Modeling Missing Maritime Objects Using an Agent Based Model

Jarrod Grewe

and Igor Griva

Department of Computational and Data Sciences, George Mason University,

4400 University Dr Fairfax VA, U.S.A.

Department of Mathematical Sciences, George Mason University, 4400 University Dr Fairfax VA, U.S.A.

Keywords: Agent Based Model, Search and Rescue, Search Theory.

Abstract: Accurate modeling the movement and behaviors of missing persons and vessels is critical in their finding and

rescuing in maritime environments. Current methods focus on using particle techniques that model several

factors including leeway and drift but lack the ability to model human factors and behaviors. This research

explores the idea of using an agent-based approach to model missing objects with the goal of developing a

methodology that accounts for missing person behavior in a maritime domain. This new approach leads to a

more accurate missing persons movement trajectories and results in finding better search plans. The results

show that an agent-based model can consider environmental elements, behavioral factors, and hazards when

modeling target movement in a maritime domain which is critical in missing object modeling. The developed

approach also shows how an agent-based model can help find optimal search plans.

1 INTRODUCTION

In this paper we examine and discuss the use of an

agent-based model (ABM) in modeling missing

maritime objects. Using a ABM could increase the

accuracy of predicting how missing maritime objects

move by modeling human factors and behavior.

The motivation of this research is to increase the

probability of search and rescue (SAR) personnel

finding missing persons and saving lives. Between

1993 and 2016, an average of 278 lives were lost

annually after the United States Coast Guard (USCG)

was notified of a missing person. (U.S. Coast Guard,

2019).

Consider a scenario that is loosely set on the

eastern shore of Delaware. Consider yourself a

manager of SAR operations who develops,

implements, and oversees SAR activities in the area.

It is a cool autumn day at a well-known coastline.

There is a strong wind that shifts from the south to the

east at 10 knots, and the sky is clear and cool. From

New Jersey, the water currents travel south before

turning east to join the Gulf Stream, which travels

northwest. There have been emergency calls, so a

search operation needs to be started.

https://orcid.org/0000-0002-9807-2410

https://orcid.org/0000-0002-2291-233X

The distress signal is sent by a fishing boat. The

boat's operators claim that electrical problems. are

impacting their motor and navigational gear. The

caller said they were travelling northeast but weren't

aware of their precise location. The call was cut off,

and attempts to reach the other party were futile. The

emergency radio call was triangulated to get the last

known location. There are helicopters, cutters, and

search boats among the search resources at hand.

Such a situation requires a quick turnaround in

terms of decision making and launching a SAR

operation. The methodology described in this

manuscript helps a SAR manager make qualified

decisions that maximize the probability of finding the

lost boat considering available resources.

2 LITERATURE REVIEW

How a search theory methodology simulates target

movement is a key element in any search plan

optimization for a mobile target. Historically,

diffusion methods have been widely applied (Lin &

Goodrich, 2010) and (Eagle, 1984), whereas

SAROPS (Search and Rescue Operations Planning

236

Grewe, J. and Griva, I.

Modeling Missing Maritime Objects Using an Agent Based Model.

DOI: 10.5220/0012317300003639

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Operations Research and Enterprise Systems (ICORES 2024), pages 236-244

ISBN: 978-989-758-681-1; ISSN: 2184-4372

System) currently employs a particle technique.

(Kratzke, Stone, & Frost, 2010) Applying an ABM in

wilderness searches has been studied in some detail

(Mohibullah & Julie, 2013). A few case studies have

also been done to use agent-based simulations to

marine search operations in order to enhance

verification and validation techniques (Onggo &

Karatas, 2016).

The majority of pertinent research on the

employment of ABM in maritime settings is

concentrated on military and security uses. Port

security (Harris, Dixon, Dunn D.L., & Romich, 2013)

and the use of UAVs for surface monitoring (Steele,

2004) are examples of this. Additionally, a number of

studies, including (Walton, Paulo, McCarthy, &

Vaidyanathn, 2005) and (Sullivan, 2016), have been

published on force protection simulations. The

employment of ABM in counter-piracy activities has

also been studied by numerous scholars (Deraeve,

Anderson, & Low, 2010), (Dabrowski & Villiers,

2015), and (Marchione, Johnson, & Wilson, 2014).

The verification and validation of these models, as

seen, for instance, while examining tactics to defend

cargo ships against pirate attack (Deraeve, Anderson,

& Low, 2010), is a frequent problem in this field of

research. However, the methods utilized to evaluate

and verify the simulations are not explicitly stated.

The Pathfinder methodology introduced in

(Grewe & Griva, 2022) and (Grewe & Griva, 2022)

allows finding optimal SAR plans that maximize the

probability of target detection with available

recourses. While these manuscripts can offer a high-

level overview of the Pathfinder methodology, the

present manuscript focuses on ABM portion of

Pathfinder.

2.1 Limitations of Diffusion Methods

Diffusion methods have been used several times to

model mobile targets and have been applied in several

search theory methodologies (Eagle, 1984); plus to

model lost persons (Lin & Goodrich, 2010). These

techniques, which rely on Bayesian statistics and

probabilities, can get more difficult as the terrain gets

more complicated. It may work in the open ocean but

terrains like bays, marches, etc are far harder to

model. The main problem is that targets'

independence as independent agents with decision-

making abilities is not considered by diffusion

methods. Additionally, they are unable to model

changes in target type or survival mode. Because of

these limitations, the diffusion method can only

adequately model simple targets or objects over a

unified terrain.

2.2 Limitations of Particle Methods

The particle method considers only environmental

factors, while in addition to that the ABM can also

account for various behavioral modes of a target.

Each agent may have a special trajectory based on

agent’s individual behavioral characteristics.

Therefore, the ABM covers a much wider range of

possible target movements, types, transitions, and

thus results in search plans with higher probabilities

of finding missing targets.

3 PATHFINDER

METHODOLOGY

This section discusses Pathfinder, starting with an

abstract overview and then breaking down Pathfinder

into its core components. Next, we will review the

relevant models, processes, and definitions.

Pathfinder is a comprehensive search theory

methodology that uses an ABM to model target

movement and a nonlinear optimization model to find

optimal search paths. This is a powerful blend of

technology that has several advantages over existing

methodologies. (Grewe & Griva, 2022).

3.1 Components

The nonlinear optimization model and the ABM are

the two main parts of Pathfinder. While each element

can be used independently to enhance an existing

search methodology, their combined use is especially

potent. The ABM incorporates both environmental

and historical data. The nonlinear optimization model

will produce the best search plans for the maritime

search operation after receiving the information from

the ABM. The relationship between these elements

and search operations and data is shown in Figure 1.

3.2 Design

Figure 1 shows the breakdown of proposed rescue

operations into logical sub-processes. It serves as the

basis for the Pathfinder design. Only two of

Pathfinder's many automated and sequential sub-

processes require human involvement. This

manuscript describes in detail each sub-process

necessary for the core components—ABM and

optimization model—to function properly.

Modeling Missing Maritime Objects Using an Agent Based Model

237

Environmental

Factors

Historical Data

Initiation of Search

Oper ation

Agent Based Model

Optimization Model

Search Operations

Search Debriefing

Figure 1: The relationship between search operations and

the two main Pathfinder components, ABM and

optimization model.

The steps in this new methodology are introduced

in this section. Each phase has a separate sub-process

that is essential to the operation of Pathfinder. The

setup procedure comes first. The search manager

chooses search-specific information in this step,

including target types, searcher types, domain, and

last known location. Pathfinder then starts processes

that load history data, topography data, and

environmental data after the search manager makes

these selections. The Epsilon model is the next phase,

and it is used to find restrictions on the searchers'

travel across the domain. The ABM is the next step,

which simulates target movement. The search

manager is presented the findings after the ABM is

concluded. The search manager enters a preliminary

search plan using this information. Once entered, the

pre-processor uses this initial search plan for the

nonlinear optimization model. In addition, the pre-

processor prepares the variables and data for the

optimization model. The nonlinear optimization

model then identifies the best search strategies for

each searcher. After the nonlinear optimization model

is finished, a post-processor is employed as a quality-

control step and to get the data ready for visualization.

The search plan is visualized at this point, along with

any necessary data files. The search plans are now

prepared for use in search operations by a search

manager.

4 MODEL

4.1 Environmental Factors

Wind and water currents are the two main

environmental elements that influence target

movement. The following equations from the USCG

(USCG, 2013) are used to compute the first element,

leeway speed, or the movement induced by wind and

waves, of a target. Assume 𝑠𝑙𝑜𝑝𝑒



and 𝑌𝑖𝑛𝑡



are

constants, plus 𝐿



and 𝑊



are the leeway speed and

wind speed, respectively. These parameters vary

based on the target type. The y-intercept and slope of

the leeway linear equation are the constants 𝑌𝑖𝑛𝑡



and

𝑠𝑙𝑜𝑝𝑒



. Regression analysis and experimentation are

used to find these constants (Morris, Osychny, &

Turner, 2008). When 𝑊



< 6 knots, the equation

changes, resulting in 𝐿



=0 at 𝑊



=0.

𝐿



=

{𝑠𝑙𝑜𝑝𝑒



𝑊



+𝑌𝑖𝑛𝑡



𝑓

𝑜𝑟 𝑊



≥ 6 𝑘𝑛𝑜𝑡𝑠

𝑠𝑙𝑜𝑝𝑒



𝑌𝑖𝑛𝑡



𝑊



𝑓

𝑜𝑟 𝑊



<6 𝑘𝑛𝑜𝑡𝑠

(1)

In the current prototype, this is a quick way to

determine the leeway speed for various target types.

For target types with a small 𝑠𝑙𝑜𝑝𝑒



, the future

implementation of Pathfinder will additionally use

the Rayleigh Method (Kratzke, Stone, & Frost, 2010).

Water currents are the second environmental

component. The vector sum of the existing currents in

the environment is used to compute the overall water

current. This calculation considers various currents,

such as wind, surface, and tidal currents. Using

historical data as well as information from

organizations like NOAA, water currents will be

gathered in a manner similar to SAROPS. Two

environmental elements are present in the SAR

scenario: a 10-knot wind and water currents that are

moving from the south to the east into the northeast-

moving Gulf Stream.

4.2 Hazards

Next we discuss hazards and their effects on target

movement. Hazards that can cause death of a

searched target are problematic to model. Hazards

that interfere with target movement, however, are

simpler and depend on other behavioral elements.

Currently there is incomplete data on the probability

of death due to hazards. There is, however, data on

survival times for cold exposure (Tikuisis, 1995) The

USCG has utilized this mathematical model to

determine when to stop looking for a missing person

in the water.

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

238

When a target agent expires, it will be due to the

whims of wind, currents, and other environmental

factors. More investigation is required to compile this

data and model death because of exposure. One can,

however, model an agent’s ability to move around

hazards such as jetties.

4.3 Behavioral Factors

Behavioral factors were based on “survival modes”

which themselves are based on historical data and

assigned to agents on setup. Koester lists eight

different "survival strategies " that people who are

lost could employ (Koester, 2008). Agents can switch

between various "survival modes" while the search

progresses. Five of the most popular survival

strategies are included in the Pathfinder prototype:

overdue, travel aide, route finding, staying put, and

wanderer. Several survival modes are a subgroup of

these five and can be modelled in the future; for

example, direction sampling is a type of route finding.

Based on the weather, geography, objective location,

time of day, and other factors, the survival mode

determines how each agent will act. The historical

information utilized in the ABM was taken from

(Koester, 2008), which has some useful information

but not all the information required for a maritime

environment. It will be crucial in the future to gather

and derive data to adjust the ABM to a maritime

environment. The next step is to go through each

survival mode and how the ABM predicts target

movement.

When the target agent is trying stay put and is not

actively moving, it is in the staying put mode. The

SAROPS concept of "stickiness," which is inherent in

this ABM, is also present. If the water is shallow

enough, an agent who has a way to stay put—like an

anchor—might decide to use the anchor. The target

may also beach and remain put if they are sufficiently

close to the shoreline. The agent will have to struggle

against the environment to remain immobile if they

are unable to drop an anchor or beach their watercraft.

The wanderer mode is for the target agent who,

individually or in combination, (a) has no idea where

they are, (b) has no idea where they wish to go, (c)

may not be mentally competent of making reasonable

decisions. When an agent is in this survival mode,

they move randomly, frequently taking the simplest

routes (Koester, 2008).

Overdue, route finding, and travel aid survival

modes are all incorporated in the same way, but they

have different end points in mind. Where the target

agent wishes to go is the target destination. This

might be a fishing spot, a boat ramp, or just a site in

general. Each of these three survival strategies has a

unique method for determining the location of this

target. The target agent in the overdue mode is just

overdue and not lost. As a result, the target agent's

perception of their location and the target location is

accurate. The travel aid mode is for a lost target agent

who possesses navigational tools like a map or

compass. As a result, a target agent's perception of its

location and the target destination is generally

accurate and becomes better as the agent approaches

its destination. The target agent does not have a

reliable estimation of their location or their

destination in the route-finding mode. The target

agent will move in a general direction until they come

across landmarks that can direct them.

The ABM employs a genetic algorithm to

simulate the target agent's route in order to model

these three survival options. The "bounded

rationality" principle is applied in this genetic

algorithm (Simon, 1982). Time, information, and

human capacity for reasoning are all constrained,

which causes rationality to be bounded. A person

seeking to navigate a space may have a map of what

lies ahead, but until they are closer, they cannot see

the specifics of the path. For instance, a boat dock

might be indicated on a map as being ahead, but as

the user approaches, they find it is damaged and

unusable. Accordingly, the path that will most likely

take place in the near future is the actual one, but the

path in the far future is just an estimate.

The following paragraph describes how the

genetic algorithm works. A straight path is made from

the target agent's current location to its destination for

t=0 and regularly during the modeled time, with each

waypoint equally spaced and within the target agent's

range of motion. If the target is late, the destination

may be an accurate assessment, but if the target is lost

and using a travel aids, the destination may be an

inaccurate assessment of where its goal location is.

For the route-finding mode, this straight line lays in

one direction that is not necessarily in the direction of

the destination. Following the creation of this first

path, the target agent's current location serves as the

starting point for the genetic algorithm to run on a

small portion of the path. The portion of the future

path that is rational can be referred to as the "genetic

segment" or the "rational section" in this case. Each

waypoint in this section is marginally altered until a

faster, simpler, safer, more realistic, and within the

target agent's capability alternate path is discovered.

The new route is assessed using a weighted score.

The target's preferences for a new path determines

these weights. A shorter path could be more valuable

to some targets than an easy one. The genetic

Modeling Missing Maritime Objects Using an Agent Based Model

239

algorithm's scoring weights are based on data and

research on previously lost individuals. Since there is

only one terrain type to consider in this study—open

water—these weights have no impact on target

movement. As a result, the shorter route is always

chosen.

The target agent advances along the path by one

step after the path is created then moves on to the next

target agent. The ABM advances to 𝑡=𝑡+1 once

all agents have moved. With analysis and integration

of historical target behavior, several ABM

components will require additional fine-tuning.

Targets can be modeled leaving a search domain,

which is another benefit of employing an ABM in this

configuration. For example, if we use the ABM to

model a lost boat in 𝛺, we also model boats leaving

the search domain 𝛺



. This is an important factor in

SAR operations that enables search manager to

calculate when to end a search.

Modeling transitions between target types and

survival modes is a crucial ability for an ABM. For

instance, if a search team is looking for a boat, they

must consider the possibility that the boat has sunk or

may not have any power. It is possible that the target

is now a life raft or someone in the water if the boat

has sunk. A methodology should take these

transitions into account in order to accurately model

target behavior and movement. An example of a

transition a boat might go through during a search is

shown in Figure 2. Keep in mind that there are a

number of possible transitions in this straightforward

example, some of which can happen repeatedly.

Boat

Boat without

power

Life-raft

Person(s) in the

water

Figure 2: Visualization of the transitions that a boat could

undergo. In order to accurately model target movement and

behavior, these transitions must be modeled.

5 PRELIMINARY RESULTS

5.1 Analyzing Illustrative Scenario

Many of the actions and behaviors of agents in

Pathfinder were modeled. Some of the agents are

moved by the environment, some are propelled

toward their objective if they have power, and some

use an anchor in shallow water. High speed

computing techniques seem to have the ability to

train, tune, and optimize this ABM. In this scenario,

there are two target kinds, and the model illustrates

three different tactics a missing boat may use. The

first visualization shows agent allocation, which is

based on the three regions given to it, is shown in

Figure 3. The agent colors are as follows; black are

boats with power, green is boats without power,

yellow are life rafts, and red are persons in water.

Initial agent types are 60% boats with power, 30%

boats without power, 5% are rafts in water, and the

remaining 5% are persons in the water.

Figure 3: The three probability regions that were given to

the initial agent allocation were: A) the 50% region, B) the

40% region, and C) the remaining 10% region. we used

1001 agents in this visualization. The agent colors are as

follows, with examples; boats with power are black (1),

boats without power are green (2), life rafts are yellow (3),

and persons in water are red (4). Initial agent types are 60%

boats with power, 30% boats without power, 5% are rafts

in water, and the remaining 5% are persons in the water.

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

240

Figure 4: The agent’s primary separated into four groups:

A) an group of agents, primarily boats without power,

that is traveling to its destination; B) a group of agents,

primarily boats with power, that is being carried by the wind

and currents; C) a group of agents, boats without power,

that has anchored; and D) a group of agents, boats with

power, that is traveling to the coastline In creating this

visualization, we used 1001 agents. The agent colors are as

follows, with examples; boats with power are black (1),

boats without power are green (2), life rafts are yellow (3),

and persons in water are red (4). Initial agent types are 60%

boats with power, 30% boats without power, 5% are rafts

in water, and the remaining 5% are persons in the water.

Figure 4 demonstrates yet another benefit of

utilizing an ABM to simulate target behavior. When

looking for a missing boat, keep in mind that it might

or might not be powered, have an anchor deployed,

capsize, sink, have life rafts in the water, or even have

passengers in the water. As a result, there are various

target categories that SAR operations may be

searching for, and each target may display a variety

of distinct characteristics. Because it can represent all

conceivable target kinds and target behaviors

simultaneously, the ABM is advantageous for search

operations.

5.2 Analysis of the Number of Agents

Needed

When employing this prototype, a crucial question

arises: How many agents are required for an accurate

analysis of target movement? While further

consideration will be given to this in future research,

our preliminary analysis demonstrates how the

probability of detection (POD) and performance

depend on the number of agents employed. We

anticipate that utilizing more agents will improve

modeling target behavior accuracy at the expense of

performance; going from 100 to 500 agents would be

preferred and advantageous for accuracy, despite an

increase in processing time. Although increased

precision from 5,000 to 50,000 agents might be

slightly better, but performance could be greatly

hampered. There must to be an ideal quantity of

agents to be employed. With the next experiment, we

will investigate how accuracy and performance are

affected by the number of agents.

We will employ the initial search strategy shown

in Figure 5 of a helicopter using a ladder pattern to

search the domain. This preliminary search plan was

made using USCG documentation.

Figure 5: The initial search strategy for a helicopter (in

orange) that will be used to assess the impact of Pathfinder's

agent count.

With 1 to 2001 agents, we will conduct a number

of experiments in Pathfinder. Then, for each series of

runs, we will compile information on the searcher's

runtime and distance covered. By looking at four

agents from various prior distribution regions from a

different run of the ABM, we will also examine POD.

These agents will display the four main ABM

movements: late, navigational aid, anchor

deployment, and current-driven drifting. The use of

these agents is necessary because the quantity of

agents in the ABM will have an impact on

Pathfinder's automatic POD calculation. So, in this

experiment, we are testing the ability to find a single

target by using these individual agents.

An almost linear growth in Pathfinder's runtime as

a function of the number of agents was the first

outcome. This was anticipated because the data

Modeling Missing Maritime Objects Using an Agent Based Model

241

source from the ABM extended the optimization

model's runtime.

Figure 6: Top: The number of agents employed in the ABM

vs the runtime in minutes for Pathfinder. Bottom, based on

the number of agents deployed in the ABM and the average

searcher travel distance in kilometers. Observe how it

reaches a plateau because of the time constraints and

searcher performance.

Next, we look at how the number of agents affect

searcher travel distance. The searcher has a limited

amount of time to search and can only move at a

certain speed, so this effect was also anticipated.

Around 1,320 km is the maximum distance that our

searcher, a helicopter, can travel. In some

experiments with 801 agents this limit was reached.

We expected that the POD would rise as the

number of agents rose, but for agents coming from the

50% region, the POD peaks between 1000 and 1600

agents. There are peaks at 400 and 1000 agents for

agents coming from the 40% region. Last but not

least, using more agents did not significantly increase

POD for agents in the 10% region. Since some

modeling techniques, like SAROPS, use up to 10,000

particles to model a probability distribution, this was

unexpected.

Future research should determine the ideal agent

count and the reasons why, after 1000 agents,

performance for agents inside the 50% region seems

to decline but only slightly improves for those outside

the 50% region. Many experiments we performed

experience a drop in POD performance at around 501

agents. The impact of agents on the significant

adjustments in search paths is related to this. The

complexity of the plans rises along with the number

of agents.

6 DISCUSSION

6.1 Verification Efforts

The output of the ABM is employed to verify

simulation findings. During the verification process,

numerous computations were used, and hundreds of

executions were scrutinized. Agents were also

examined to make sure they were produced properly

and moved realistically inside the domain. This

entails verifying calculations for movement, leeway,

and drift.

An active verification process was used in the

prototype after the static verification techniques. This

was achieved by placing checkpoints throughout the

prototype to resolve errors in calculations. For

instance, targets situated on terrain types that are

incompatible.

6.2 Validation Efforts

A critical research direction involves collecting more

data for the ABM. More behavioral data is needed.

For example, how often people in boats without

power deploy their anchor or how often a missing

kayaker will beach their kayak to conserve energy?

This data needs to be collected and analyzed to

finetune the ABM. The ABM is the component of

Pathfinder that will need the most research and

development in the future. This research will focus on

both maritime and land scenarios.

7 CONCLUSION

The obtained results demonstrated that an ABM can

aid in developing the search plans in a marine

environment. When simulating target movement, an

ABM may take environmental factors, behavioral

aspects, and hazards into account. This is crucial in

scenarios where a missing person may choose various

modes of behavior. Environmental elements are

similar to those used in earlier techniques, such as

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242

SAROPS. The results also provide some guidance on

the number of agents needed in the ABM to

accurately detect target activity and movement. At the

same time we believe that the number of agents as

well as finding the probabilistic distribution of

various modes of agents' behavior require more

investigation.

8 FUTURE RESEARCH

A crucial study direction entails obtaining more ABM

data. More behavioral information is required, such

as how frequently anchors are dropped by vessels

without power or how frequently a missing kayaker

beaches their kayak to save energy. Finding the path

score weights for the genetic algorithm will also be

important for land searches. Depending on the

geography, this will influence the preferred paths of

lost people. For the ABM to be improved, this

information must be gathered and examined. The part

of Pathfinder that will require the most future

research and development is the ABM. Both maritime

and land-based scenarios will be the focus of this

study.

Data can be gathered in a variety of ways for

adaptation and validation. One could first collaborate

with the USCG and ask for authorization to gather

data from their search efforts. With volunteers

equipped with GPS devices, field experiments might

be conducted. This strategy has limitations since

people who are missing behave differently than others

who are following the instruction to "act as if you are

in a life threating situation." Modeling how people

move across a wilderness or maritime terrain may

benefit from data collection and analysis from

wilderness parks and habitats like those mentioned by

(Crooks, et al., 2015). Land SAR analysis will also be

helpful. For instance, a right-handed person is more

likely to turn right when there is a choice in direction

(Koester, 2008). Finally, historical data can be

employed, but it is challenging to get and it may have

gaps. Many missing persons do not know the exact

path they took before being found although data on

where they were found can generally be ascertained.

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