455
1 INTRODUCTION
The latest reports from Ding et al. [10], Ehrgott et al.
[11, 14], and Odu et al. [40] on the use of multi-criteria
optimization show that they occur in various areas of
application: in medicine, agriculture, product and
production design, financing, and the design of
moving objects (vessels, cars, aircraft, and drones),
wherever you need to make optimal decisions in the
face of compromises between two or more conflicting
goals.
Thus, Balraj [2] presents the multi-criteria
optimization of a rotary electrical discharge
machining process. Cotton et al. [7] describe multi-
criteria optimization for mapping programs to multi-
processors. The use of multi-criteria optimization
methods in radiation therapy planning is proposed by
Craft [8]. Glavac et al. propose [16] the multi-criteria
optimization of a car structure using a finite-element
method. Another interesting application of multi-
criteria optimization in humanitarian aid is proposed
by Gutjahr et al. [17]. Hirsch et al. [19] present a multi-
criteria optimization approach to the design and
operation of a district heating supply system over its
life cycle. The application of multi-criteria analysis
methods for the determination of priorities in the
implementation of irrigation plans are described by
Karleusa et al. [21]. Maniowski [34] proposes the
multi-criteria optimization of chassis parameters of
Nissan 200 SX for drifting competitions. Multi-criteria
optimization and its application to earthwork
processes is presented by Paulovicova [41]. Sheikus et
al. [48] describe the static optimization of rectification
processes using mobile control actions. A multi-
criteria optimization technique for SSSC-based power
oscillation dumping controller design is proposed by
Swain et al. [53]. Tahvili [55] presents the multi-
criteria optimization of system integration testing.
Roy [47] describes a multi-criteria supporting
decision.
Compromise of Two-criteria Final Payoff of the Game
Ship Control in Collision Situations
J. Lisowski
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: The essence of the article is the use of multi-criteria static optimization of object motion, based on a
set of optimal Pareto points in the space of possible variants of solutions for a new approach to the problem as a
game control. Using the example of the two-criteria optimization of the final payoff of the object game control
during the safe evasion of the encountered objects, six methods of multi-criteria static optimization are
presented—Bentham's utilitarian rule, Rawls's principle of justice, Salukvadze's benchmark, Benson's weighted
sums, Haimes's constraints, and goal-oriented programming. In the end, the results obtained by the two-criteria
optimization are compared with regard to the values of the components of the final game payoff—the risk of
collision and the deviation of the object from the safe route of the set trajectory of movement. The directions for
the development of multi-criteria optimization methods, both static and dynamic, and the game are indicated.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 2
June 2021
DOI: 10.12716/1001.15.02.25
456
Analyses included in the literature [1, 8, 13, 38, 42,
43, 47, 52] show that multi-criteria optimization plays
an important practical role, e.g., maximizing profit
while minimizing production costs, maximizing
efficiency while reducing the fuel consumption of a
moving object, or reducing the weight of a device
while increasing the strength of its individual
components.
At the end of the eighteenth century, the English
philosopher and economist Jeremy Bentham [3]
formulated the following utilitarian principle: "The
greatest utility for the largest number of criteria". He
promoted the principle of utility as a standard for
proper action on the part of governments and
individuals. Actions are acceptable when they are
aimed at promoting happiness or pleasure, and
rejected when they tend to cause unhappiness or pain.
By combining these criteria, we are actively trying to
promote overall happiness.
The literature [9, 13, 23] shows that when
implementing these requirements, very often there are
contradictions, i.e., in a given space of decision
variables, individual criteria cannot simultaneously
achieve their extreme values, and their participation is
measured by a weight factor.
Among all technical objects, moving objects
constitute a significant amount, for which the method
of controlling their movement significantly affects
both the operating costs and the accuracy and safety
of the transport tasks. This applies to land, sea, and air
objects in terms of manned and unmanned facilities.
Remote sensing devices, such as radar, lidar, and
other highly specialized measurement solutions are
used to identify detection processes and control
moving objects. When planning and implementing the
motion control of objects, there are many possible
acceptable solutions, from which the best or optimal
solution should be selected.
Different static and dynamic optimization methods
can be used to find the optimal solution. Lazarowska
[27] presents a multi-criteria trajectory base path
planning algorithm for a moving object in a dynamic
environment as an intelligent control system.
Summarizing the literature review, in the scientific
studies conducted so far, the encountered moving
objects have been treated as a limitation of the process
state, and not as control objects [22, 25, 26, 28, 32, 33,
39, 51, 54, 57]. There is the possibility that active
control of the encountered objects leads to cooperative
or non-cooperative game control. In the work of [31],
a game control method comparison was made when
avoiding collisions with multiple objects using radar
remote sensing, ensuring the lowest final payoff of the
positional or matrix game, only in the form of the
amount of deviation of the safe route of the cruise
from the set trajectory.
The purpose of this article is to extend the
scientific analysis of the single-criteria optimization of
the final payoff to the two-criteria optimization of the
final payoff, consisting of both the final deviation
from the set trajectory and the final risk of collision. In
order to determine a compromise between these two
criteria, a comparative analysis of the six most
frequently used methods of multi-criteria static
optimization was performed.
The article presents an original scientific topic,
previously unpublished, assigned to the scientific
discipline - automation, electronics and electrical
engineering, concerning the synthesis of systems for
safe and optimal ship traffic control with the use of
artificial intelligence methods and game theory.
2 MULTI-CRITERIA STATIC OPTIMIZATION
TASK
Multi-criteria optimization is the most natural method
of inference, consisting of determining the optimal
solution and its acceptability from the point of view of
the adopted criteria. When implementing these
criteria, there are most often contradictions that, in a
given space of decision variables, individual criteria
cannot reach their extreme values at the same time.
Then, there is a need to find a compromise solution.
2.1 Control Quality Index
The synthesis of the optimal control of moving objects
is most often carried out as convex optimization, a
special class of mathematical optimization problems
that covers least squares and linear programming
problems, and can be solved numerically very
efficiently. According to Boyd and Vandenberghe [5],
a mathematical optimization problem has the
following form:
( )
minimize Fx
(1)
( )
subject to 0, 1,2,...,
s
g x s S=
(2)
( )
0; 1,2,...,
w
h x w W==
(3)
to describe the problem of finding an x that minimizes
F(x) among all x that satisfy conditions (2) and (3).
We call x
R
n
the optimization variable, and
function F: R
n
→
R is the objective function or cost
function. The inequalities gs(x) 0 are called
inequality constraints, and the corresponding
functions gs: R
n
→R are called the inequality constraint
functions. The equations hw(x)=0 are called the
equality constraints, and the functions hw: R
n
→
R are
the equality constraint functions. The set of points for
which the objective and all of the constraint functions
are defined is as follows:
11
SW
sw
sw
D domg dom h
==
=
(4)
which is called the domain of the optimization
problem (1). A point x
D is feasible if it satisfies the
constraints gs(x) 0, s = 1, …, S and hw(x)=0, w=1,…,
W. Problem (1) is said to be feasible if at least one
feasible point exists, and is infeasible otherwise. The
set of all feasible points is called the feasible set or the
constraint set.
The optimal value F* of problem (1) is defined as
follows:
( ) ( ) ( )
*
inf | 0, 1,..., , 0, 1,...,
sw
F F x g x s S h x w W= = = =
(5)
457
The task of multi-criteria optimization is to find
such a vector of decision variables, x, as shown in the
following equation:
12
[ , ,..., ,..., ]; 1,2,...,
iN
x x x x x i N== =
(6)
which optimizes the vector of the decision objective
function F as a control quality index:
( )
1
( ), 1,2,...,
C
cc
c
F x k F x c C
=
==
(7)
where kc is the weight factor for the Fc component of
the control objective function, taking into account
both its percentage share and the physical units of the
components themselves.
2.2 Pareto Optimal Front
The well-known 80/20 rule states that 80% of the
results come from only 20% of the causes, in other
words, more modest means can be achieved with less
effort. The development of this principle was made in
1897 by Italian economist Vilfred Pareto.
The definition of a set of optimal Pareto points in
the space of variants can be expressed as follows, "A
given variant is Pareto optimal if none of its grades
can be corrected without worsening at least one of the
others".
According to the considerations of Messac et al.
[37], the set of non-dominated solutions from the
entire permissible search space is called the optimal
set in the Pareto sense, and these solutions form the
so-called Pareto front. The solutions from this set are
not dominated by any others, so in this sense, they are
optimal solutions for the problem of multi-criteria
optimization.
Eshenauer et al. [12] show that as the non-Pareto
optimal variants can be improved for all criteria, the
introduction of the optimal Pareto concept reduced
the problem of finding a solution to a task with
multiple criteria for selecting a point from this set.
3 GAME CONTROL OF SHIP
As an example of a multi-criteria static optimization
task, one can consider the process of game control of
the ship in situations of passing many encountered
objects, which is illustrated in Figure 1.
Figure 1. Block diagram of the system for the game control
of the ship in collision situations: pr—reference trajectory;
p—real position of ship; ψr—reference course; α—rudder
deflection; z—disturbances (wave, wind, and sea current);
ψ—ship course; V—velocity of ship
Ship controlling their movement by means of
course and speed changes are characterized by the
mutual distance and bearing from the ARPA radar
remote sensing system, allowing for determining the
risk of collision. The task of two-criteria static
optimization of the ship safe trajectory is to look for
the minimum final payoff value of the control
objective function:
2
1 1 2 2 1 2 min
1
c f f
c
F F k F k F k r k d F
=
= = + = + =
(8)
where rf (%) is the final value of risk collision; df (m) is
the final deviation of ship safe determined route from
the set trajectory, shown in Figure 1; and k1 (%
-1
) and
k2 (m
-1
) are sought compromise values of solutions to
the static optimization problem.
According to the author of [31], the ship collision
risk is defined as a reference to two assessments of the
navigation situation, shown in Figure 2. The first
assessment contains the parameters Djmin and Tjmin of
the real situation of the proximity of the objects. The
second assessment concerns the same situation, but
the safety is determined by parameters Ds, Ts, and Dj.
Thus, this reference has three relative elements,
namely, Djmin/Ds, Tjmin/Ts, and Dj/Ds, all of which are
proposed to express the risk of collision, rj, as the
following mean square form of these three relative
elements:
0.5
2 2 2
min min
1 2 3
j j j
j
s s s
D T D
r
D T D
−
= + +
(9)
where ε1, ε2, and ε3 are the weighting factors,
depending on the visibility at sea and the intensity of
marine traffic.
Figure 2. Displaying the situation of passing ship with
encountered objects, in particular with the j-th object; ψ—
ship course; V—velocity of ship; ψj—j-th object course; Vj—
velocity of j-th object; Xr, Yr—ship reference coordinates;
pr—reference position of ship; Dj —distance to j-th object;
Nj—bearing to j-th object; Djmin—distance of the closest point
of approach; Tjmin—time to the closest point of approach;
Ds—a safe distance of approach
Figure 3 illustrates an example of set of acceptable
solutions of the task of safe control of the ship in a
458
situation of passing a larger number of encountered
objects as a task of two-criteria optimization of control
due to the risk of collision and deviation from the set
motion trajectory. The Pareto-optimal front shape is
shown as a set of non-dominated solutions to the
game control task due to the final payoff value of the
control objective function, which consists of the final
value of risk collision and the final deviation of the
ship safe determined route from the reference
trajectory.
Figure 3. Front Pareto multi-criteria optimization of the ship
game controlling while safe passing the encountered
objects: F1 = rf (%)—value of the final collision risk; F2 = df
(m)—value of the final deviation trajectory
4 MULTI-CRITERIA STATIC OPTIMIZATION
METHODS
Many practitioners [4, 15, 20, 24, 29, 30, 50] have
worked for many years to answer the question of
whether the optimal Pareto point is the best
optimization method.
The methods of solving this task can be
distinguished by the following: Bentham's
utilitarianism rules (UR), Rawls' principle of justice
principle (JP), Salukvadze reference point (RP),
Benson weighted sum (WS), Haimes ε-restrictions
(εR) and Goal programming (GP).
4.1 Bentham’s Utilitarianism Rule UR Method
The use of the J. Bentham [3] principle allows for
accepting the criterion of the sum of the partial Fc
criteria (Figure 4).
First, lines with a constant value of the sum of the
components of the objective function were drawn.
Then these lines were shifted in parallel in the
direction of decreasing the value of this sum of
components. The last line, tangent to the Pareto-
optimal front, marks the point of the UR of the two-
criteria optimality of the safe passing of the ship while
passing the encountered objects.
The coordinates of this point determine the values
of the weighting coefficients k1 and k2 of the
components of the final payoff value of the control
objective function. The location of the UR point in the
k1 and k2 coordinates system allowed to assess the
compromise of the quality of safe control of the ship
between the risk of collision and deviation from the
set cruise route, convertible into the costs of transport
operating and the time obligations of the shipowner.
Figure 4. The sum of partial criteria according to J. Bentham,
and the optimal solution Bentham's utilitarianism rule (UR)
on the Pareto front; weighting values of optimal game final
payoff: k1=13.9 %
-1
, k2=0.007 m
-1
The sum of partial criteria according to J. Bentham,
and optimal solution Bentham's utilitarianism rule
(UR) on Pareto front; weighting values of optimal
game final payoff: k1=13.9 %
-1
, k2=0.007 m
-1
.
Figure 5. Optimal ship trajectory while safely passing 19
encountered objects for the Bentham's utilitarianism rule UR
method multi-criteria optimization of the final payoff value
of the control objective function: rf = 24 %; df = 150 m;
min
334.65
UR
F =
—minimum value of objective function (8)
459
4.2 Rawls' Principle of Justice JP Method
In 1971, American philosopher John Rawls formulated
[44] the following principle of justice, "Least usability,
as big as it can". In his theory, Rawls refers to the
principle of "Justice as Fairness"—the distribution of
goods is justice (just) if it is impartial (fair), i.e., if it
offers everyone the same opportunities. Figure 6
presents the principle of max-minimization of J.
Rawls.
Figure 6. The max-minimization of partial criteria according
to J. Rawls, and the optimal solution on the Pareto front;
weighting values of optimal game final payoff: k1=5.0 %
-1
,
k
2
=0.052 m
-1
The position of the optimal point on the Pareto-
optimal front results from the condition of the
minimum value of the logical sum of the components
of the control objective functions.
Figure 7 shows the results of a computer
simulation of the optimal controlling own object while
passing 19 encountered objects, using the Rawls'
principle of justice JP method on the Pareto front.
Figure 7. Optimal ship trajectory while safely passing 19
encountered objects for the Bentham's utilitarianism rule JP
method multi-criteria optimization of the final payoff value
of the control objective function: rf = 9 %; d
f
= 1037
m;
min
98.91
JP
F =
—minimum value of two-criteria objective
function (8)
The appointment of a fair solution, according to J.
Rawls, is a more difficult issue than finding a solution
when using the aggregate criterion for choosing a
weighted sum.
4.3 Salukvadze Reference Point RP Method
In 1971, the Georgian automatist Mindia E.
Salukvadze [48] proposed an approach based on the
concept of a reference point, namely, "In the Pareto
collection, the nearest point in relation to the reference
point is sought", presented by Stadler [49]. The Pareto
collection looks for the nearest point in relation to the
reference point.
Salukvadze proposed the intersection point
tangent as a point of reference to the set of acceptable
solutions (Figure 8).
Figure 8. An approach using a reference point, according to
M. E. Salukvadze, and an optimal solution on the Pareto
front; weighting values of optimal game final payoff: k1=5.1,
k2=0.05
The Salukvadze reference point method was
developed by Wierzbicki [58, 59], who developed the
mathematical foundations of reference point methods
based on the conical separation of sets.
Figure 9 shows the results of a computer
simulation of the optimal controlling the ship while
passing 19 encountered objects, using the Salukvadze
reference point RP method on the Pareto front.
460
Figure 9. Optimal ship trajectory while safely passing 19
encountered objects for the Salukvadze reference point RP
method multi-criteria optimization of the final payoff value
of the control objective function: rf = 12 %; df = 1000
m;
min
111.21
RP
F =
—minimum value of the two-criteria
objective function (8)
4.4 Benson Weighted Sum WS Method
In the method of the American computer scientist
Harrold Phillip Benson, described in 1988, the metric
is used to measure the distance of the tested solution
from an ideal solution that meets all of the criteria. In
the literature [35, 36, 46], it is shown that minimizing
the distance between the ideal solution and the tested
solution allows for finding to the best solution
belonging to the set of acceptable solutions.
The initial solution is randomly selected from
among the acceptable solutions to the problem.
The graphical interpretation of this method is the
search for a tangent to the permissible set, inclined at
an angle determined by the weight coefficients w (w1
and w2). The vector W, formed from the w coefficients,
is perpendicular to the tangent sought, and the
solution is the common points of the set edge and
tangent.
This method, with a correctly drawn starting point,
can find the optimal Pareto solutions, even for non-
convex decision spaces. One of the disadvantages of
this solution is the non-differentiable purpose
function. In this case, you cannot use gradient-based
methods to solve this problem (Figure 10).
The advantage of this method is the ability to find
all Pareto optimal solutions when determining the
abstract ideal (abstract) solution. The disadvantage of
this method is the need to normalize the objective
function, which is not always an easy task. In
addition, an ideal solution should be determined,
which requires the optimization of each criterion
separately. Using this method as the a'priori method,
the task of the decision-maker is to provide an ideal
point, which, in many cases, can be determined
intuitively, based on knowledge of the decision
problem.
Figure 10. The Benson weighted sum method and the
optimal solution on the Pareto front; weighting values of
optimal game final payoff: k1=7.9, k2=0.03
Figure 11 shows the results of a computer
simulation of the optimal controlling the ship while
passing 19 encountered objects, using the Benson
weighted sum WS method on the Pareto front.
Figure 11. Optimal ship trajectory while safely passing 19
encountered objects for the Benson weighted sum WS
method multi-criteria optimization of the final payoff value
of the control objective function: rf = 17 %; df = 593 m;
min
149.69
WS
F =
—minimum value of the two-criteria objective
function (8)
4.5 Haimes ε-Restrictions εR Method
The method developed by Yacov Y. Haimes [18] in
1971 consists of selecting one of the criterion functions
as a function of the goal and creating constraints from
the other criteria functions. The most important
criterion to be optimized is selected, assuming that the
values of the other criteria meet the minimum
assumed requirements (Figure 12).
461
Figure 12. The Himes method of ε-restriction and optimal
solution on the Pareto front; weighting values of optimal
game final payoff: k1=2.53, k2=0.128
Figure 13 shows the results of a computer
simulation of the optimal controlling the ship while
passing 19 encountered objects, using the Haimes ε-
restrictions εR method on the Pareto front.
Figure 13. Optimal ship trajectory while safely passing 19
encountered objects for the Haimes ε-restrictions εR method
multi-criteria optimization of the final payoff value of the
control objective function: rf = 3 %; df = 2481 m;
min
325.16
R
F
=
—minimum value of the two-criteria objective
function (8)
The advantages of this method are finding
different optimal Pareto solutions using different
values for the ε parameter. The main advantage of this
approach over the weighted sum method is the ability
to find a solution belonging to the set of Pareto-
optimal solutions when the problem space is both
convex and concave. However, the disadvantage of
such a solution is the significant dependence of the
result on the selected parameter ε and the original
optimization function. In some cases, the wrong
choice of parameters for this method may not find any
solution or may give the entire searched domain as a
solution. However, the most important problem of
this method is the fact that in reality, a simple one-
criterion problem is solved on the basis of only one
parameter, after the prior elimination of solutions that
do not meet the ε criterion.
4.6 Goal Programming GP Method
The goal programming method [6] consists of
replacing a multi-criteria task with the following task:
min min
()
x
K K K
F
F x w c
=
−
(10)
where (c1, c2, ..., cK) represent the coordinates of the C
point defining the purpose of the search, and (w1, w2,
..., wK) are the coordinates of the vector W, defining
the direction of the search.
Then, according to the authors of [45, 56], the task
is reduced to searching for the C point from the set of
acceptable solutions, in which the values of the
criteria are closest to some of the ideal values
determined by the coordinates (c1, c2, ..., cK).
The optimal search is carried out in the criterion
space, starting from point C in the direction
determined by vector W. The solution is a rectangular
point with sides parallel to the system axis, a lower
left corner at point C, and a diagonal parallel to the
vector W (Figure 14).
Figure 14. The method of goal programming and the
optimal solution on the Pareto front; weighting values of
optimal game final payoff: k1=3.52, k2=0.075
The coordinate values of point C (c1 and c2) come
from the person making the arbitrary decision. The
choice of vector components W (w1 and w2)
determines the importance of the individual
optimization criteria.
Figure 15 shows the results of a computer
simulation of the optimal controlling the ship while
passing 19 encountered objects, using the goal
programming GP method on the Pareto front.
462
Figure 15. Optimal ship trajectory while safely passing 19
encountered objects for the goal programming GP method
multi-criteria optimization of the final payoff value of the
control objective function: rf = 7 %;
min
132.94
GP
F =
—
minimum value of the two-criteria objective function (8)
5 COMPARISON OF METHODS
Figure 16 shows a comparison of the multi-criteria
optimization methods of the object traffic control
process at the reference trajectory.
In the case of safe control of an object in collision
situations, the most optimal compromise solution for
two-criteria optimization tasks is the Rawls principle
of justice (JP) method, i.e., controlling the movement
of the ship, ensuring both a small final deviation in
the cruise route and a small final risk of collision,
providing the smallest value of the control objective
function. But in other tasks of multi-criteria optimal
control, depending on the shape of the Pareto-optimal
front, there may be another better method, among the
six presented in the article.
The most extreme optimal solutions to this
problem are provided by the Haimes ε-restrictions
(εR) and Bentham utilitarianism rule (UR) methods.
The Haimes ε-restrictions (εR) and goal
programming (GP) methods provide the lowest final
risk of collision, but with a large final cruise route
deviation. The weighted sum (WS) and utilitarianism
(UR) methods provide the highest final collision risk
within the allowable range, but with the smallest
deviation from the prescribed voyage route.
The degree of cooperation in the anti-collision
maneuvers between objects has a significant impact on
the value of the final optimal solution.
Figure 16. Comparison of multi-criteria optimization
methods of the ship game control process in collision
situations: εR—ε-restrictions; GP—goal programming; RP—
reference point; JP—justice principle; WS—weighted sum;
UR—utilitarianism rule; F1 = rf—the final collision risk; F2 =
df—the final deviation trajectory; Fmin—minimum value of
the two-criteria objective function (8)
6 CONCLUSIONS
The methods of static multi-criteria optimization
presented here constitute the most described part of
all of the multi-criterial optimization methods. The
differences in the value of the determined optimum
are the most dependent on the shape of the Pareto
front of the specific optimization task.
Commonly accepted solutions for multi-criteria
optimization tasks are sets bringing the front of Pareto
optimal solutions closer. The basis for building
approximate collections is the relation of domination
in the sense of Pareto. It allows for introducing a
partial order in the set of assessments of acceptable
solutions and for selecting from the non-dominant
solution assessments in order to build approximate
sets. The size of the approximate set is not specified
and, in practice, contains many assessments of
equivalent solutions, without objective possibilities to
indicate the best solution or the best solutions in the
approximate set.
The relation of the dominance of solution
assessments can be extended to approximate sets and
can be used to determine the relation of the
preferences of approximate sets, and thus to the
preliminary assessment of the quality of approximate
sets or the effectiveness of the optimizers that were
used to obtain these sets.
In summary, traditional multi-criteria optimization
methods are still very popular. This is because they
give good results when finding potential solutions for
a small number of solutions in the sense of Pareto, and
also because knowledge about them and the
availability of materials is currently widespread.
Nevertheless, these methods are not without flaws.
For a small amount of the optimal sets they do quite
well, however, a larger set causes a significant
463
increase in the cost of calculations. This is because,
usually, traditional methods need to be run several
times to determine the optimal Pareto set. In addition,
some techniques, such as the weighted criteria
method, are sensitive to the shape of the Pareto-
optimal front.
Despite the constant popularity presented in the
article traditional multi-criteria optimization methods,
in many problems, evolutionary algorithms are
increasingly becoming their alternative. This is
because they are better at dealing with a potentially
large number of solutions in the Pareto sense.
This review of methods does not exhaust all of the
issues related to multi-criteria optimization, especially
regarding moving objects—land, air, and sea—in
terms of manned and unmanned vehicles.
Future works could also consider methods of
multi-criteria dynamic optimization. Particular
attention should also be paid to the multi-criteria
optimization of differential games problems related to
the motion control of many moving objects.
ACKNOWLEDGMENT
This research was funded by a research project of the
Gdynia Maritime University in Poland, no. WE/2020/PZ/02,
“Methods of static and dynamic optimization of ship
movement control”.
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