53
1 INTRODUCTION
A new weather ship routing service is being
developed in the framework of European research
projectIONIO
5
andItalianindustrialresearchproject
TESSA
6
. The service will assist the shipmaster in
taking decisions for a safe and efficient navigation.
TheinitialDecisionSupportSystem(DSS)outlinedin
this paper will make use of meteo‐marine and
oceanographic operational information data for all
relevant environmental field variables (wind, waves
and currents) at high spatial and ti
me resolution.
Furthermore, the DSS will provide web‐based real‐
timeinformation.
Academic research in the field of ship routing
developedseveraldifferentapproaches, andsomeof
themarebrieflyreviewedinthefollowing.
Takashima et.al. (2009) propose a method for
optimizing fuel consumption. It is based on a
5
http://www.ionioproject.eu/
6
http://tessa.linksmt.it/
Dijkstra’salgorithmforcomputingtheoptimalroute.
Thegridisbuiltstartingfromthestandardshiproute
and adding vertexes on lines perpendicular to the
standard route. The authors apply the method to
routesalongJapan’scoastusingmodelenvironmental
forcing with at least 6 miles resolution, and the
voyagedurationsareoftheorderofoneday.
In Wei & Zhou (2012) a dynamic progra
mming
method is used in which both ship speed and ship
course are control variables. They show that
accounting for voluntary ship speed modification
leads to extra fuel savings with respect to the
optimization with respect to ship course only. Their
grid is ma
de up of stages ofnodes perpendicular to
thegreatcircle.Thecasestudyisarouteclosetothe
Equatorwithvoyagelengthoftheorderof10days.
Szłapczynska & Smierzchalski (2009) perform a
multicriteria weather routing optimization with
respecttovoyageti
me,fuelconsumption,andvoyage
risk. Their method is based on an evolutionary
algorithm. The authors also develope a method of
ranking of routes based on the decision‐maker’s
preferences.TheyapplyittoanAtlanticroute.
A Prototype of Ship Routing Decision Support System
for an Operational Oceanographic Service
G.Mannarini&G.Coppini
CentroEuro‐MediterraneosuiCambiamentiClimatici,Lecce,Italy
P.Oddo
IstitutoNazionalediGeofisicaeVulcanologia,Bologna,Italy
N.Pinardi
UniversitàdegliStudidiBologna,Bologna,Italy
ABSTRACT: A prototype for an operational ship routing Decision Support System using ti
me‐dependent
meteo‐oceanographic fields is presented. The control variable is ship course, which is modified using a
directional resolution of less than 27 degrees. The shortest path is recovered using a modified Dijkstra’s
algorithm.Safetyrestrictions foravoidingsurfridingandpa
rametricrollingaccordingtotheguidelinesofthe
International Maritime Organization (IMO) are implemented. Numerical experiments tailored on a medium‐
sizevesselarepresentedandperspectivesofdevelopmentofthesystemareoutlined.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 7
Number 1
March 2013
DOI:10.12716/1001.07.01.06
54
Montes (2005) provides a detailed documentation
of Optimum Track Ship Routing (OTSR), an
automation of the weather ship routing service
providedbytheUSnavy.Therouteisretrievedbya
binary heap version of Dijkstra’s algorithm. The
system employs model fields with ½ degree spatial
resolution for both wind
and waves in the Western
Pacific Ocean. The safety is taken into account by
restricting navigation to grid points where
windspeedand wave height are within ship’s
predefinedlimits.
FortheDSS under developmentthefocus will be
on the Mediterranean Sea, where an operational
distribution of oceanographic fields
is already
running
7
(Pinardi & Coppini 2010) and subregional
models with high spatial temporal resolution are
under development in the framework ofIONIO and
TESSA projects. This willprovide a special focus on
Southern Italian seas, and in particular on their
coastalzone.TheprototypeDSSillustratedheretakes
into account the safety
restrictions from the most
recent technical guidelines for avoiding dangerous
situations on the ship. The prototype uses time‐
dependent environmental information for
computationoftheoptimalroutewithrespecttototal
navigation time. Route optimization with respect to
fuel consumption and other parameters is at the
planningstage.
The present paper
is organized into 4 sections,
which besides Introduction include a description of
thestructureoftheprototype(Sect.2),theapplication
oftheprototypetoseveralidealizedand yet realistic
situations(Sect.3),theconclusionsandabriefoutlook
offuturedevelopments(Sect.4).
2 PROTOTYPESTRUCTURE
In this section, the main features
of the prototype
systemapplicationaredescribed:thegridresolution,
the input fields, the ship response parametrization,
the constraints for navigational safety, and the
minimizationalgorithm.
2.1 Grid
The prototype DSS is based on a shortest path
algorithmonagraph.
Graphsaregridsforwhicheachgridpoint(“node”
or“vertex”)
isconnectedtoasubsetoftheremaining
nodes.Toeachconnection(“edge”or“link”)aweight
isassigned.Ifsuchweightdependsontheorientation
of the edge, the graph is said to be “directed”. The
objective of a shortest path algorithm is to find a
sequenceofedges
betweengivenstartandendnodes,
which lead to a minimum sum of the weights. If
chosenedgeweightisthetimeneededfornavigating
between edge nodes, then upon termination the
shortestpathalgorithmdeliverstheminimumvoyage
time.
7
http://gnoo.bo.ingv.it/myocean/
Model grid (i.e. the grid on which the meteo‐
oceanographic information is available) and graph
gridareingeneraldifferent.Sinceforthemomentwe
usesyntheticdataonly,wefindconvenienttoidentify
modelandgraphgrid.
A regular squared grid is constructed, with N
y
rows and N
x columns of nodes (see Table 1 for the
numericalvaluesoftheseandotherparameters).
In the work of Montes (2005), 8 edges and 8
directions per node are used, corresponding for the
northeasternquadrant oforiginnodeOto thenodes
marked with A and C in Figure 1.
This implies an
angularresolutionof45°.
Inourprototypeinstead,eachnodeisconnectedto
atotalof24edges,allowingfor16distinctdirections.
In Figure 1, points marked by A’, B’, C’, and D’
corresponds to the 4 possible directions in the
northeastern quadrant of origin node O.
Such an
organizationoftheedgesenablesreachinganangular
resolution
12givenby
o
6.26)2/1arctan(
12
(1)
Wedeemthatinanincreaseinangularresolution
iscomputationallymoreeffectivethananincreasein
grid resolution obtained by reduction of the
intermodal distance. Indeed, doubling the angular
resolution (
12 ~ 45°/2) increases the computational
cost by a factor of 3 (=24/8). Doubling the spatial
resolution instead would introduce a factor of 4
(=2^2).
Table1. Parameters of the spatial graph discretization and
inputfieldtimeresolutionemployedintheprototype.
_______________________________________________
Symbol NameValue Units
_______________________________________________
Nx=Ny Linearnumberofnodes 30‐
inthespatialgrid
D
x=Dy Spacingofthespatialgrid 4 Nautical
Miles(NM)
D
tTimeresolutionofinputfields 1 Hours
_______________________________________________
Figure1. Sample of the plot of graph edges (safegram). At
eachnode,theedgesaredisplayedasarrowspointingtothe
connected nodes. For clarity, the arrows do not reach the
nodetowhichtheypoint.Instead,theedgescorresponding
to all possible directions in the North‐Eastern quadrant of
the central node O are drawn as solid lines spanning the
whole internodal distance. Note that in the vicinity of the
graphborder,therearelessthan24edgespernode.
55
Coastline, islands and other types of obstructions
can be represented on the grid as polygonal chains,
termed “barriers” in the following. Edges containing
at least one node laying within or on a barrier are
removedfromthegraph.
2.2 Inputfields
Sea state fields taken into consideration are wave
height,
wave direction, and wave period. At the
presentstageof developmentof theprototype, these
fields are not yet model output but rather synthetic
fields, designed for an idealized testing of the
prototype.
WaveheightandwaveperiodfieldsareGaussian
shaped. Allowing peak position of these fields to
change
with a prescribed velocity generates time‐
dependentwaveheightandwaveperiodfields.Time
resolution D
t (Table 1) corresponds to the resolution
ofmeteo‐marinemodelfieldstobeusedinthefuture.
The field of wave direction instead is taken to be
homogeneousinspaceandconstantintime.
2.3 Shipresponseparametrization
The edge weight used is time dt required for
navigating between edge
nodes, given the
involuntary ship speed reduction due to meteo‐
oceanographicconditions.Thatis:
})({Mv
dx
dt
(2)
where dx is the edge length (Euclidean distance
betweennodes)andv({M})istheinvoluntaryreduced
ship speed due to a set {M} of meteo‐oceanographic
inputfields.
For the moment, the effect of wave height and
wave direction only is taken into account. Also,
voluntary speed reduction is
not yet implemented.
Themotorboatresponseisparameterizedas
2
0
)(),(})({ HfvHvMv
(3)
where H is the significant wave height and
is the
ship‐waverelativedirection.Equation3isafitofdata
displayedin Fig.3703 of Bowditch (2002).Thevalues
ofcoefficientfarereportedinTable2.
Table2.ValuesofcoefficientfinEquation3.
_______________________________________________
Configurationnamef[kn/ft
2
]
_______________________________________________
0°≤≤45°Followingseas.0083
45°<<135°Beamseas.0165
135°≤≤180° Headseas.0248
_______________________________________________
Bytakingintoaccounttheaddedresistancedueto
the environmental conditions and the ship response
operator,amorerealisticmodelization of shipspeed
is possible, see e.g. Padhy (2008) and Lloyd (1998).
However, such a detail is beyond the purpose of
presentpaper.
We note that, according to Equation 3,
edge ship
velocityand,consequently,edgeweightdependsnot
only on position on the graph but also on direction.
Thus,wehaveadirectedgraph.
2.4 Safetyrestrictions
The prototype takes into account some safety
restrictionscorrespondingtotherecommendationsof
the International Maritime Organization (IMO) for
avoiding dangerous situations
in adverse weather
and sea conditions (IMO circular no. 1228). Angle
being the ship‐to‐wave relative direction (=180
o
for
followingseas),withintheprototypeitischeckedfor:
Surf‐riding and broaching‐to (shortly termed
“surfriding” in this paper). It occurs when both
conditionsarefulfilled:
135
o
225
o
(4.1)
1.8
cos(180 - )
ship
ship
o
L
v
(4.2)
Parametricrollingmotions.Itoccurswhenoneof
thefollowingconditionsisfulfilled:
|-|
E
RR
TT T
(5.1)
|2 - |
E
RR
TT T
(5.2)
where the encountered wave frequency 1/TE is
Doppler shifted with respect to wave frequency
1/Tw,as
)cos(3
3
2
shw
w
E
vT
T
T
(6)
and
is the relative tolerance in frequency
matching.
Equation6holdswhenwaveperiodsT
EandTware
expressedinsecondsandspeedv
shinknots.
In the case that navigation along a given edge
leads to a potentially unsafe situation, that edge is
removed from the graph. For this reason, we call
“safegram” every plot like the one displayed in
Figure1.
2.5 Algorithm
Once the grid and the input fields are correctly
prepared, the barrier configuration set up, the ship
response provided, and the safety restrictions taken
into account, a shortest path algorithm is run to
compute the optimal route. A Matlab®
implementation of Dijkstra’s algorithm by Joseph
Kirk
8
is used. The edge weight is computed using
8
http://www.mathworks.com/matlabcentral/fileexchange/12850‐
dijkstras‐shortest‐path‐algorithm
56
Equation 2 by evaluating ship velocity through
Equation 3 and field values H,
at the geometrical
meanpointbetweenedgenodes.
Kirk’s routine has been modified in order to
recover the shortest path even in presence of time‐
varying fields. In this case indeed, edge weight is a
functionoftime.Inthemodifiedroutine,edgeweight
is evaluated at the time step closest to ship ti
me of
arrivalatthefirstnodeofeachedge.
3 RESULTS
Preliminary results obtained using artificial
configurations of barriers and synthetic meteo‐
oceanographicfieldsarepresented.
First,theshortestpathintheabsenceofanyinput
fields is investigated (Section 3.1) and the
convergence to the analytical solution is discussed.
Then,theeffectofsafetyrestrictionsaccordingtoIMO
(IMO circular no. 1228) in the ab
sence of barriers is
presented(Section3.2).Finally,thecombinedeffectof
barriersandsafety restrictions inpresence offorcing
fieldsiscomputed(Section3.3).
3.1 Convergencetestintheabsenceofforcing
First,wecheck theroleofspace discret
izationin the
computationoftheshortestpath.
Figure2. Routes in presence of a barrier (rectangle). Solid
lines correspond to the analytical solution, while dots
indicatethe routes recovered by the algorithm. The panels
correspond to different number of edges per node:
Respectively4,8,16,24forpanelsa),b),c),d).
We prepare the graph by including a box‐shaped
barrier and setting to zero all meteo‐oceanographic
forcingfields(Figure2.a‐d).Forthisconfiguration,it
is straightforward to find the analytic shortest path.
Indeed,it is a polygonal chain which comes as close
aspossibletothebarrier(solidlinesinFigure2.a‐d).
Thisimplies tha
ttheangles formed bytheanalytical
solutionwithrespecttothe“meridians”aregivenby
arctan(14/24)and arctan(15/4),see Figure2a.Neither
of these angles is permitted by the existing graph
edges, as shown by Figure 1. The analytical solution
indeed is retrieved when each node is linked to all
other nodes (complete graph). Within our graph
however, (like in every sparse graph) each node is
connected to a few nodes only. In Figure 2.a‐d we
display the results of the shortest route computation
(dot
s)for varioustypes ofgraphs, depending on the
number of edges per node. It is seen tha
t, as the
number of edges per nodes increases, the computed
routesgetcloserandclosertotheanalyticsolution.
Figure3summarizestheresultsbycomparingthe
lengthsof theshortest pathsin Figure 2.a‐d with the
length of the analytic solution. The 24 edges case
proposed in thi
s work agrees with the analytic
solutionwithin1.5%,improvingbyafactorof5with
respectto the route obtained using the method used
e.g.inMontes(2005).
Figure3. Route lengths for the configurations of Figure 2.
Thedotscorrespondtotheroutelengthsinpanels(a,b,c,d),
whilethesolidlineistheanalyticalsolution.
3.2 Effectofsafetyrestrictionsintheabsenceofbarriers
A domain free of any barriers, in which time‐
dependent sea‐state fields are switched on, is now
considered.Alongallfollowingsimulationswestrive
to use realistic combinations of parameters for both
weatherandshipmodelization.
Somesnapshotsoftheti
meevolutionofsignificant
wave height and wave period field for parameter
valuesgiveninTable3aredisplayedinFigure4.
Figure4. Synthetic significant wave height fields for the
surfridingexperiments(a‐b)andwaveperiodfieldsforthe
parametric rolling experiments (c‐d). For each field,
snapshotsatthetimestepscorrespondingto1hand2hafter
shipstartareshown.Initialpositionsy
0aredifferentinthe
twoexperiments.
57
Since sea‐state model outputs indicate that wave
heightand wave period fieldsarehighlycorrelated
9
,
Gaussiansyntheticwaveperiodfieldswiththesame
peak position of wave height fields are synthetized.
However, different peak initialpositions y
0 are used
inthesurfridingandparametricrolling experiments.
Wavevelocity(knots)isestimated inthedeepwater
approximation,leadingtov
W=3TW(s),whenthefields
are expressed in the units given between brackets.
Wave direction is always towards the South in our
experiments.
Table3. Weather fields parameters. Values corresponding
respectively to the surfriding and parametric‐rolling
experiments are separated by a semicolon. Wave period
parametersarenotusedinthesurfridingexperiments.
_______________________________________________
ParameternameSymbol Values Units
_______________________________________________
Peaksignificantwaveheight Hmax 10;10 ft
Standarddeviationofsignificant
H 20;20 NM
waveheight
PeakwaveperiodT
w ‐;10 s
StandarddeviationofWavepeak
T‐;64 NM
period
Wavevelocity V
w 30;30 kn
Initial(t=0h)peakpositiony
0 34;26 grid‐
units
_______________________________________________
Used ship parameters are reported in Table4.
They are chosen in order to mimic a medium size
passengervessel(Ro/
Pax).
Furthermore, the side of the simulation domain,
(N
x‐1)Dx=116NM, is intherangeoftypicaldistances
forItaly‐GreeceorItaly‐Albaniaferryboatroutes.
Table4.Shipparameters.Valuescorrespondingrespectively
to the surfriding and parametric‐rolling experiments are
separatedbyasemicolon.
_______________________________________________
ParameternameSymbol Values Units
_______________________________________________
Cruisespeedv0 19;18 kn
Length L
ship 100;100 m
NaturalrollingperiodT
R‐;20 s
Toleranceinperiodmatching ‐;10% ‐
_______________________________________________
Figure5. Zoom on the safegram for preventing surfriding
andbroaching‐toattimestep2haftershipstart.Thepeakof
thewavefieldislocatedinthevicinityofnode(15,15).
9
SeeforinstanceMFSproductsathttp://www.sea‐
conditions.com/en/
First, we present an experiment set for avoiding
surfriding.InFigure5itisshownthat,forthechosen
parameters, accounting for this safety restriction
implies avoiding southbound motion. This is due to
the fact that the threshold velocity for dangerous
motionislowestforaconfigurationoffollowingseas
(=180
o
in Inequality 4.1). The corresponding IMO
guideline, Inequality 4.2, does not prescribe a
minimum wave height for surfriding to occur, thus,
for the chosen ship length L
ship and cruise speed v0,
such a forbidden southbound motion applies to the
wholedomain.
Figure6.Routespreventingsurfridingforashipleavinga)
fromtheNorth–navigationtime:7h 03’‐andb)fromthe
South –navigation time: 6h 10’‐in presence of waves going
southwards (dots: safe routes, dashed line: geometrically
shortestpaths).
Theconsequencesofthisstructureofthesafegram
areshowninFigure6,whichshowsthetime‐shortest
routesavoidingsurfriding,inpresenceoftheforcing
due to a wave field moving southwards. In the left
(right)panel,asouthbound(northbound)shipmotion
is considered. The southbound motion implies a 32
NM westward diversion, leading to a “knee” in the
route.Theshipgetsatthenodecorrespondingtothe
kneea
pproximatelyby thetime (+4h) the wave field
reaches the southern border of the domain. Instead,
the northbound voyage is not affected by the safety
restrictionand,fromthegeometricalpointofview,it
isidenticaltothestraight‐linebetweenstartandend
point.However,thenavigationti
meinthelattercase
is about 4 minutes longer than the no‐weather time
(6h 06’). This delay roughly corresponds to the time
theshipneedsfortraversingthewavefieldwithhigh
relativevelocity(v
0+Vw=49kn).
Figure7. Zoom on the safegram for preventing parametric
rollingattimestep2haftershipstart.WaveperiodT
Watthe
nodessouthwesternofthedashedcurveislargerorequalto
9s.
58
As a second realistic experiment, we set the
prototypeforsimulatingarouteavoidingparametric
rolling. In Figure 7 it is shown that, for the chosen
parameters, accounting for this safety restriction
impliesthatseveraldirectionsareforbiddenwhenthe
ship is in the vicinity of the wave field. They
are
=90
o
and
=180
o
12.
Indeed, for a route at constant latitude, in the
presentexperiment,thewavefrontismetat90degree
(beamseas),thusaccordingtoEquation6thereisno
Doppler’sshift.Asaconsequence,theEquation5.2is
fulfilled whenever 2T
W=TR, within the prescribed
tolerance
. For the actual parameters, this implies
that this condition is fulfilled wherever T
W=9 s or
larger.
Furthermore, the T
E=TRcondition (Equation 5.1)is
fulfilledfor
=180
o
‐
12andvshintherange15‐17knots
which,duetotheinvoluntaryshipspeedreduction,is
alsorealizedwithinthegraphregionwhereT
W=9sor
larger.
Figure8. Routes preventing parametric rolling for a ship
leavinga) from theNorth–navigation time: 6h 33’‐ andb)
fromtheWest–navigationtime:6h41‐inpresenceofwaves
going southwards (dots: safe routes, dashed line:
geometricallyshortestpaths).
Theconsequenceofthisstructureofthe safegram
areshowninFigure8,whichshowsthefastestroutes
avoidingparametricrolling,inpresenceoftheforcing
due to a wave field moving southwards. The
southbound route (left panel) is the straight‐line
between start and end node. The eastbound route
(right
panel) isaffectedbythestormbeginningfrom
the time the ship gets within the envelope of the
T
W>9s area. Since eastbound motion would lead to
parametricrolling,atthattimestepthecomputedsafe
route diverts northwards by 8 NM. The diversion
leads the ship into a safe region, where parametric
rolling is inhibited for all subsequent time steps
thanks to the fact that the wavefront moves
southwards.
Finally, we investigate a situation in which both
environmental forcing and barriers are present.
Figure 9 shows a domain with 3 “islands”, set in a
way that the narrow channel between the lower 2
islandsdoesnotallowapassagewithananglelarger
than arctan(1/3) with respect to
the meridians. We
notethatsuchanangleissmallerthan
12definedby
Equation 1. Thus, just strictly northbound or
southbound ship motions are allowed within the
channel.However,theexperimentisruncheckingfor
thesurfridingcondition.Aswehavealreadyseenin
Figure 5, this rules out exactly southbound motions.
Thus,nosaferoutecanpassthroughoutthechannel.
Since passing eastern of the southeastern island
would take an even longer time, the route begins as
westbound.Thus,werealizethat,asaconsequenceof
asafetyrestriction,fromtheverybeginningthe ship
routedivergesfromtheno‐weatherroute.
Figure9. Route preventing surfriding for a ship leaving
fromtheNorthinpresenceofwavesgoingsouthwardsand
several barriers (dots: safe route –navigation time: 8h 40’;
dashed line: geometrically shortest path –navigation time:
7h23’).
3.3 Shortestpathinpresenceofbothbarriersandsafety
restrictions.
Itisinterestingtoincreasegridresolutionandrepeat
the same experiment, as shown in Figure 10, where
D
x=Dy=2NM.Thedenserspatialgridnowallowsfor
amotionthroughthechannelwithanangle
12,which
is still compliant with the safety restriction. The
quality of the resulting route is completely different
with respect to the route on the grid with original
resolution(itsdurationisnearly1hshorter).
Figure10. Like Figure 9 but with doubled grid resolution
(dots: safe route –navigation time: 7h 42’; dashed line:
geometricallyshortestpath–navigationtime:7h18’).Inset:
zoom on the channel region, showing that the safe route
formsanangle
12withthemeridians.
Since grid resolution affects ship route, the
question arises how to set such a resolution. In our
opinion, it is probably not meaningful to increase
resolution besides any limit for the sakeof allowing
sudden course changes. Indeed, real ships have a
limited manoeuvrability, and a tight zig‐zag motion
might
be not always possible. Thus, thequestion on
59
gridresolutionshouldbeansweredinthecontextofa
moredetailedmodelizationofshipdynamics.
4 CONCLUSIONSANDOUTLOOK
Wehaverealizedaprototypeofanautomatizedship
routingsystem.Theprototypeisbasedonamodified
Dijkstra’salgorithmforadirectedgraph.Thegraphis
constructedusing24edgespernode,allowingforan
angular resolution of ab
out 27 degrees. The route
beingshortestintermsoftimeandsafeinthesenseof
IMO guidances (for preventing surfriding and
parametric rolling) is retrieved. The algorithm takes
into account time‐dependent environmental fields,
such as wave height and wave direction. The
prototype has been tested in idealized situations,
usinghoweverrealist
iccombinationsofdomain‐ship‐
weatherparameters.
According to the deliverables of the funding
projectsIONIOandTESSA,theprototypewillevolve
into a full DSS for an operational oceanographic
service. To this end, several developments of the
algorithmandtheuserint
erfaceareplanned. Among
nextsteps,wearegoingtoallowforintentionalspeed
reduction as a control variable. Also, route
optimization with respect to other parameters, in
particular fuel consumption, will be realized. The
ship‐weatherinteractionwillbemodelizedinamore
realisticway.Inparticular,alongwithsea‐statefields,
also sea currents andsea‐surface wind will be used.
Highspatial and tempora
lresolution model data for
meteorological and oceanographic fields will be
employed. Eventually, model data from the
Mediterranean Ocean Forecasting System (MFS)will
replacethesyntheticfields.
ACKNOWLEDGMENTS
Funding through EU‐project IONIO and It
alian
projectTESSAisgratefullyacknowledged.
REFERENCES
Bowditch, N. 2002. The American Practical Navigator‐an
epitome of navigation. National Imagery and Mapping
Agency.
International Maritime Organization 2007. Revised
guidance to the master for avoiding dangerous
situations in adverse weather and sea conditions, IMO
circularno.1228
Krata, P. & Szlapczynska, J. 2012 Weather Hazard
Avoidanceinmodeling safety of motor‐drivenship for
m
ulticriteriaweatherrouting.TransNavvol.6,n.1
Lloyd,A.R.J.M1998.Seakeeping–ShipBehaviourinRough
Weather.
Montes, A.A. 2005. Network shortest path application for
optimumtrackshiprouting.PhD‐Thesis,MontereyNaval
PostgraduateSchool.
Padhy, C. P. et. al. 2008. Application of wave model for
weatherroutingofshipsintheNorthIn
dianOcean.Nat.
Hazards44:373–385
Pinardi, N. and Coppini, G. 2010, Operational
oceanography in the Mediterranean Sea: the second
stageofdevelopment.OceanSci.,6,263‐267
Szłapczynska, J. & Smierzchalski, R. 2009. Multicriteria
optimizationinweatherrouting.TransNavvol.3,n.4
Takashima et. al. 2009. On the fuel saving operation for
coastalmerchantshipsus
ingweatherrouting.TransNav
vol.3,n.4
Wei, D. & Zhou, P. 2012. Development of a 3D Dynamic
Programming Method for Weather Routing. TransNav
vol.6,n.1
