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ships. For the estimation of the optimal course to
avoid a collision, a negotiation system is used: Each
vessel in a possible collision is modeled as an agent.
Based on a monotonic concession protocol the agents
have to make concessions in order to achieve an
agreement. If they cannot agree on a strategy, a so-
lution based on another algorithm will be used.
A multi-agent system for the maritime surveil-
lance is presented by Mano et al. (2010). Each vessel
in an area is monitored by an individual agent. These
agents estimate the criticality value for the assigned
vessel as a combination of different rules with respect
to the vessel’s state and the area around the vessel. As
the conditions in the monitored area will evolve, it is
designed as an adaptive system.
Agogino and Tumer (2012) introduce a multi-
agent system for managing air traffic flow. Reinforce-
ment learning methods are used in order to reduce
congestion. Each agent is responsible for a specific
area. For each plane passing the area, the responsi-
ble agent has to chose its action: to change the dis-
tance between airplanes, to order delays, or to reroute
an aircraft. The system is evaluated by using simula-
tions.
Dynamic Bayesian networks are used by Fischer
et al. (2014) in order to model situations of interest,
e.g. smuggling of goods. As a dynamic Bayesian net-
work has several parameters, which domain experts
might not be able to intuitively choose, Fischer et al.
developed an approach to estimate these parameters
by giving only a few more intuitive parameters as in-
put. For the evaluation, a specific situation is modeled
and results for different sets of parameters are given.
Two different kinds of similarity measures are
analysed by de Vries and van Someren (2014). On
the one hand, alignment measures such as dynamic
time warping, and, on the other hand, measures based
on the integral between two trajectories are used.
Both types of measures are utilized in kernel meth-
ods for clustering and classification tasks as well as
for anomaly detection. For the evaluation, a dataset
from the maritime domain is used.
Soleimani et al. (2015) assume, that vessels in the
maritime domain take the shortest possible route be-
tween the start harbor and the destination. Therefore,
they use the A* algorithm to generate a reference tra-
jectory, which is compared to the real path of a vessel.
If the deviation is large, the vessel’s behavior is con-
sidered an anomaly.
As the amount of data processed in surveillance
tasks can be huge, Cazzanti et al. (2015) show how
big data technologies can help to face the arising chal-
lenges. They use these methods to handle incoming
data efficiently and to do geospatial analyses on the
stored data.
An algorithm for the identification of anomalies in
spatio-temporal data based on b-spline interpolation
is introduced by Anneken et al. (2016). They use the
control points of the b-spline representation of a tra-
jectory as a feature vector for different machine learn-
ing methods. As the training data is annotated, the
machine learning algorithm will be trained to identify
two classes, the normal and abnormal. The whole al-
gorithm is evaluated on a dataset from the maritime
domain.
Millefiori et al. (2016) developed a method to pre-
dict the state of vessels under way in open sea. They
use an Ornstein-Uhlenbeck process in order to esti-
mate the long-term state. During their evaluation,
they compare the Ornstein-Uhlenbeck based method,
with a classic approach based on a white noise ran-
dom process on the velocity.
3 ALGORITHM
A bargaining game
B = (N, P, c) (1)
is defined by the set of players N = {1, . . . , n}, the
payoff space P ⊂ R
n
and the conflict or disagreement
point c ∈ P. The conflict point represents the payoff c
i
which will be obtained by the player i, if no agreement
is reached.
Each player i ∈ N has its own strategy space S
i
. A
strategy for i is denoted by s
i
∈ S
i
. The set of possible
strategy combinations is then given by S = S
1
× ··· ×
S
n
. The payoff for a player i ∈ N is given by the utility
function u
i
: S → R. The whole payoff vector for a
strategy combination s ∈ S is given by u : S → R
n
.
3.1 Nash Bargaining Solution
The Nash bargaining solution as introduced by Nash
(1950) satisfies the following axioms: pareto optimal-
ity, independece of irrelevant alternatives, symmetry,
and invariance to affine transformations. These ax-
ioms are said to characterize a fair solution of a bar-
gaining game. It can be shown, that for a bargaining
game as given in equation (1) the solution to the opti-
mization problem
max
u
n
∏
i=1
(u
i
− c
i
) (2)
s.t.: u ∈ P
u
i
≥ c
i
∀i ∈ N
satisfies these axioms. The objective function in equa-
tion (2) is called Nash product. Unlike for example
A Multi-agent Approach to Model and Analyze the Behavior of Vessels in the Maritime Domain
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