Task allocation under uncertain conditions is a key
problem for agents attempting to achieve harmony in disaster environments.
This paper presents an agent-based simulation to investigate task allocation
considering appropriate spatial strategies to manage uncertainty in urban
search and rescue (USAR) operations. The proposed method is based on the
contract net protocol (CNP) and implemented over five phases: ordering
existing tasks considering intrinsic interval uncertainty, finding a
coordinating agent, holding an auction, applying allocation strategies (four
strategies), and implementing and observing the real environment. Applying
allocation strategies is the main innovation of the method. The methodology
was evaluated in Tehran's District 1 for 6.6, 6.9, and 7.2 magnitude
earthquakes. The simulation began by calculating the numbers of injured
individuals, which were 28 856, 73 195, and 111 463 people for each
earthquake, respectively. Simulations were performed for each scenario for a
variety of rescuers (1000, 1500, and 2000 rescuers). In comparison with the
CNP, the standard duration of rescue operations with the proposed approach
exhibited at least 13 % improvement, with a maximal improvement of 21 %.
Interval uncertainty analysis and comparison of the proposed strategies
showed that increased uncertainty led to increased rescue time for the CNP
and strategies 1 to 4. The time increase was less with the uniform
distribution strategy (strategy 4) than with the other strategies. The
consideration of strategies in the task allocation process, especially
spatial strategies, facilitated both optimization and increased flexibility
of the allocation. It also improved conditions for fault tolerance and
agent-based cooperation stability in the USAR simulation system.
Introduction
Preparation to manage an earthquake crisis requires optimal and appropriate
management. Agent-based modeling of search and rescue operations after an
earthquake is a good model for decision-making compared with traditional
computational approaches (Hooshangi and Alesheikh, 2018). Multi-agent
systems consist of several automatic and autonomous agents that coordinate
their activities to achieve a target (Crooks and Wise, 2013; Sabar et
al., 2009). Multi-agent systems are suitable for the modeling and simulation
of complex systems (Mustapha et al., 2013). They allow for the
division of the system into subdivisions (agents) and the modeling of the
relationships among these agents (Uno and Kashiyama, 2008). The
use of multi-agent systems is necessary for disaster management (Hawe et
al., 2015; Grinberger and Felsenstein, 2016). Importantly, multi-agent
systems can be used to implement various scenarios of search and rescue
operations, as well as distributions of facilities, in the crisis area
(Crooks and Wise, 2013).
Task allocation is one of the main coordination challenges among sets of
agents in a multi-agent system (Liu and Shell, 2012; Nourjou et al.,
2011; Chen and Sun, 2012). Agents fail to reach their ultimate goal without
proper assignment of tasks (Reis and Mamede, 2002). In disaster
environments, urban search and rescue (USAR) and the assignment of tasks are
dynamic processes occurring under uncertain conditions (Hooshangi
and Alesheikh, 2017). Generally, task allocation on a large scale is
influenced by uncertainties and various factors (Cai et al., 2014).
Uncertain conditions have a major impact on the initial planning and results
of rescue operations (Hooshangi and Alesheikh, 2018). Despite various
investigations, an optimal task allocation solution has not been established
(Olteanu et al., 2012).
In many instances, the initial allocation may result in problems or new
tasks may be added to the worklist; therefore, reallocation is necessary.
Reallocation is an effective reaction to environmental uncertainties and
changes and has important roles in both reducing the wasted time during an
operation and increasing operation profitability (Zhang et al., 2014).
Reallocation after instantaneous disruption is very important, especially in
large-scale distributed systems (e.g., USAR operations) (Olteanu et al.,
2012). An effective task allocation approach in USAR operations should
include strategies for replanning to manage future situations. Because tasks
may not be performed well for various reasons, strategies such as minimum
location displacement should be applied to initial responses to preserve
additional time during reallocation or future task allocation. This approach
to task allocation optimizes planning performance to achieve better
performance time and provides conditions for fault tolerance.
The present article is the final part of a research project in Iran. This
research project was carried out over three phases. In the first phase,
uncertainty in task allocation among agents was considered, and task
allocation was performed only by considering the proximity (spatial
distance) to the tasks. The developed method was evaluated in a
square-shaped random environment without a sensitivity analysis
(Hooshangi and Alesheikh, 2017). In the second phase, the
feasibility of the developed method was investigated in a simulated
environment using real regional data. In this phase, the operational
environment of a crisis was simulated, and the developed method was examined
in a real environment. In the simulated system, damage for a 6.8 magnitude
earthquake was calculated for District 3 of Tehran, and rescue
operations were modeled (Hooshangi and Alesheikh, 2018). In the third
phase using the concepts of previous articles (Hooshangi and Alesheikh,
2018, 2017), spatial strategies were included in task allocation among
agents and simulated with real-environment data. The present paper is the
output of the third phase of the research project. The main purpose of the
research is to improve task allocation in crisis-ridden conditions for
agent-based groups by considering proper strategies to manage uncertainties.
This paper first develops an agent-based simulation system for USAR
operations, then applies uncertainties in agent decision-making by improving
an interval VIKOR method to perform task allocation, and defines strategies
for conditions under which the initial assignment has encountered a problem
and requires reallocation (i.e., managing availability uncertainty during
implementation). The innovation of the study is the establishment of an
approach to improve conditions during reallocations or future allocations
when initial allocations encounter problems, due either to availability
uncertainties or the addition of a new task. In general, strategies are
selected in such a manner that the final cost of the system will not
increase abnormally if the initial allocations encounter problems. By
applying spatial strategies in the assignment of tasks, it is expected that
the assignment of tasks in conditions of uncertainty will be done optimally
and more quickly.
Literature review and backgroundAgent-based USAR simulation
An agent-based model is a class of computational models for simulating the
actions and interactions of autonomous agents. Agent-based simulations have
been used in various investigations including crisis/disaster management
(Wang et al., 2012; Hooshangi and Alesheikh, 2018), emergency supply
chains (Ben Othman et al., 2017), tsunamis (Erick et al.,
2012), and collective behavior (Welch et al., 2014).
These simulations can be effective in both planning and policymaking
(Fecht et al., 2014). Simulation of the operating system
involves a simplified real environment, which is used to model a wide range
of agents in complex systems. Various researchers have modeled a portion of
the behavior of agents in simulated environments (Erick et al., 2012;
Wang et al., 2012; Matarić et al., 2003) and demonstrated collaboration
among agents. However, agent cooperation in catastrophic environments has
been less extensively studied, such that uncertainty in collaboration among
agents has generally not been considered. In previous studies, a geospatial
information system platform was used when preparing the environment and
creating a simulation base map (Welch et al., 2014).
Spatial analysis and related tools are used in most research endeavors in
USAR operations after an earthquake.
Approaches to applying uncertainties in task allocation
Agents should include environmental uncertainties in their performance with
respect to planning goals. There are four common approaches to considering
uncertainty: probabilistic, fuzzy logic, rough set, and interval set
(Hooshangi and Alesheikh, 2017). Uncertainty in task allocation
has been investigated in various studies that can be categorized as sensor
noise (Liu and Shell, 2011; Bertuccelli et al., 2009; Matarić et al.,
2003), an accidental event during execution (Lee and Al-yafi, 2010; Li
and Cruz, 2005), the occurrence of new tasks (Xiao et al., 2009;
Kayır and Parlaktuna, 2014), the number of groups (Quiñonez et
al., 2011; Dahl et al., 2009), the relationship among agents (Choi et
al., 2009; Su et al., 2016), and decision parameters (Hooshangi
and Alesheikh, 2017).
The above-mentioned methods have been used in various applications such as multiple
unmanned aerial vehicles (Bertuccelli et al., 2009), supply chains
(Dahl et al., 2009), moving plants (Tan and Barton, 2016), and
disaster environments (Su et al., 2016). There is no dominant approach
to model uncertainty for all phenomena. The appropriate method is determined
based on the characteristics of the phenomenon and the purpose of the study.
In crisis environments, there is uncertainty in all decision parameters. In
the category of uncertainty in decision parameters, which is suitable for
multi-agent systems, uncertainties are associated with the decision
parameters for assigning tasks. Therefore, all information needed for task
allocation is considered uncertain. Various methods such as the contract net
protocol (CNP) (Hooshangi and Alesheikh, 2017), stochastic
scheduling (Tan and Barton, 2016), and genetic algorithms (He et al.,
2014) have been used in these contexts. Here, we present an approach that
includes uncertainties in decision parameters and strategies in the CNP. The
CNP produces local optimal solutions that are abundantly used in multi-agent
systems (Choi et al., 2009). This method is simple and practical and
is popularly used in agent-based modeling. In USAR operations, complete
individual expertise is impossible due to a lack of environmental knowledge;
therefore, determining membership function and the probability distribution
is a complex and time-consuming step. We used interval analysis to manage
these shortcomings and to consider the intervallic nature of available data
within a rescue operation. In the interval set method, due to the
uncertainty in a parameter's value, that parameter is specified as an
interval regardless of the probabilistic distribution (unlike in
probabilistic theory) or membership function (unlike in fuzzy logic)
(Hooshangi and Alesheikh, 2017).
Reallocation and reassigning methods
Distinct algorithms have been proposed for scheduling and task reallocation
in accordance with the tasks and available conditions within an environment
(Gokilavani et al., 2013). Some reallocation methods (e.g., data
envelopment analysis; Barnum and Gleason, 2010) and exact algorithms
(e.g., a branch-and-bound algorithm with column generation) resolve problems
on a smaller scale (e.g., 10 jobs and three vehicles). In such methods, the
process is time-consuming and slow for resolving large-scale problems
(Cai et al., 2014). Therefore, they are not suitable for the allocation
of tasks that should be performed dynamically and instantaneously in
large-scale problems.
In some research, such as the investigation of gate reassignment problems,
initial assignment tables have been created using heuristic methods in such
a manner that a succession delay is minimized (Cheng, 1997). The
incidence of adverse events may disrupt the original table. Notably, this
method is not suitable for a large number of tasks. Some other task
allocation methods are interdependent with the plan's ongoing tasks, such as
in construction operations (Olteanu et al., 2012). In those mathematical
calculations, when a task fails, all other tasks that were based on its
correct implementation must be replanned.
An appropriate reallocation method must be applied with respect to the
nature and scale of the problem. In USAR, a rescue process generally occurs
independently of any other rescue processes, and only a portion of the
workflow is ready to be implemented and assigned. Moreover, because of the
large number of rescue groups in USAR operations, as well as the available
uncertainties and dynamic nature of multi-agent systems in disaster
environments, the concept of general planning is uncommon, and appropriate
plans should be produced both locally and cross-sectionally. Most available
methods to resolve the problem of assigning tasks cannot be developed for
uncertain conditions and restrictions such as in critical rescue
environments (e.g., USAR after earthquakes).
With respect to USAR operations, task allocation methods must include
different strategies for all conditions and be dynamically generated in a
real-time environment. In contrast to previous studies, we define an
approach based on spatial strategies, such that the results of the initial
task allocation are used for future task allocations and are appropriate in
the rescue environment. Time limitations constitute another issue in the
reallocation and reassignment of rescue teams. Therefore, the present study
aims to expand the CNP method for rapid problem resolution.
Case study and data
The proposed approach can be implemented in various study areas. This study
used a part of Tehran (District 1 in the capital of Iran) to evaluate the
feasibility of the proposed method on the basis of available data. District 1 is one of 22 central districts of Tehran Province, Iran. District 1 has an
area of 210 km2 and is located in the northernmost part of the city of
Tehran (Fig. 1). Its population is 433 500.
Location of case study: (a) peak ground acceleration map of Iran for a return period of 2475 years and approximate location of Tehran and (b) location of District 1 and active faults in Tehran. (c) Map of District 1 (study area) and active faults, Tehran.
The recent Tehran earthquake (5.2 magnitude) in December 2017 attracted the
attention of many urban planning organizations. Tehran is a highly seismic
area because it is surrounded by the Rey, Masha-Fasham, and North Tehran
faults (Fig. 1b). Tehran is located in the southern part of the Alborz
Mountains, where a magnitude 7.3 earthquake occurred in 1990
(Berberian and Yeats, 2016; Hamzehloo et al., 2007).
Seismologists have reported that a severe earthquake may occur in Tehran in
the future (Hosseini et al., 2009). The North Tehran fault is the city's
largest fault and is approximately 175 km long (Kamranzad et al.,
2020). For this purpose, the North Tehran fault scenario, with the capacity
to cause the most destructive potential earthquake in Tehran, was selected
in the present study. Various scenarios have been simulated in seismic
studies in Tehran, such as 6.8 and 6.9 magnitude earthquakes. The method
developed in this research can be implemented for any scenario. In
accordance with the previous earthquakes and suggestions of seismologist
experts, we simulated 6.6, 6.9, and 7.2 magnitude earthquakes. The basic
data used in environment simulation were block maps, population, distance
from the fault, building material, agent location, year of building
construction, and building height.
Materials and methods
In this section, the simulated scenario and proposed method are described.
Scenario of proposed agent-based USAR simulation
We assume the presence of a disaster environment in which events are
uncertain. In this scenario, the crisis is assumed to be an earthquake. The
injured individuals are trapped under rubble, and the number of such
individuals in each building block is uncertain. Rescuing injured people is
the main goal. Saving each person is a task that must be performed through
the cooperation of rescue agents. After an earthquake, the numbers of
injured and deceased people can be estimated using different formulas by
determining the magnitude and location of the earthquake, as well as the
urban context data of the buildings (Kang and Kim, 2016). Furthermore,
the possible locations of injured individuals can be predicted using
building damage assessment models. Therefore, the simulation inputs are the
injured individuals' locations and their characteristics, which are
available with some uncertainty. The rescue agents are attempting to save
injured individuals by moving toward the task location. Given the results
of previous studies (He et al., 2014; Hooshangi and Alesheikh, 2017;
Sang, 2013; Chen et al., 2012) and in accordance with expert opinion on USAR
operations, the uncertainties include the number of injuries, severity of
the victims' injuries, duration of the operation, infrastructure priorities,
agent energy, route status, task runtime by an agent, and risk level for
each agent. These are important uncertainties in task allocation. All
parameters are specified as intervals during the task allocation process.
After task identification, an agent is assigned a task and pursues it. If an
agent fails to complete an assigned task because of any existing
disruptions, the task is updated with respect to uncertainties and reported
to the central agent, resulting in the reinitiation of the task allocation
process. In this process, task allocation strategies are applied to minimize
the cost of the system.
In this scenario, there is a central agent, as well as several coordinators,
rescuers, and injured agents in the environment. These independent agents
are rational and can communicate with each other. The agents have the
following roles and characteristics:
Central agent. This agent is responsible for sorting the tasks,
specifying the coordinators, determining the results, announcing rescuers,
and applying allocation strategies.
Coordinating agent. The coordinator is a rescue agent who is
responsible for sending work details to rescuers, receiving their proposals
(bids), holding auctions, and submitting the results and rescuer
prioritization data to the central agent.
Rescue agent. This agent identifies and moves to the task location,
searches for injured individuals, sends the task uncertainty to the central
agent, and rescues injured individuals from the debris.
Injured agent. This agent exists in the environment and has a
critical condition that changes continuously. This agent has no activity or
communication with other agents.
USAR simulation
In preparation for the USAR operation simulation, there are three main
parts: (1) calculating the damage rate of the area and people (simulating an
earthquake-damaged environment), (2) defining agents and their
characteristics, and (3) implementing the suggested method for task
allocation between agents.
To simulate an earthquake-damaged environment, an earthquake risk assessment
model was developed based upon the Japan International Cooperative Agency
(JICA) model. The JICA model is the output of cooperation between the Center
for Earthquake and Environmental Studies of Tehran and the JICA. The results
of this project and its implementation have been presented previously
(Mansouri et al., 2008) and used in various studies (Hooshangi
and Alesheikh, 2018; Vafaeinezhad et al., 2009). This model can calculate
the buildings' level of destruction and the number of injured people based
on the earthquake intensity, earthquake location, building vulnerability,
and the population in these buildings.
In our scenario, we included four types of agents: injured individual,
rescuer, coordinator, and central agent. The tasks described in the previous
section were implemented for each agent. The initial locations of injured
agents were based on building damage, and the locations of rescue groups were
randomly generated in the environment. The definitions of agents and their
characteristics were described in detail in our previous article
(Hooshangi and Alesheikh, 2018).
The proposed method
The proposed model for task allocation with uncertainties in earthquake USAR
operation is shown in Fig. 2.
Task allocation flowchart in the proposed approach, separated into five steps within an environmental simulation.
The five steps of the proposed approach are the ordering of existing work,
specifying the coordinators, holding an auction, applying reassignment
strategies (the innovation of this paper), and implementing and observing
environmental uncertainties (performed by an agent). The proposed method is
presented below.
Ordering existing tasks
In crisis-ridden areas, there are varying degrees of urgency (Chen et
al., 2012). Tasks with a higher priority must be performed first. Four
parameters are used to prioritize tasks: the number of victims, severity of
injuries, time required for a rescue operation, and infrastructure
priorities. The initial tasks with their uncertainties in the environment
(four priority parameters) are available to the central agent. Therefore,
for each task feature, an interval such as that expressed in Table 1 is
specified.
To manage interval data in the CNP, various multi-criteria decision-making
methods are proposed. The interval-based VIKOR method is used extensively to
coordinate agents in the assignment of tasks with interval data
(Hooshangi and Alesheikh, 2017). The interval-based VIKOR method
has been previously described (Sayadi et al., 2009). Ordering is
performed by the central agent.
Finding the coordinating agent
For each task defined by the central agent, the most appropriate agent is
identified as the coordinating agent. The coordinating agent is an agent who
is located near that task and is not currently working. The selection of a
coordinating agent and creating groups to execute any task can be achieved
through different methods and is based on various criteria (Chen and
Sun, 2012; Su et al., 2018). In this study, to simplify the calculations,
only the criterion of proximity (spatial distance) is used to identify the
coordinating agent. Therefore, the nearest agent to the task is selected as
the coordinator and is responsible for the auction. Selection of a
coordinating agent leads to the performance of calculations at a distributed
point. By selecting coordinating agents, the computational overhead of the
central agent is reduced.
Holding an auction
Coordinating agents hold auctions after receiving the task characteristics
and the list of agents in the subgroup. In the CNP, agents bid for tasks,
and the agent who offers the highest value for the task is the winner.
During the auction, rescue agents offer intervals (rather than values) for
the route conditions, the time required for the agent to execute the task,
the agent's possible risk level, and their energy. Accordingly, the agent
calculates numbers for each of the four decision-making criteria, such as
variable X, based on Eq. (1). In Eq. (1), the distance (in meters),
severity of the victims' injuries, and task priority are based on values
declared by the central agent. Based on the rate of uncertainty presumed for
a given environment (for example, 30 %), an interval for this number is
estimated. The first number of this interval is in the range between [X, X+30 %X] and the second number is in the range [X-30 %X, X].
Agent energy (energy level, distance, number of people)=energy level-distance/500-number of people rescued⋅0.3Task runtime by an agent (distance, number of people, severity)=distance/150+number of people rescued⋅15+severity⋅2Risk level for an agent (energy level, priority)=priority-energy levelRoute status (distance)=distance
In the real world, each person can introduce intervals according to their
experience and their knowledge of the environment. In this study, we used
the above equations based on expert opinion to simulate the real
environment. The coordinating agent applies the interval-based VIKOR method
to order the agents' bids. The coordinating agent sends the results to the
central agent after ordering the agents. The use of a central agent in this
phase provides the opportunity to make the best decision considering the
task priorities and capacities of other agents.
Applying allocation strategies
In operations where there is uncertainty, the issue of task allocation
cannot be definitively resolved. In this phase, the initial allocation
should be done in such a manner that a potential reallocation would waste
the smallest amount of time. Based on different strategies at this stage,
the central agent begins to assign tasks after obtaining all lists from
coordinating agents. In each strategy, a priority is assigned to specific
tasks. In this section, four different strategy-based approaches are
described, as follows:
Task allocation according to priority (strategy 1). In
this strategy, task allocation begins with the assignment of higher priority
tasks, following establishment of the task order and priorities of the
rescue team in the previous stage (prioritization and auction). Therefore,
the agent with the best performance is selected for high-priority tasks and
is subsequently excluded from the lists of agents with no tasks.
Subsequently, the tasks of lower priority are assigned in the same order.
The limitation of this strategy is that it may cause some agents to not
receive tasks.
Assigning tasks to all agents, preferably to specific agents with optimal outcomes (strategy 2). This strategy is based on the optimal
use of all rescue teams. In this strategy, all agents are assigned a task.
For this purpose, a task is first assigned to an agent who has applied for
the minimum number of tasks. The agent and task are then eliminated from the
agent and task lists, and the allocation continues with the next agent who
has made few requests. Using this strategy, a task will be assigned to all
agents.
Task allocation on a strategic spatial basis (strategy 3). Using this strategy, agents who play important and strategic roles
in the task allocation process are excluded to ensure their availability for
the implementation of tasks if problems are encountered during the task
allocation process. Agents with strategic roles may be defined differently.
Agents who participate in the auctions of more tasks are those with
strategic locations. In such instances, these agents are close to many tasks
(have strategic spatial locations) and can be used when these tasks are not
implemented. Figure 3 shows the difference between the task allocation
results for strategies 2 and 3. In Fig. 3, a rescue agent located
centrally has a strategic position and will try to maintain this position.
Although the total movement may increase, if there are problems in
performing other tasks, this agent can help all other groups.
Assigning tasks by creating the best density in the environment (strategy 4). This strategy is based on the optimal density of
rescue agents. Using this strategy, task assignments are made in a manner
that ensures the uniform distribution of agents in the environment.
Generally, no exact information is available concerning the conditions of
the tasks; therefore, this strategy aims to ensure a uniform distribution of
rescue teams within the environment if the uncertainty is high. In disaster
environments such as earthquakes, the incident occurs over a wide area, such
that the damage and injured population are uniformly distributed due to the
texture of the area. Therefore, the highest number of injured people is not
accumulated in any one spot. Furthermore, applying this strategy prevents
the convergence of rescue teams. To apply this strategy, the tasks of the
highest priority in the task lists should be given to the available agents
where the environmental density is the highest. The concept of optimal
density can be solved through innovative algorithms. In our study, the
simulated annealing method was used to determine uniform density. The
implementation stages of simulated annealing have been described previously
(Sabar et al., 2009). Figure 4 shows the difference between task
allocation outcomes for strategy 2 and strategy 4.
Strategic agent illustration. Blue arrows show the final results for strategy 2, and red arrows show the successful rescuers in strategy 3.
Best density strategy illustration. Blue arrows indicate the successful rescuers in strategy 2, and red arrows indicate the final results for strategy 4.
Implementation and observation of real values in the environment
During the implementation phase, tasks are implemented by agents in a
dynamic environment where there are always uncertainties during task
execution. The rescuer observes the difference between predicted values and
the actual environment after the work begins. In this study, a random number
in the [X-30 %X, X+30 %X] interval was chosen to model the real
environment. In the real world, the difference between the predicted
environment (through building vulnerability estimation models) and the real
environment will determine the agent's performance.
If the agent observes a large difference between the auction information and
the real environment, the agent abandons that task. In this instance, the
agent updates the task's values and uncertainties and returns the work to
the central agent. The new uncertainty interval will be 80 % smaller than
the original interval. There are various conditions under which agents will
reallocate a task if the environment differs from the expected scenario. For
example, the agent can abandon the task if three of eight decision-making
parameters are out of range by 5%. Otherwise, the agent finishes the
rescue work by accepting the new conditions. The central agent assigns newly
added tasks within the reallocation framework. When a new task is assigned,
the task allocation is combined with that of both new and incomplete tasks.
Evaluation method
Assessment of a task allocation algorithm is typically performed in the
first phase through modeling and simulation due to the dynamic and
heterogeneous nature of different environments (Olteanu et al., 2012).
Simulation is a suitable approach for the implementation and validation of a
proposed method (Nourjou et al., 2011). In a real test situation, the
situations and conditions of the implementation scenario are difficult to
reproduce. In the present study, we simulated three scenarios for
earthquakes in Tehran's District 1 with magnitudes of 6.6, 6.9, and 7.2. We
also estimated the numbers of deceased and injured individuals who are
distributed in the centers of relevant building blocks and need to be
rescued by 1000, 1500, or 2000 rescue agents. In the uncertainty analysis of
the suggested method, the lower and upper bounds of uncertain values were
also calculated. The proposed method was compared with the traditional CNP.
The intended task allocation was considered efficient if profitability
parameters were maximized. In accordance with several recent studies
(Liu and Shell, 2012; Sang, 2013; Hooshangi and Alesheikh, 2017), three
criteria were used to evaluate the performance of the proposed method: the
number of deceased victims, number of incorrect allocations, and rescue
time.
Some of the major problems in reallocation and in the task allocation
environment include scalability, reliability, performance, and dynamic
resource reallocation (Gokilavani et al., 2013). In this study, the
results of two analyses (scalability of the proposed method and interval
uncertainty analysis) are presented.
The first analysis focused on the evaluation of the proposed approach at
different scales and for different criteria. Comparison and assessment were
carried out at different scales to measure the effectiveness of the proposed
approaches in USAR operations. Nine scenarios were applied in this study and
compared with the traditional CNP.
The second analysis focused on interval uncertainty analysis and studied the
rescue operation duration in the 6.9 magnitude earthquake at different
levels of uncertainty. In this analysis, time changes in rescue operations
were investigated according to different levels of uncertainties. The
duration of a rescue operation in the simulation model depended on two main
components: prioritization of tasks and outputs of each operation in each
phase (Hooshangi and Alesheikh, 2018). Equation (2) defines the final
model for calculating the operation duration based on these two components.
Variables x1 to x8 constitute the number of injuries, severity of injuries,
duration of the operation, infrastructure priorities, energy, route status,
task runtime by agents, and risk level for agents, respectively. αn is the function of task prioritization, and βw is the
function of bidding.
To the best of our knowledge, interval uncertainty analysis has rarely been employed.
The method used in this research was adapted from previous literature
(Lan and Peng, 2016). In our analysis, Chebyshev points are used.
Equation (3) depicts a Chebyshev formula for generating m collocation points
in the interval [0, 1] (Lan and Peng, 2016):
numberi=0.5×1-cosπ(i-1)m-1forj=1,ifm=10.5forj=1,ifm=1.
Equation (3) was used to create different numbers for the decision-making
parameters. The output of the model was then calculated for various numbers
within the intervals. This technique created different values for the output
of the model.
Results and discussion
Multiple scenarios and experiments were designed to evaluate the proposed
methods and strategies. The results are presented in this section. In
accordance with expert opinion, three probable earthquakes were simulated
with magnitudes of 6.6, 6.9, and 7.2. Figure 5 shows the vulnerabilities of
buildings in these scenarios in the ArcGIS environment.
Vulnerability maps for District 1, based on earthquakes with
magnitudes of (a) 6.6, (b) 6.9, and (c) 7.2 on the Richter scale.
Based on the level of building destruction, the numbers of injured and
deceased people can be calculated using the JICA model. The numbers of
injured and deceased people in scenarios with 6.6, 6.9, and 7.2 magnitude
earthquakes are listed in Table 2.
The computational scale of the JICA model uses urban blocks. Therefore, the
numbers of deceased and injured individuals in each urban block were
calculated. The locations of injured individuals were presumed to be in the
centers of the respective blocks.
The environmental simulation and proposed method were implemented in
AnyLogic software. This software can process geospatial information system
data. To simplify the environment and reduce the calculation volume, each
agent was regarded as a group in the real world. Figure 6 shows the
simulated environment.
Overview of the USAR simulator.
There are many injuries in the environment. The central agent first sorts
the tasks according to their priorities. After the coordinating agent has
been determined, the central agent sends the task properties to the
coordinating agent. The coordinator holds an auction. Rescue agents bid in
accordance with their environmental and working conditions. Rescuers are in
a ready state at the start of the operation. Each successful rescue agent
moves to the task's location. After reaching the task position, the rescue
agent begins rescuing the injured agents. During the execution of their
assigned work, the agents may find considerable differences between the
real-world information and the information expressed in the auction. In such
instances, the agents may stop performing their tasks and report the
discrepancies to the central agent.
Table 3 shows the durations of USAR operations as estimated using
scalability analysis with the proposed method. In creating this table, an
uncertainty of 30 % was considered. For this purpose, the range of task
characteristics used the intervals [X, X+30 %X] and [X-30 %X,
X]. At each stage, a given agent participated in the auction. For that
agent's decision-making parameters, the numbers were randomly converted into
an interval. The average range of agent tasks and decision-making was used
for implementation of the CNP, rather than interval values.
Comparison of operation duration in hours between the proposed
method and the CNP (based on 30 % uncertainty).
The operational time decreased when the number of agents in rescue
operations increased, with the number of tasks remaining fixed. The reduction
rate ranged from 54 % to 60 % when the number of agents was doubled. The
duration of a USAR operation increased when the number of tasks increased
for a given number of agents. Therefore, the duration of the rescue
operation was related to the number of rescue agents and the number of
available tasks in a scenario. There was an inverse relationship between the
duration of the USAR operation and the number of rescue agents and a direct
relationship between the duration of the operation and the number of tasks.
The inclusion of uncertainty in any allocation strategy provided better
results compared with the CNP method. Using the proposed strategies, the
smallest improvement in results with uncertainty was 2.9 h (13 %) for a
scenario with 2000 agents and 28 856 tasks (6.6 magnitude earthquake). The
maximum improvement was 60.6 h (21 %) for 1000 agents and 111 463
tasks.
Numbers of deceased people with (a) 1000, (b) 1500, and (c) 2000
rescue agents.
Numbers of incorrect allocations with (a) 1000, (b) 1500, and (c) 2000 rescue agents.
Among the task allocation strategies in this study, strategy 1 produced the
worst response. At each scale for the discussed scenarios, strategy 1
resulted in USAR operations with the longest durations compared with other
strategies. Strategies 1 and 2 provided similar results at different scales,
although strategy 2 achieved better results. Strategy 4, which involved
spatial information in task allocation, produced better results at all
scales, including improvements of 21 %, 24 %, and 23 % with 1000 agents
for a 6.6 magnitude earthquake, 1500 agents for a 6.9 magnitude earthquake,
and 2000 agents for a 7.2 magnitude earthquake, respectively, compared with
the CNP. The average improvement for strategy 4 was 26.6 h in rescue
operations. The use of strategies 3 and 4 is more suitable in a larger
environment with high numbers of both injured people and rescue agents
because controlling agent distribution with respect to expansion of the
environment and the uncertain environmental conditions can be effective in
future task allocations. In a real-world crisis-ridden environment, the
overall environment is damaged, and the injured people are well distributed.
Therefore, the spatial distribution of agents is an important parameter to
control in USAR operations.
The simulation results in terms of deceased people for 1000, 1500, and 2000
agents with different numbers of tasks are shown in Fig. 7. In these
figures, for each of the four priority parameters and decision parameters
associated with agents, a 30 % uncertainty level was considered.
Figure 7 illustrates the numbers of deceased people in the rescue process
with different numbers of agents and tasks. Based on Fig. 7, an increased
number of tasks led to an increased number of deceased people, but an
increased number of rescue agents led to a decreased number of deceased
people. Regarding the numbers of deceased people at all three scales, the
CNP method produced the worst response. An average of 7253 people were
deceased in the CNP model with 1000 agents. Conversely, 5853 people were
deceased in the model employing strategy 1 with 1000 agents. Overall, when
all strategies were considered, strategies 4 and 1 resulted in the best and
worst responses, respectively. As illustrated in Fig. 7, the numbers of
deceased people were approximately equivalent in strategies 1 and 2.
Figure 8 illustrates the simulation results for the incorrect allocation of
1000, 1500, and 2000 agents with several different tasks.
The overall trend in each chart was approximately similar if all charts were
considered simultaneously. Any incorrect allocation was unrelated to the
number of rescue agents because there were no changes when the number of
agents was increased. The number of incorrect allocations changed with the
number of tasks, such that it increased with an increasing number of tasks.
This increase is evident in all panels in Fig. 8. Incorrect allocations
usually occurred at a nearly fixed rate.
Based on the results, the traditional CNP model produced the worst response.
The total incorrect allocations in the CNP model with 1000 agents and 28 856
tasks, 1500 agents and 73 195 tasks, and 2000 agents and 111 463 tasks were
3780, 10 027, and 14 604 tasks, respectively. The numbers of incorrect
allocations assigned by strategy 1 were 3174, 8014, and 12 455 tasks,
respectively. Furthermore, the evaluation criteria showed the advantages of
including uncertainty in task allocation. Therefore, the proposed approaches
for all three evaluation parameters resulted in better performance compared
with the traditional CNP method. The results indicate that the reallocation
of tasks through the proposed approaches and strategies offered a better
response, based on the scale of the event, because their differences from
the CNP model increased at a larger scale.
The results of interval uncertainty analysis were achieved with 1000
randomized runs of each scenario (Fig. 9).
Uncertainty analysis of the proposed method for USAR operations,
for nine simulated scenarios.
As shown in Fig. 9, there is a direct relationship between interval length
and operational time. According to Eq. (2), assigning fewer tasks leads
to less operating time and causes less uncertainty in the simulated
environment.
As mentioned in Sect. 4.3.3, the rescuers use [X, X+30 %X] and [X-30 %X, X] to determine the intervals. Another analysis was performed
for values other than 30 % in the estimations. The results are shown in
Fig. 10. An average event scale (1500 agents and 73 195 tasks) was used,
and different levels of uncertainty (uncertainty between 5 % and 55 % at
five-unit intervals) were randomly generated, investigated, and evaluated.
This realistic test aimed to assess the proposed scenarios for each
uncertainty value.
Uncertainty analysis when different values were used in determining intervals.
Figure 10 indicates a relationship between increased in uncertainty (from
5 % to 55 %) and an increased rescue time. The increases differed among
strategies. The increase was 67.7 h for the CNP (from 66.8 to 134.4 h),
whereas increases of 63.4, 63.2, 61.7, and 56.5 h were obtained for
strategies 1–4, respectively. Based on the evaluation results, the proposed
methods are more efficient and present better responses in the presence of
various uncertainties. Therefore, increased in uncertainty leads to a delay
in USAR operations and possible task elimination. Accordingly, delaying
rescue operations or removing tasks from the rescue list will increase USAR
time.
Conclusion
Providing a suitable method for assigning tasks under uncertain conditions
is important, according to the results of simulated USAR operations. This
study presented a task allocation approach that aimed to better assign
initial tasks, thus ensuring better conditions for potential reallocations
of tasks and wasting the least time possible for rescue teams if problems
were encountered during the initial allocations or a new task emerges. Some
of the characteristics and advantages of the study include the focus on the
necessity of task reallocation in disaster environments, the provision of an
innovative approach for managing uncertainties that cause non-performance of
tasks in the CNP method (the most widely used task allocation method in
multi-agent systems), and the definition of spatial strategies for better
task reallocation. The proposed approach can be used in combination with a
wide range of algorithms for assigning tasks in accordance with the
structure of the system.
The results obtained from simulations with the proposed approach revealed
that the duration of rescue operations when the proposed strategies were
implemented was always shorter than the time required using the CNP method.
The worst improvement was identified for 2000 agents with 28 856 tasks
(13 %) and the best for 1000 agents with 111 463 tasks (21 %).
Furthermore, the results at different scales showed that the application of
uncertainty in task allocation could improve the duration of USAR
operations. There is a relationship between an increase in uncertainty and
increased rescue operation duration. Furthermore, the results revealed a
significant decrease in the numbers of deceased people and wrong allocations
due to uncertainties, which demonstrated the importance of uncertainty
inclusion in task allocation. The implemented method can be used for
cooperation among agents. In an earthquake-stricken environment, rescuers
can use assistant agents (devices such as mobile phones and tablets) to
implement this methodology.
However, regarding comparisons of the proposed strategies, it is
insufficient to consider only uncertainty in initial decision-making
concerning task allocation because the working environment is quite dynamic,
and the assigned tasks may encounter various problems. An effective
assignment approach should consider both uncertainties in decision-making
and strategies for reallocation to waste the least time during system
disruptions. This optimizes planning to achieve better implementation time
and allows for fault tolerance. The strategies for applying uncertainty during
the implementation of task allocation improve the efficiency, performance,
and stability of agent-based cooperation. Task allocation strategies lead to
flexibility in decision-making and decrease the system's overall costs.
Furthermore, spatial task allocation strategies can propose a specific
arrangement of the rescue team within an environment to prevent time-wasting
in the event of environmental uncertainties or task reallocation.
Additional research is recommended to provide new strategies and combine the
proposed task allocation strategies of the present study with a
coalition-forming method to select an appropriate coordinating agent in our
proposed approach. Future studies should also consider other groups and
other uncertainties within a range of dynamic simulations.
Code and data availability
District 1 data were purchased online and cannot be published. Codes are
available upon request.
Author contributions
NH collected the data, performed most of the result analyses, and
wrote the draft. AAA has advised on implementation and helped
interpret the results and also helped revise the manuscript. MP supported
the writing and editing of the paper. SL provided critical proofreading
with valuable suggestions. All the authors were involved in the editing of
the manuscript.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The authors highly appreciate the anonymous reviewers and the editor for their
constructive comments that helped us to improve the paper.
Financial support
This research has been supported by the Basic Research Project of the Korea Institute of Geoscience and Mineral Resources (KIGAM) and the Project of Environmental Business Big Data Platform and Center Construction, funded by the Ministry of Science and ICT. Furthermore, this work has been supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (grant no. 2019R1A6A1A03033167).
Review statement
This paper was edited by Paolo Tarolli and reviewed by three anonymous referees.
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