International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 6
Number 1
March 2012
Weather routing methods and tools deal with a prob-
lem of finding the most suitable vessel route. During
the route optimization process they take into account
changeable weather conditions and navigational
constraints. Such a problem is mostly considered for
ocean going ships where adverse weather conditions
may impact both, often contradictory, economic and
security aspects of voyage. Most of recent scientific
researches in weather routing focus on shortening
the passage time or minimization of fuel consump-
tion alone.
One of the first weather routing approaches was a
minimum time route planning based on weather
forecasted data. Proposed by R.W. James (James
1957) an isochrone method, where recursively de-
fined time-fronts are geometrically determined, was
in wide use through decades. In late seventies based
on the original isochrone method the first computer
aided weather routing tools were developed. Numer-
ous improvements to the method were proposed
since early eighties, with (Hagiwara 1989, Spaans
1986, Wisniewski 1991) among others. Nonetheless,
even the improved method has recently been dis-
placed by genetic algorithms.
Evolutionary approach as a natural successor of
genetic approach has become popular in the last two
decades and has been successfully applied to anti-
collision maneuver modeling. Modern weather rout-
ing tools often utilize evolutionary algorithms
(Wisniewski et al. 2005) instead of the deprecated
isochrone time-fronts. Due to multiobjective nature
of weather routing the multicriteria versions of evo-
lutionary algorithms have been also recently applied
to the ship routing problem (Marie et al. 2009,
Szlapczynska et al. 2009)
One of the authors has already proposed a mul-
ticriteria weather routing algorithm - MEWRA
(Szlapczynska et al. 2009) designed especially for a
ship with hybrid propulsion. In this paper an adjust-
ed for a motor-driven ship and revised version of the
algorithm is presented. One of the key amendments
is related with modeling the safety measure. Here a
new measure, based on reducing the impact of
weather hazards on ship is proposed. The new ap-
proach towards modeling of ship safety is based on
dynamical phenomena taking place while sailing in
rough sea. As the ship behavior is strongly nonlinear
and difficult for exact prediction (Landrini 2006) a
sort of generalization is used. The proposed method
is based on the IMO Circ. 1228, concisely compris-
ing significant hazards resulting from complex inter-
actions of ship’s hull and waves, especially follow-
ing and quartering seas.
Weather Hazard Avoidance in Modeling Safety
of Motor-Driven Ship for Multicriteria Weather
P. Krata & J. Szlapczynska
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: Weather routing methods find the most suitable ocean’s route for a vessel, taking into account
changeable weather conditions and navigational constraints. In the multicriteria approach based on the evolu-
tionary SPEA algorithm one is able to consider a few constrained criteria simultaneously. The approach ap-
plied for a ship with hybrid propulsions has already been presented by one of the authors on previous Trans-
Nav’2009. This time a motor-driven version of the solution is presented. The paper is focused especially on a
proposal of ship safety measure, based on restricting the impact of weather hazards on the ship. Besides the
weather conditions and navigational restraint the safety of a vessel is one of more important factors to be con-
sidered. The new approach towards a safety factor modeling is described and implemented.
The paper is organized as follows: section 2 re-
calls the optimization model and key technical back-
ground of original MEWRA algorithm for a hybrid
propulsion ship. Section 3 describes the amendments
required to suit MEWRA to motor-driven ship mod-
el. Section 4 addresses ship stability and seakeeping
performance as optimization factors. Then again in
section 5 the new measure of safety for MEWRA is
introduced. Finally, section 6 summarizes the mate-
rial presented.
The following subsections recall the optimization
model and the general framework of the Multicrite-
ria Evolutionary Weather Routing Algorithm -
MEWRA (Szlapczynska et al. 2009) designed for a
ship with hybrid propulsion.
2.1 Optimization model
A proposed set of goal functions in the weather
routing optimization process is presented below:
(1) (1)
– [h] passage time for given route and ship model,
[t] total fuel consumption for given route and
ship model,
– [-] safety coefficient for given route and
ship model. It is defined as a value ranging [0;1], de-
scribing a level to which the route is safe to be
passed. “0” depicts totally impassable route and “1”
absolutely safe route.
Exact formulas for goal functions (1) (3)
strongly depend on the assumed ship model. Thus,
the explicit formulas for a ship model with hy-
brid-propulsion can be found in (Szlapczynska et al.
Set of constraints in the considered optimization
problem includes the following elements:
landmasses (land, islands) on given route,
predefined minimum acceptable level of safety
coefficient for given route,
shallow waters on given route (defined as waters
too shallow for given draught of ship model),
floating ice bergs expected on given route during
assumed ship’s passage,
tropical cyclones expected on given route during
assumed ship’s passage.
2.2 Mutlicriteria Evolutionary Weather Routing
Algorithm (MEWRA)
The Multicriteria Weather Routing Algorithm
(MEWRA), presented in Figure 1, searches for an
optimal route (according to goal functions (1) (3))
for the assumed ship model. The input data for the
algorithm are:
geographical coordinates of route’s origin & des-
weather forecasts (wind, wave and ice) for con-
sidered ocean area and time period of the voyage
being planned.
Figure 1. Multicriteria Evolutionary Weather Routing Algo-
rithm (MEWRA)
The algorithm starts with a generation of initial
population i.e. a diversified set of routes including
the outermost elements of the searching space (Fig-
ure 2). The modified isochrone method (Hagiwara
1989) with extensions described in (Szlapczynska et
al. 2007) is a source of single-criterion time-optimal
and fuel-optimal routes. The routes are then a base
for random generation of initial population. Also the
original routes are included in the population.
In the next step SPEA algorithm iteratively pro-
ceeds the evolution on the initial population towards
achieving Pareto-optimal set of routes. Once the
evolution cannot improve on the Pareto set anymore
the first optimization procedure is stopped. Then,
from the set of Pareto-optimal routes (Figure 3) a
single route must be selected, becoming a route rec-
Yet another problem might be encountered: how
to decide which route should be recommended? To
solve this problem decision-maker’s (e.g. captain’s)
preferences to the given criteria set should be de-
fined. Hence a tool for sorting the Pareto-optimal set
is provided Fuzzy TOPSIS method. First the deci-
sion-maker has to set their preferences for given cri-
teria set. In MEWRA these preferences are ex-
pressed by means of linguistic values (Table 1) with
fuzzy sets assigned accordingly. The decision-maker
selects a linguistic value of the predefined set to
each of optimization criteria. Then the correspond-
ing fuzzy sets build a weight vector for the ranking
method. The last step of MEWRA Fuzzy TOPSIS
is responsible to apply given weight vector to the
decision matrix built of the goal function values of
the Pareto-optimal routes. The route having the
highest value of ranking automatically becomes then
a route recommendation (Figure 4). Exemplary
MEWRA results (Figures 2 4) have been obtained
for hybrid propulsion ship model, Miami-Lisbon
voyage on 2008-02-15 (departure time 12:00 pm)
and decision-maker preferences given in Table 2.
Table 1. Linguistic values and corresponding triangular fuzzy
values, utilized to express decision-maker’s preferences to the
criteria set
Linguistic value Triangular fuzzy set
(0.7; 1.0; 1.0)
(0.5; 0.7; 1.0)
quite important (0.2; 0.5; 0.8)
(0.0; 0.3; 0.5)
(0.0; 0.0; 0.0)
Figure 2. Initial population generated by MEWRA for Miami-
Lisboa voyage on 2008-02-15 (departure time 12:00 pm)
Figure 3. Pareto-optimal set of routes generated by MEWRA
for Miami-Lisbon voyage on 2008-02-15 (departure time 12:00
Table 2. Linguistic values assigned by a decision-maker to the
criteria set
Criterion name Linguistic value Triangular fuzzy set
Passage time Important (0.5; 0.7; 1.0)
Fuel consumption
quite important
(0.2; 0.5; 0.8)
Voyage safety
very important
(0.7; 1.0; 1.0)
Figure 4. Recommended route selected by MEWRA according
to the preferences given in Table 2 for Miami-Lisbon voyage
on 2008-02-15 (departure time 12:00 pm)
MEWRA application for the motor only propulsion
has been constructed based on its hybrid propulsion
predecessor. The key differences between applica-
tion versions for hybrid and motor driven ship model
are as follows.
1 The safety coefficient i
(utilized by goal func-
tion (3) and appropriate constraints) in case of the
hybrid propulsion model is based on wind speed
and heading only (assuming strict correlation be-
tween wind and wave conditions). In the motor-
driven model the coefficient has been redefined
as a percentage part of a route that is free from
disturbances caused by weather hazards. Howev-
er, regions with severe wave threat are still by-
passed by means of fulfilling a new constraint for
restricted course sectors. More details on both
these elements are given in the following sec-
2 Weather input forecasts for the motor-driven
model has been enlarged by wave period and
wave angle. Also MEWRA’s graphical user inter-
face (GUI) has been changed accordingly to al-
low displaying the new data on the screen.
3 In the hybrid propulsion case there is a possibility
to use one of the three propulsion modes, namely
“motor only”, “sails only” or “motor & sails”.
The “sails only” mode for a route segment re-
quires the engine to be temporarily switched off,
which in return may significantly decrease the
fuel consumption. In the motor-driven case there
is only one propulsion mode i.e. “motor only”,
which drastically limits possible fuel savings.
The most straightforward attitude towards ocean
voyage routing and route optimization is about to
find the shortest way from a point of origin to a des-
tination. However, getting rid of any other important
aspects of navigation seems to be too simple and in-
complete. Thus, a set of objectives has been imple-
mented in the MEWRA’s optimization model with
voyage safety as the most important element, with
the highest degree of significance as given in Table
2, of the goal function set Thus, it is required to
elaborate on safety of the vessel modeling.
The desirable course of ship exploitation requires
not only fast steaming of a vessel but also a lack of
ship and cargo damage. The analysis of historical
data regarding LOSA casualties reveals that their
causes may be attributed to interacting elements pre-
sented at the Venn diagram in Figure 5 (Kobyliński
Figure 5. Four-fold Venn diagram for ship stability system
(Kobylinski 2007a)
The interaction of all four groups of conditions
from Venn diagram can lead to stability accident of
a vessel and perturb a voyage. To avoid such a situa-
tion a set of stability standards are worked out. The
ship’s loading condition of insufficient stability may
induce a list, a strong heel and even a capsizing.
Vessels’ stability calculation and evaluation, per-
formed on-board nowadays, is based on the stability
criteria published by the ship’s classification socie-
ties. These criteria are mainly based on the A749(18)
Resolution of International Maritime Organization.
The resolution and their later amendments are
known as the Intact Stability Code.
The ship stability criteria are to ensure the rele-
vant level of safety against capsizing and strong
heel. The capsizing is not often occurring phenome-
non at the sea, although it cause considerable num-
ber of fatalities. The most significant feature influ-
encing the capsizing rate is the size of a vessel
(Krata 2007). Generally the smaller is the vessel, the
bigger is the risk of capsizing. This is due to the
scalability in vessel stability. It depends on the
square-cubed rule; i.e. the heeling forces, which de-
pends on water and wind impact areas, go up with
the square of the dimensions, but the righting mo-
ment which depends on the displacement, goes up
with the cube of the dimensions (Womack 2002).
Taking into account the square-cubed rule of ship
stability and simultaneously the same stability
standards for all size of vessels, the Intact Stability
Code cannot be applied as a basis for safety factor
estimation for the purpose of route optimization.
Moreover, ISC stability standards are related to one
state of weather and one state of a sea, described by
the wind pressure and ships rolling amplitude, while
the optimization procedure has to follow variable
weather and sea conditions to be passed by a vessel
on her way.
The state-of-the-art solution to the stability as-
sessment problem is a risk based approach. The core
idea of this approach is presented in Figure 6.
The risk based approach to ship stability assess-
ment reveals a list of advantages but the simplicity
comparing to proscriptive stability standards based
on IS Code. It comprises a seakeeping performance
of a ship and a wide range of possible weather and
sea conditions, however cannot be computed rela-
tively easy. The researches are still underway and no
complete practical tool has been established yet.
Furthermore, application of such an approach would
be extremely time-consuming which is unacceptable
for the purpose of multicriteria evolutionary weather
routing algorithm described in the paper.
Figure 6. Block diagram of risk based approach related to ship
stability (Kobylinski 2007b)
Consideration of characteristic features of contem-
porary methods of ship stability assessment (de-
scribed in section 4) and the main aim of the study
i.e. weather routing optimization, leads to the con-
clusion that there is a need for new measure of ship
safety. The index or coefficient of safety should
comprise safety aspects related to ship stability and
seakeeping performance and simultaneously it has to
be reasonably applicable. Both, time of computation