International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 3

Number 4

December 2009

393

1 INTRODUCTION

In weather routing one is about to find the most suit-

able ocean’s route for a vessel, taking into account

changeable weather conditions and navigational

constraints. One of the first approaches to the prob-

lem was a minimum time route planning based on a

weather forecast called an isochrone method. The

method was based on geometrically determined and

recursively defined time fronts, so called isochrones.

Originally proposed by R.W. James (James 1957),

isochrone method was in wide use through decades.

In late seventies based on the original isochrone

method the first computer-aided weather routing

tools were developed. However, along with comput-

er implementation some problems arose, i.e. with so

called “isochrone loops”. Numerous improvements

to the method were proposed since early eighties,

with (Hagiwara 1989, Spaans 1986, Wiśniewski

1991) among others. Since then several different ap-

proaches to the optimisation problem was in use,

with dynamic programming (Bijlsma 2004) or ge-

netic and evolutionary algorithms (Wiśniewski et al.

2005) among others.

It is a prime goal of weather routing tools to find

a route between given origin and destination ports

that is the safest, the shortest and the least expensive

possible. Unfortunately, these criteria are often con-

flicting, especially the ones expressing safety and

economics. A single route, time-optimal,

cost-optimal and safety-optimal at one time, hardly

exists. Thus, an acceptable trade-off between the cri-

teria is sought instead. A mathematical approach to-

wards solving such a problem involves multicriteria

(sometimes referred to as multiobjective) optimisa-

tion. Because the currently available solutions hardly

apply such an approach, thus it is well-founded to

propose a new multicriteria weather routing method,

presented previously in (Szłapczyńska 2007).

This paper focuses on presenting a solution, im-

plementing the multicriteria weather routing method,

together with some examples of usage. The remain-

der of the paper is organized as follows: section 2 in-

troduces definition of the optimisation. Section 3

provides description of a model of the researched

ship. Further details on weather modelling, such as

weather data sources, formats, etc., can be found in

(Szłapczyńska, in press). Section 4 describes the

MEWRA solution. In section 5 some examples of

usage of the solution are provided. Finally, section 6

summarizes the material presented.

2 DEFINITION OF THE OPTIMISATION

PROBLEM IN WEATHER ROUTING

The proposed multicriteria set of goal functions in

the weather routing optimisation process, revised

comparing to (Szłapczyńska 2007), is presented by

equations 1 – 3:

min)(

→=

rrtimepassage

ttf

(1)

min)(

→=

fcfcnconsumptiofuel

qqf

(2)

min)()(

→=

riskriskrisksvoyage

iif

(3)

j safety

risk

∑

)1(

(4)

Multicriteria Optimisation in Weather Routing

J. Szłapczynska & R. Smierzchalski

Gdynia Maritime University, Gdynia, Poland

ABSTRACT: The paper presents a new weather routing solution fully supporting multicriteria optimisation

process of route finding. The solution incorporates two multicriteria optimisation methods, namely multicrite-

ria evolutionary algorithm (SPEA) and multicriteria ranking method (Fuzzy TOPSIS). The paper focuses on

presenting the proposed multicriteria evolutionary weather routing algorithm (MEWRA). Furthermore, it in-

cludes some experiment results together with a short description of the assumed ship model.

394

where:

– [h] passage time for given route and ship

model,

– [g] total fuel consumption for given route

and ship model,

risk

– [/] risk coefficient for given route and the

ship model,

k – [/] number of route’s segments with i

j safety

< 1,

j safety

– [/] fractional safety coefficient for

(j-1)-th and j-th waypoints and given ship model;

values of the coefficient ranges [0; 1], where 1

depicts completely safe section of route and 0 –

unacceptably dangerous section.

The assumed set of constraints in the weather

routing optimisation problem includes:

− landmasses (land, islands) on given route,

− predefined minimum acceptable level of frac-

tional safety coefficient i

j safety

for given route,

− floating ice bergs expected on given route during

assumed ship’s passage,

− predefined maximum acceptable ice concentra-

tion on given route.

The next section provides a description of a ship

model and the way of modelling the goal functions

(1) – (3).

3 MODEL OF THE RESEARCHED SHIP

The researched ship model (Oleksiewicz, in press) is

based on a B-470 bulk carrier. Its basic parameters

are shown in Table 1. The model ship is equipped

with a hybrid propulsion including Sultzer RTA 48T

engine and a palisade of six textile sails (Figure 1).

Each sail has 522m

sail surface area. The ship is

equipped with a semi-adjustable B-Wageningen

screw propeller.

Table 1. Basic parameters of the model

_________________________________

Parameter name Value

_________________________________

Length 172 m

Width 22.8 m

Draught 9.5 m

Height 14.3 m

Service speed 15 kn

Displacement 30 288 t

Block coefficient (C

) 0.786

_________________________________

Figure 1. Sail model

3.1 Modelling of passage time

Ship speed forecast is a key element in passage time

modelling. Speed characteristic of the model ship is

based on algorithms presented in (Oleksiewicz, in

press). Speed prognosis for the model ship is based

on wind speed and wind angle forecasts. Then,

speed reduction factor due to wave impact is applied

to the prognosis. Detailed description on the model

ship’s speed modelling is given by (Szłapczyńska et

al. 2007).

It is assumed that the ship model moves between

two consecutive waypoints with constant velocity

and propulsion type (“only motor engine” or “hybrid

propulsion”). Thus the passage time for a route is

given by:

∑

..2=

(5)

where:

– [h] passage time for a route and given ship

model,

n – [/] number of routes’ waypoints,

– [kn] speed of the ship model between (j–1)-th

and j-th waypoints,

– [Nm] distance between (j–1)-th and j-th way-

points.

3.2 Modelling of fuel consumption

Forecasted fuel consumption per hour for the ship

model is calculated by:

BSFCPFCPH *=

(6)

where:

FCPH- [g/h] fuel consumption per hour,

P - [kW] engine power,

BSFC - [g/kWh] break specific fuel consumption.

Based on the model’s engine (Sultzer RTA 48T)

catalogue data the BSFC value is assumed to be

395

171 g/kWh. Values of engine power P belong to a

discrete set, depending of current telegraph com-

mand, as presented in (Szłapczyńska et al. 2007).

Another aspect of fuel consumption is connected

to starting the engine. Additional portion of fuel is

required to every start of the engine, which might

become significant when it is possible to turn the

engine on and off during the voyage. Thus, the total

fuel consumption of the model ship for a route is

given by:

FCPS mFCPH tq

jjfc

+)(=

∑

..2=

(7)

where:

– [g] total fuel consumption for given route

and ship model,

– [h] passage time between (j-1)-th and j-th

waypoints,

FCPH

– [g/h] FCPH valid between (j-1)-th and

j-th waypoints,

m – [/] number of engine starts,

FCPS – [g] fuel consumption per start.

3.3 Modelling of the voyage risk

It is assumed that the wind causes the prime safety

threat during the voyage. Thus, the definition of the

fractional safety coefficient i

j safety

, utilized by (4) to

calculate the risk of a voyage i

risk

, is given by:

max

j w w

safetyj

v-v

(8)

efd efd w

vλ-vv

maxmaxmax

Δ=

(9)

where:

w max

– [kn] maximum allowable wind speed,

w j

– [kn] wind speed between (j-1)-th and j-th

waypoints,

max def

– [kn] threshold wind speed, assumed as

35 kn,

– [/] shape coefficient (Figure 2), dependent of

the ship propulsion type and wind heading angle,

∆

max def

– [kn] possible threshold wind speed

margin, assumed as 10 kn.

Figure 2.

shape coefficient (solid line - hybrid propulsion;

dotted line - only motor engine) as a function of wind heading

angle γ

The main purpose of the

shape coefficient is to

differentiate the maximum allowable wind speed

w max

dependent of the wind heading angle. The co-

efficient discriminates (by greater

values) mainly

the following winds.

The i

j safety

= 0 depicts a totally dangerous route

sector (with v

w j

≥ v

w max

). In contrary, i

j safety

= 1 de-

picts a completely safe route sector (with v

w j

= 0).

4 WEATHER ROUTING WITH

MULTICRITERIA OPTIMISATION

The proposed weather routing algorithm is based on

the optimisation criteria set (1) - (3), defined in sec-

tion 2. The solution utilizes two basic multicriteria

mechanisms, namely multicriteria evolutionary algo-

rithm – Strength Pareto Evolutionary Algorithm

(SPEA) and multicriteria ranking method – Fuzzy

TOPSIS.

4.1 Multicriteria evolutionary weather routing

algorithm (MEWRA)

The SPEA framework in the proposed algorithm is

responsible for iterative process of population de-

velopment. The result of SPEA is a Pareto-optimal

set of solutions. The multicriteria ranking method

(Fuzzy TOPSIS) is responsible for sorting the result-

ing Pareto-optimal solutions according to the given

preferences of the decision-maker. The preferences

are represented by linguistic values with fuzzy

weights assigned to the decision criteria. The main

algorithm’s flow is illustrated in Figure 3.

396

Figure 3. Multicriteria evolutionary weather routing algorithm

4.2 Chromosome structure

An individual in the evolutionary approach, also re-

ferred to as a solution, represents a route. The route

includes an array of waypoints constituting ship’s

trajectory, where the first one is equal to the position

of the origin port and the last one – to the destination

port. A single entry of the waypoints array includes:

− geographical coordinates (longitude, latitude) of

the waypoint,

− motor engine relative settings valid from the pre-

vious to the given waypoint, ranging [0;1],

− propulsion type (there are two different propul-

sion modes distinguished for the assumed ship

model: “motor only” and “motor & sails”),

− time of reaching given waypoint,

− velocity of the ship, assumed constant on a sector

between two waypoints, valid from the previous

to the given waypoint,

− uncertainty index for given waypoint (value rep-

resenting uncertainty of the waypoint’s data).

Only the first three elements of the waypoint en-

try are in direct control of the evolutionary mecha-

nisms: the coordinates, motor settings and propul-

sion type. All the other values can be calculated as

functions of the former and are stored in the chro-

mosome in order to improve on efficiency of the al-

gorithm.

4.3 Initial population

The first step towards evolutionary computation is

always building an initial population. In the consid-

ered weather routing case, a preliminary set of basic

routes is generated at first. For given pair of origin

and destination ports the set includes the following

routes:

− an orthodrome,

− a loxodrome,

− a time-optimized isochrone route (Spaans 1986,

Hagiwara 1989,Wiśniewski 1991), referenced

further as IZO_REF_TIME,

− a route given by fuel-optimization applied to the

time-optimized isochrone route, referenced fur-

ther as IZO_REF_FUEL.

The isochrone routes (IZO_REF_TIME &

IZO_REF_FUEL) are generated with time step 2h.

The initial population is generated by creating

random mutations of the basic routes. Also pure

basic routes are included in the initial population.

4.4 Specialized operators

There are several specialized “genetic” operators re-

quired by the evolutionary framework, each custom-

ized to the established chromosome structure. The

set of specialized operators in the multicriteria evo-

lutionary weather routing algorithm includes:

− one-point crossover,

− non-uniform mutation,

− route smoothing by means of average weighting.

4.5 Final ranking of routes

When SPEA completes its computations, the availa-

ble result set includes the Pareto-optimal set of indi-

viduals (routes) and a corresponding Pareto front.

Unfortunately (or fortunately, but from the other

perspective) the Pareto-optimal set is numerous.

Thus it would be inconvenient for the user (e.g. a

captain) to browse manually through the complete

set of resulting routes in search of the most suitable

one.

Yet another problem might be encountered: how

to decide which route is the best within given mul-

ticriteria optimisation environment? To solve this

problem decision-maker’s (e.g. captain’s) prefer-

ences to the given criteria set should be defined.

Hence a tool for sorting the Pareto-optimal set is

provided – Fuzzy TOPSIS method. The method cre-

ates a ranking of routes based on the decision-

maker’s preferences expressed by linguistic values

with triangular fuzzy values assigned (Table 2). The

decision-maker picks one linguistic variable per cri-

terion. The variable should describe the most accu-

rately the significance of the criterion and its impact

397

on the decision. The first route in the final ranking

will be the most suitable one from the Pareto-

optimal set, with reference to the previously defined

preferences to the criteria set.

Table 2. Linguistic values and corresponding triangular fuzzy

values, utilized to express decision-maker’s preferences to the

criteria set

___________________________________________________

Linguistic value Triangular fuzzy value

___________________________________________________

very important (0.7; 1.0; 1.0)

important (0.5; 0.7; 1.0)

quite important (0.2; 0.5; 0.8)

less important (0.0; 0.3; 0.5)

unimportant (0.0; 0.0; 0.0)

___________________________________________________

5 EXAMPLES OF USAGE

This section presents two experiment results with the

proposed multicriteria evolutionary weather routing

algorithm. The experiments’ origin and destination

ports as well as the departure dates vary to present

performance of the algorithm for various weather

conditions. In both cases output of the algorithm is

compared with the routes found by the time-

optimised and fuel-optimised isochrone method re-

spectively. Output routes of the multicriteria evolu-

tionary weather routing algorithm (depicted as

MEWRA) were selected by means of linguistic val-

ues assigned to the criteria set as given in Table 3.

Table 3. Linguistic values assigned to the criteria set in the

multicriteria evolutionary weather routing algorithm

___________________________________________________

Route Passage Fuel Voyage

description time consumption risk

___________________________________________________

MEWRA_TIME very unimportant unimportant

important

MEWRA_FUEL unimportant very unimportant

important

MEWRA- important less very

_COMPROMISE important important

___________________________________________________

5.1 Lisbon – Miami, departure 2008-09-02 at 00:00

The initial population generated for the Lis-

bon-Miami voyage is presented in Figure 4. The set

of Pareto-optimal solutions (routes), obtained after

100 of generations during evolutionary optimisation,

is then presented in Figure 5. The resulting ME-

WRA_TIME, MEWRA_FUEL and ME-

WRA_COMPROMISE routes are then presented by

comparison to the isochrone routes in Figure 6-8 re-

spectively. Basic performance parameters of the

MEWRA and reference isochrone routes are collated

in Table 4.

Figure 4. Initial population of routes for Lisbon-Miami voyage,

departure 2008-09-02 00:00

Figure 5. Set of Pareto-optimal routes for Lisbon-Miami voy-

age, departure 2008-09-02 00:00

Figure 6. Output of the algorithm MEWRA_TIME compared

to the time-optimal isochrone route for Lisbon-Miami voyage,

departure 2008-09-02 00:00

Figure 7. Output of the algorithm MEWRA_FUEL compared

to the fuel-optimal isochrone route for Lisbon-Miami voyage,

departure 2008-09-02 00:00

Figure 8. Output of the algorithm MEWRA_COMPROMISE

compared to the time-optimal and fuel-optimal isochrone

routes for Lisbon-Miami voyage, departure 2008-09-02 00:00

398

Table 4. Comparison of basic performance parameters of the

reference isochrone routes and output of the algorithm (ME-

WRA routes) for Lisbon-Miami voyage, departure 2008-09-02

00:00

___________________________________________________

Route Passage Fuel Voyage Avg

description time [h] cons. [t] risk [/] speed[kn]

___________________________________________________

IZO_REF_TIME 234.29 308.81 0.149 15.37

IZO_REF_FUEL 531.56 48.36 0.124 6.77

MEWRA_TIME 233.30 307.50 0.132 15.49

MEWRA_FUEL 373.54 8.45 0.094 10.24

MEWRA-

_COMPROMISE 288.91 225.79 0.058 13.51

___________________________________________________

During the period of 2008-09-01 and 2008-09-15

the Tropical Weather Outlook of National Hurricane

Centre reported activities of three tropical storms

and cyclones in Atlantic region, namely Hanna, Ike

and Josephine. However, the considered routes were

threatened directly with Josephine only. The outlook

of wind speed forecast (NOAA Wave Watch III) on

2008-09-10 is presented in Figure 9. The remnant

low of Josephine continued moving to the west for

the next several days.

Figure 9. Wind speed forecast (NOAA Wave Watch III) on

2008-09-10 for the Northern Atlantic region with indicated po-

sition of tropical depression Josephine

As depicted by the Figure 5, all the Pareto-

optimal routes bypass Josephine. The ME-

WRA_TIME route compared to the time-optimal

isochrone route (IZO_REF_TIME) is shorter almost

1h, requires over 1.3t less fuel and is safer (lesser

voyage risk factor) the same time. The similar

tendencies can be found for the MEWRA_FUEL

and IZO_REF_FUEL pair of routes. But this time

passage time saving in almost 30%, fuel saving ex-

ceeds 80% and voyage risk is reduced by almost

25%. The MEWRA_FUEL route owes its suprema-

cy the utilization of favourable winds with possibil-

ity to turn off the engine. Another aspect of the su-

premacy is that the IZO_REF_FUEL route is not a

fully fuel-optimized one (it is a fuel-optimized time-

optimal isochrone route). Due to that it is better to

compare MEWRA_FUEL with IZO_REF_TIME. In

such case fuel reduction exceeds 97% and voyage

risk reduction is almost 37%, but for the cost of in-

creasing passage time by almost 60%. On the other

hand, the MEWRA_COMPROMISE route allows

reduction of the risk factor by 60% (mostly due to

bypassing the remnant of Josephine by means of “34

knot wind radius rule”) comparing with

IZO_REF_TIME. The route allows over 26% fuel

saving for cost of increasing passage time by less

than 24%.

5.2 Halifax – Plymouth, departure 2008-02-15 at

12:00

The initial population generated for the Halifax –

Plymouth voyage, is presented in Figure 10. The set

of Pareto-optimal routes, obtained after 100 of gen-

erations, is then presented in Figure 11. The result-

ing MEWRA_TIME, MEWRA_FUEL and ME-

WRA_COMPROMISE routes are presented by

Figures 12-14 respectively. Basic performance pa-

rameters of the MEWRA and reference isochrone

routes are collated in Table 5.

Figure 10. Initial population of routes for Halifax - Plymouth

voyage, departure 2008-02-15 12:00

Figure 11. Set of Pareto-optimal for Halifax - Plymouth voy-

age, departure 2008-02-15 12:00

Figure 12. Output of the algorithm MEWRA_TIME compared

to the time-optimal isochrone route for Halifax - Plymouth

voyage, departure 2008-02-15 12:00

Figure 13. Output of the algorithm MEWRA_FUEL compared

to the fuel-optimal isochrone route for Halifax - Plymouth voy-

age, departure 2008-02-15 12:00

399

Figure 14. Output of the algorithm MEWRA_COMPROMISE

compared to the time-optimal and fuel-optimal isochrone

routes for Halifax - Plymouth voyage, departure 2008-02-15

12:00

Table 5. Comparison of basic performance parameters of the

reference isochrone routes and output of the algorithm (ME-

WRA routes) for Halifax - Plymouth voyage, departure 2008-

02-15 12:00

___________________________________________________

Route Passage Fuel Voyage Avg

description time [h] cons. [t] risk [/] speed[kn]

___________________________________________________

IZO_REF_TIME 157.89 208.14 0.290 15.58

IZO_REF_FUEL 420.84 14.77 0.312 5.75

MEWRA_TIME 152.99 201.68 0.340 15.62

MEWRA_FUEL 259.66 1.23 0.245 10.25

MEWRA-

_COMPROMISE 206.34 191.98 0.159 14.03

___________________________________________________

During the period of 2008-02-15 and 2008-02-28

neither tropical storms nor cyclones were reported

by NHC. However, strong wind fields originating on

US Atlantic coast, heading towards eastern coast of

Greenland, were expected repeatedly during the pe-

riod. A non-zero ice concentration was observed

during the period at northern coast of New Funland.

Also rare icebergs transported by Labrador Current

were expected in the area.

The Pareto-optimal routes (Figure 11) avoid the

strong wind fields as well as the ice threat zone. The

MEWRA_TIME route compared with the

IZO_REF_TIME is shorter by almost 5h, requires

over 6t less fuel for a cost of slightly higher voyage

risk (less than 18%). On the other hand the ME-

WRA_FUEL route compared to IZO_REF_FUEL is

significantly shorter (over 38%), allows enormous

reduction of fuel consumption by over 91% and also

improves route’s safety (voyage risk reduced by

over 21%). Again, when compared to

IZO_REF_TIME, the MEWRA_FUEL achieves al-

most 99.5% of fuel reduction and 15% voyage risk

reduction, but for the cost of almost 65% longer pas-

sage. On the other hand, the ME-

WRA_COMPROMISE route allows further minimi-

zation of the risk factor, with 45% reduction of the

factor (due to bypassing strong wind fields on the

south from New Funland) comparing with

IZO_REF_TIME. The route allows 7% fuel saving

with passage time increased by less than 31%.

6 CONCLUSION AND FUTURE WORK

The proposed multicriteria evolutionary weather

routing algorithm (MEWRA) was presented here in

application to the hybrid propulsion ship model.

With MEWRA it was possible to obtain significant

reductions of passage time, fuel consumption and

risk factor, however (time in most cases) not all at

the same. Based on the results presented in the pre-

vious section, the following tendencies can be ob-

served:

− MEWRA_TIME routes, when compared with the

time-

optimal isochrone routes

(IZO_REF_TIME), slightly shorten passage time

(0.5% & 3.1%) and reduce fuel consumption

(0.5% & 3.1%), but in one out of two cases may

increase voyage risk (here: by 18%). The similar

percentage values of passage time and fuel con-

sumption reduction depict that the fuel savings

are caused by the shortened passage only. The

average service speed on MEWRA_TIME is

3.5% - 4.1% greater than the original service

speed.

− MEWRA_FUEL routes, when compared with the

fuel-optimized time-optimal isochrone routes

(IZO_REF_FUEL), significantly shorten passage

time (30% & 38%), reduce fuel consumption

(80% & 91%) and decrease voyage risk (21% &

25%). The surprisingly good MEWRA passage

time performance is caused here by the fact that

the IZO_REF_FUEL route is suboptimal. Fuel

consumption reductions are caused by the possi-

bility of turning the engine off during the voyage.

The average speed on MEWRA_FUEL routes is

30% - 35% lesser from the original service speed.

− MEWRA_FUEL routes, when compared with the

time-

optimal isochrone routes

(IZO_REF_TIME), even more significantly re-

duce fuel consumption (97% & 99.5%) and de-

crease voyage risk (15% & 37%). The lengthened

passage time (60% & 65%) is the cost of the sav-

ings in this case. Such a good MEWRA fuel con-

sumption performance is caused, again as in pre-

vious comparison, by the very nature of the

hybrid propulsion model. Allowing, during the

voyage, the possibility of turning the engine off

and finding the best possible wind conditions, one

(at least theoretically) is able to achieve 100%

fuel reduction. The question is, whether it is ac-

ceptable to drastically lengthen the passage to

achieve such fuel savings.

− MEWRA_COMPROMISE routes try to establish

a practical trade-off between the basic routes’ pa-

rameters. The routes, when compared with the

time-

optimal isochrone routes

(IZO_REF_TIME), significantly reduce voyage

risk (45% & 60%) due to bypassing the main en-

countered security threats. The routes also reduce

400

fuel consumption (7% & 26%), but lengthen the

passage time (24% & 31%). Actions taken to in-

crease routes’ safety are the major factors induc-

ing longer passage. The average speed of ME-

WRA_COMPROMISE is only 6.4 % - 10%

lesser from the original service speed.

To conclude, MEWRA is a new weather routing

solution and, as proved by the experiment results,

competitive towards other single-objected methods,

such as e.g. the isochrone method. The solution ex-

pands functionality of typical weather routing tools

by introducing the trade-off routes (ME-

WRA_COMPROMISE), yet preserving the possibil-

ity to search for single-objected routes (MER-

WA_TIME & MEWRA_FUEL). In addition to that,

it is possible to define another set of result routes by

assigning simple linguistic values (such as “im-

portant”, “less important” or “unimportant”) to each

of the optimisation criterion.

It is worth mentioning that MEWRA execution

time in the both presented cases (Lisbon – Miami &

Halifax - Plymouth) was shorter than 20 min. The

execution times seem to be acceptable, taking into

account the future plans to improve MEWRA to-

wards dynamic route update mechanisms. Other

plans include expanding MEWRA to support a cus-

tom ship model with traditional motor engine.

ACKNOWLEDGEMENTS

The authors would like to thank MicroOLAP Tech-

nologies for supporting the research by granting a

free licence for EasyMAP VCL component (a GIS

control).

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