTA is to perform task assignments and path planning for space robots. Specifically, the RTA algorithm employs a Random Path planning (RP) approach to determine the next node for each space robot and a General Task Assignment (GTA) strategy to assign tasks to robots. The aim is to provide a baseline for comparison with more advanced algorithms such as the Neighborhood Search-based Task Assignment (BTA) algorithm.

    • Improved Genetic Algorithm (IGA) As mentioned in detail in Sect. 2, this approach involves the integration of a coordination mechanism into the fitness function used in the genetic algorithm. The goal is to improve the performance of the genetic algorithm in emergency management by promoting effective coordination among responders and penalizing solutions that lead to conflicts or duplication of effort.

    • Multi-objective Swarm Particle algorithm (MOPSO) This algorithm was adapted from the state-of-the-art [42]. MOPSO has shown promising results in solving task assignment and supply allocation problems during emergencies. The algorithm aims to optimize multiple objectives, such as minimizing response time and maximizing resource utilization, using a swarm-based approach to search for the optimal solution. The effectiveness of the algorithm in handling uncertainties and dynamic changes in an emergency environment makes it a suitable tool for decision-making support in emergency management scenarios.

    • Collection Path Ant Colony Optimization (CPACO) This algorithm was adapted from the state-of-the-art [43]. An Ant Colony Optimization (ACO) for task allocation in multi-agent systems. The algorithm is used to determine the optimal allocation of tasks to agents based on their skills and current workload. The goal is to find an optimal allocation of tasks to agents that minimize the completion time and maximizes the quality of the output.

    • Greedy Algorithm (GRA) The greedy algorithm for the Assignment Problem solves the problem by iteratively assigning a job to a machine that provides the lowest cost [44]. It is simple and efficient, but may not always provide an optimal solution. It is also possible that it may not be possible to assign all jobs if there are insufficient machines available.

  5. 5.

    Analysis of the data and identification of the significant factors or interactions that affect the performance of service facilities and coordination.

Fig. 7
figure 7

Emergency parameter input section

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Table 2 Experiments scenarios
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5 Results

As mentioned before, the system internally runs the Random Task-Assignment Algorithm (RTA), the proposed approach of an Improved Genetic Algorithm (IGA) with coordination enhancement, the Multi-objective Swarm Particle algorithm (MOPSO), the Collection Path Ant Colony Optimization (CPACO), and the Greedy Algorithm (GRA). During the emergency simulation, the emergency metrics are displayed to check in simulation time the performance of the emergency providing the multi-agent operation to manage the disaster. The emergency level and type determine the agent’s tasks in managing the situation. According to the DOE presented in the previous section, the tests were divided into three sections: low, medium, and high-severity emergencies. This classification is based on the initial Severity Level value, which determines the required tasks to address the emergency, and the number of agents available to achieve this goal, which has a direct impact on the estimated response time. It should be noted that the tasks derived from the simulated scenario were taken from the National Fire Protection Association [45], which provides a framework for emergency management and business continuity. It includes a section on emergency planning and preparedness, which is helpful for identifying specific tasks and procedures. To evaluate the effectiveness of the approach in enhancing the performance of emergency management systems, an analysis of 45 case scenarios is conducted.

The results obtained for a low emergency level are shown in Fig. 8. The IGA showed consistently high performance across all metrics. In comparison with the MOPSO algorithm, the algorithms show similar performance, but the IGA has a better final overall performance. The IGA achieved the highest score in the Risk Index, Coordination Level, and Task Efficiency Rate. This indicates that the IGA is particularly effective at managing resources and coordinating tasks in emergency situations, while also minimizing risk and cost. The MOPSO algorithm also appears to be a suitable option for the results, suggesting that the MOPSO algorithm can effectively prioritize and allocate tasks while minimizing Cost and Response Time. The CPACO algorithm performed relatively well in Coordination Level and Risk Index, indicating that it is effective at coordinating tasks, but it scored lower in other metrics, such as Cost Index and Response Time. The GRA and RTA algorithms scored relatively low across all metrics, indicating that they may not be the best options for managing emergencies. However, they performed better in terms of operation rate metrics.

Fig. 8
figure 8

Low-severity-level emergency results

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The bar chart in Fig. 9 shows the weighted performance of each algorithm. This graph provides valuable insights by enabling an easy comparison of the overall performance of each algorithm. The highest weighted performance value was achieved by IGA, followed by MOPSO, and CPACO. This indicates that IGA is the most effective algorithm based on the given metrics.

Fig. 9
figure 9

Overall algorithm performance for low-severity emergencies

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Figure 10 shows the performance of different algorithms for a medium-severity-level emergency. The IGA algorithm performs similarly to the MOPSO algorithm in terms of Response Time but outperforms it in other metrics. Although the RTA and GRA algorithms do not rank the highest overall, they exhibit a good level of performance in terms of Operation Rate and Cost Index metrics. Figure 11 displays the weighted performance of each algorithm, highlighting the superior performance of the IGA.

Fig. 10
figure 10

Medium severity-level emergency results

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Fig. 11
figure 11

Overall algorithm performance for medium-severity emergencies

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Finally, for the high emergency level, the results of the emergency shown in Fig. 12 indicate that in most of the evaluation metrics, the IGA surpasses the performance of most of the algorithms. It is important to note that in the specific case of the Operation Rate, CPACO, and GRA show better performance. This case can be addressed by the fact that the task numbers and difficulty in a high-level emergency are more complex to handle and coordinate for the IGA algorithm; on the contrary, the GRA simplification is not affected in this aspect, despite the high level. MOPSO also performed relatively well, surpassing IGA in Response Time, and showing competitive scores in other metrics. Figure 13 shows the weighted performance of each algorithm. The graph highlights the similar response performance of the IGA and MOPSO for this level.

Fig. 12
figure 12

High severity-level emergency results

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Fig. 13
figure 13

Overall Algorithms Performance for high severity emergencies

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In Fig. 14, a comparison is made on the time performance of each algorithm in terms of solution time (emergency time response) for each emergency level case (High, Medium, Low). In general, the IGA exhibited a more efficient performance, with solution times almost half the value of RTA. The MOPSO algorithm also exhibited a suitable performance, followed by CPACO. The GRA performed exceptionally well in high-level emergencies.

Fig. 14
figure 14

Comparison of emergency time responses by severity level

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Figure 15 shows a comparison of the convergence behavior of the algorithm for each Severity Level. It was observed that the best solution was obtained at approximately the same number of generations for all three emergency Severity Levels. This demonstrates the scalability of the algorithm, as the problem conditions, resources, and task requirements vary significantly for each Severity Level. Therefore, the ability of the algorithm to converge in a consistent manner for each case highlights its robustness and effectiveness for task assignment optimization.

Fig. 15
figure 15

Convergence analysis of IGA for each severity level

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To evaluate the effectiveness of the approach in improving the performance of emergency management systems, 45 case scenarios are analyzed. For each scenario, the IGA’s total value score was calculated across the six defined metrics, and the same was performed for the state-of-the-art algorithms (MOPSO, RTA, GRA, and CPACO). In addition, the relative error [46] was calculated for each evaluated algorithm using Eq. 6. The total relative error was the average of the relative errors for each algorithm. The results showed that the IGA algorithm’s metric value (\(V_2\)) was 15.3% greater than the state-of-the-art algorithm’s metric value (\(V_1\)), indicating the effectiveness of the proposed approach in enhancing the performance of emergency management systems compared to other algorithms.

$$\begin{aligned} \text{Error} = \frac{\Delta V}{V_1} = \frac{V_2 - V_1}{V_1} \end{aligned}$$
(6)

6 Discussion

This study aimed to develop a computational intelligence strategy that enhances emergency response to technological disasters by implementing coordinated decision-making among the agents involved.

To achieve this goal, it is necessary to develop the following key points. The first is the identification and characterization of the variables related to multi-agent coordination for emergency management, such as severity level, emergency type, and service facilities. Second is the selection of appropriate metrics to evaluate emergency response performance, such as the response time, coordination level, and cost index. Finally, the implementation of the emergency management system for running the developed algorithms, the approach (IGA) algorithm, and the selected state-of-the-art algorithms to compare the results.

The results demonstrate the efficacy of a coordinated decision-making system rooted in CI techniques, notably the proposed Improved Genetic Algorithm (IGA), in enhancing emergency responses within the realm of technological disasters. The proposed approach surpasses alternative methodologies from state-of-the-art methods, including the Random Task-Assignment Algorithm (RTA), Collection Path Ant Colony Optimization (CPACO), Multi-objective Particle Swarm Optimization (MOPSO), and Greedy Algorithm (GRA), by optimizing task assignments, resource allocation, and coordination for multiple agents engaged in emergency response. The evaluation encompassed 45 scenarios designed from the key factors of an emergency (Sect. 4). One practical implication of this study is the potential application of real emergency cases to assess agent distribution and their tasks. Using real emergency scenarios as test cases, the system’s ability to effectively allocate agents and tasks in response to actual emergencies can be evaluated. This provides valuable insights into the practicality and performance of the developed algorithms in real-world situations.

The strengths of this research lie in its meticulous investigation, which ensures that the system in which the algorithms operate accurately characterizes the relevant variables for managing and evaluating agents in this context. Additionally, various alternatives are compared to determine which emergency metrics benefit the most from the proposed approach. However, there are some limitations to future research. In an emergency management system, for example, additional sections in the system interface can be used to introduce disturbances, such as adding more incident points, altering tasks, changing agent profiles, or introducing new disruptions. This would provide users with enhanced control over emergency scenarios, allowing for the recreation of emergency situations.

Future research also could integrate other intelligent techniques to enrich the system capabilities. Additionally, a robustness study of both the system and algorithms was conducted to determine the limits regarding the maximum number of agents it can effectively handle in various emergency scenarios without affecting, for example, the overall performance and scalability.

In conclusion, the proposed CI-based approach serves as a valuable tool for evaluating techniques aimed at enhancing coordinated decision-making among agents during emergencies. Therefore, it represents a supportive strategy for the appropriate selection of CI techniques based on the specific objectives of emergency management.

7 Conclusion

In conclusion, this study demonstrates that a coordinated decision-making system based on CI techniques, specifically the proposed Improved Genetic Algorithm (IGA) can significantly improve emergency responses in the context of technological disasters. The proposed approach outperformed other approaches, including the Random Task-Assignment Algorithm (RTA), the Collection Path Ant Colony Optimization (CPACO), the Multi-objective Particle Swarm Optimization (MOPSO), and the Greedy Algorithm (GRA), by optimizing the task assignment for multiple agents involved in emergency response. The performance was evaluated in different scenarios designed with proposed metrics, including Scalation Rate, Risk Index, Response Time, Severity Level, Coverage Area, and Operation Rate.

The proposed approach can potentially enhance the performance of emergency management systems by up to 15.3%. In low-severity emergencies, IGA enhanced performance by 9.68%, medium severity by 15.80%, and high severity by 18.02%.

Furthermore, the design and development of comprehensive metrics and algorithms are essential components of the proposed approach. The design and development of a graphical simulator enabled the creation of different scenarios for emergency response, whereas the proposed metrics complemented the state-of-the-art approaches for evaluating the performance of emergency management systems. The development of the IGA algorithm fulfilled the objectives of emergency management for optimizing task assignments.

However, the successful implementation of the proposed algorithm also highlights the need for deeper integration of emerging CI techniques into emergency management. Further research and development of comprehensive metrics, standards, and protocols for emergency response and scalability is necessary to improve the effectiveness and applicability of CI-based systems.

In summary, the proposed CI approach is supportive for future research on the development of effective strategies to mitigate the impact of technological disasters. The results emphasize the importance of leveraging the power of CI techniques to enhance coordinated decision-making among agents during emergencies, thereby facilitating effective responses to disasters in a timely and efficient manner.