Maritime University of Szczecin
Akademia Morska w Szczecinie
2010, 21(93) pp. 57–61 2010, 21(93) s. 57–61
The influence of the diversified passenger population on safe
evacuation from a passenger ship
Wpływ zróżnicowania populacji pasażerów na bezpieczną
ewakuację ze statku pasażerskiego
Dorota Łozowicka
Maritime University of Szczecin, Faculty of Navigation, Institut of Marine Navigation Akademia Morska w Szczecinie, Wydział Nawigacyjny, Instytut Nawigacji Morskiej 70-500 Szczecin, ul. Wały Chrobrego 1–2
Key words: evacuation modeling, passenger ships, genetic algorithm, optimization Abstract
This article states theoretical assumptions for the method of identifying disadvantageous evacuation times from ships relating to diversified populations of passengers. The influence of age, sex and physical fitness of people is examined. The presented optimization uses the genetic algorithms method as well as Genetic Algorithm and Direct Search Toolbox included in Matlab software. Examples of calculations of the time of passenger evacuation from a passenger ship are given to verify the operation of the developed method.
Słowa kluczowe: ewakuacja, statki pasażerskie, algorytmy genetyczne, optymalizacja Abstrakt
W artykule podaje się teoretyczne założenia do metody poszukiwania niekorzystnych czasów ewakuacji ze statków pod kątem zróżnicowania populacji pasażerów. Analizuje się wpływ wieku, płci oraz predyspozycji fizycznych ludzi. Do optymalizacji wykorzystuje się metodę algorytmów genetycznych, a także Genetic Al-gorithm and Direct Search Toolbox programu Matlab. Podaje się przykładowe obliczenia czasu ewakuacji ze statku pasażerskiego w celu zweryfikowania poprawności działania opracowanej metody.
Introduction
We should take into account a number of para-meters affecting evacuation when calculating its time. Those relating to the human factor make up a major set of such parameters. This analysis will look into the impact of diversified population of individuals taking part in an evacuation, depending on their age, sex and physical fitness on the evacu-ation time. Possibly, the time of evacuevacu-ation should not exceed the time available for its execution. However, in the event of disadvantageous diversifi-cation of evacuee population there is a risk that passengers will not manage to abandon ship in time available.
We will attempt to search for the maximum evacuation time in order to verify existing or designed solutions of escape routes. Of many
opti-mization methods, the genetic algorithm method has been chosen for the purpose. One positive point of the genetic algorithm method is that is enables reaching an optimal solution in a reasonable time. As a method, genetic algorithms were inspired by Darwin’s theory of evolution. The procedure in the method aims at seeking a maximum (minimum) of a function. It consists in imitating living organisms which through evolutionary processes, such as natural selection and inheritance, adjust to the changing natural environment. Each successive generation are better adjusted than their predeces-sors, while weaker and worse-fitted individuals have less chance for survival and reproduction. We propose solving the problem by means of genetic algorithms and application of Matlab soft-ware. The Matlab language environment enables programming user’s own software, adding it and
utilizing along with the existing tools. Besides, Genetic Algorithm and Direct Search Toolbox will be employed to solve the problem [1].
Theoretical assumptions of the method
In the first stage we assume that there is a spe-cific number X of people in a room to be evacuated. In the next step these people will be divided into categories depending on their specific travel speeds {x1, … xn}, where n denotes the number of
catego-ries.
Therefore, the chromosome will have this form:
where : f(x1, x2, … xn) is the fitness function.
In the next step constraints are determined. In the examined problem we have to adopt bound values for population diversification, i.e. we reject unlikely cases, such as a 100% population of mobi-lity-impaired persons. Therefore, intervals of par-ticular categories of people have to be defined.
1. x1 + x2+ … + xn = X
2. a ≤ x1 ≤ b
3. c ≤ x2 ≤ d
4. e ≤ x1 ≤ f etc. (1)
The fitness function defines the travel time of an assumed number X of people from the starting room to a muster station through a verified layout of escape routes.
f (x1, x2, ... xn) = t (2)
The evacuation route is divided into sections for which particular travel times are calculated.
The total time t of passing the whole route results from this formula [2]:
tw tfmax
t (3)
where: tw – individual time of passing an escape
route (free flow), tf – group time of passing an
es-cape route calculated for an assumed movement intensity and route width.
Times tw and tf are calculated for each section of
the route (doors, corridors, stairways) between the assembly and starting evacuation points for each group of evacuees.
The time t is calculated by adding individual times of passing particular sections ∑tw and the
maximum group time tfmax.
Each individual travel time is calculated from this formula: ) ( ... ) ( , ) ( max 2 1 n w S x L x S L x S L t (4)
where: L – route length [m], S – mean speed of travelling, dependent on specific characteristics of population [m/s].
For further calculations of t the longest of tw
times is assumed, i.e the time of slowest-moving category of evacuees.
The value of group travel time is calculated as follows: c s f F W X t (5)
where: X – number of persons in a group, Wc –
width of passage route [m], Fs – movement
intensi-ty [persons/s∙m].
The values Wc, L depend on the geometry of
es-cape route. The value Fs was empirically set in [3]
for some values of persons’ density D in corridors. To determine the remaining values Fs the
approxi-mation by fourth-order polynomial was utilized (Fig. 1). The values Fs for doors are 1.3 according
to [3].
Fs = 0.034D 4 – 0.18D 3 – 0.14D 2 +
+ 1.4D + 0.004 (6)
Fig. 1. Movement intensity dependent on persons density in corridors
Rys. 1. Zależność natężenia ruchu od zagęszczenia ludzi na korytarzach
Genetic Algorithm and Direct Search Toolbox solves the problem of the objective function mini-mization:
) ( minf x
x (7)
In the problem under consideration we wish to find the maximum of the objective function, there-fore to maximize f(x) we have to minimize –f(x). [x1, x2, … xn] – chromosome
gen (function variable)
D [persons / m2] Fs [p erso ns / (m s)]
Calculations of evacuation time for a given ship
In the method herein presented we will utilize the evacuation plan of the motor ferry “Gryf”, a typical car-passenger ferry. The analysis will deal with an evacuation of 160 passengers from a restau-rant located on the passenger deck (Fig. 2). Passen-gers proceed according to the fixed evacuation plan to assembly (muster) stations on the same deck. For simplification, it was assumed that the group will divide into equal sub-groups matching the number of available escape exits.
PP MZ K1 K2 K3 K4 K5 K6 D1 D2 D3 D4
MZ- muster station, PP- public space (room), K- corridor, D- door
Fig. 3. Schematic layout of spaces and evacuation direction: MZ – muster station, PP – public space (room), K – corridor, D – door
Rys. 3. Schemat rozkładów pomieszczeń i kierunku ewakuacji: MZ – muster station, PP – public space (room), K – korytarz, D – drzwi
Figure 3 shows a schematic layout of spaces and evacuation direction in the form of the directed graph. Table 1, in turn, shows dimensions of corri-dors, doors and calculated floor space of corridors denoted as A.
Table 1. Corridors and doors dimensions Tabela 1. Wymiary korytarzy i drzwi
Parameters L [m] Wc [m] Area [m2] K1 14.7 1.84 27.048 K2 14.7 1.84 27.048 K3 11 1.66 18.26 K4 11 1.66 18.26 K5 33.16 2.66 88.2 K6 33.16 2.66 88.2 D1 – 1.6 – D2 – 1.6 – D3 – 1.2 – D4 – 1.2 –
The examined population was divided into eight categories. Each category was attributed specific travel speed based on [4]. Table 2 shows the cate-gories and corresponding speeds.
Table 2. Characteristic speeds for each category of passenger population
Tabela 2. Prędkości charakterystyczne dla poszczególnych kategorii populacji pasażerów
Groups in passenger population Number of individuals S [m/s]
Females younger than 30 years x1 1.24
Females 30–50 old x2 0.95
Females older than 50 years x3 0.75 Females older than 50, mobility impaired x4 0.57 Males younger than 30 years x5 1.48
Males 30–50 years old x6 1.30
Males older than 50 years x7 1.12 Males older than 50 years, mobility
impaired x8 0.85
The following length of route section was as-sumed:
Lmax
LK1LK3LK5
; LK2LK4LK6
(8)The number of persons in each category was set in the program by defining lower and upper bounds, whereas the size of examined population (160 indi-viduals) by linear constraints. Implementing the formulas (4), (5), (6) and (7) into the example under consideration, the following formulas were utilized in creating the fitness function:
4 8 4 2 4 1 4 2 8 2 8 2 2 2 2 2 1 2 1 2 1 8 1 8 1 2 1 2 1 1 1 1 1 3 . 1 2 / 3 . 1 2 / 3 . 1 2 / 2 / ... 2 / 2 / 2 / ... 2 / 2 / cD cD cD fD cK sK cK sK cK sK fK cK sK cK sK cK sK fK W x W x W x t W x F x W x F x W x F x t W x F x W x F x W x F x t (9)Fig. 2. Layout of deck 10, m/f “Gryf” Rys. 2. Plan pokładu 10, m/f „Gryf”
where: 004 . 0 2 / 4 . 1 2 / 14 . 0 2 / 18 . 0 2 / 034 . 0 ) ( 004 . 0 2 / 4 . 1 2 / 14 . 0 2 / 18 . 0 2 / 034 . 0 ) ( 004 . 0 2 / 4 . 1 2 / 14 . 0 2 / 18 . 0 2 / 034 . 0 ) ( 004 . 0 2 / 4 . 1 2 / 14 . 0 2 / 18 . 0 2 / 034 . 0 ) ( 004 . 0 2 / 4 . 1 2 / 14 . 0 2 / 18 . 0 2 / 034 . 0 ) ( 6 8 2 6 8 3 6 8 4 6 8 8 6 2 2 2 2 2 3 2 2 4 2 2 2 2 1 2 2 1 2 3 1 2 4 1 2 2 1 2 1 2 2 1 3 2 1 4 2 1 1 2 1 1 2 1 1 3 1 1 4 1 1 1 1 k k k k sK k k k k sK k k k k sK k k k k sK k k k k sK A x A x A x A x x F A x A x A x A x x F A x A x A x A x x F A x A x A x A x x F A x A x A x A x x F (10) Then the fitness function has this form:
x1,x2...x8
[tw max(tfK1,tfK2...tfD4)]f (11)
The following algorithm parameters were as-sumed:
population size: 20 chromosomes, fitness scaling: rank,
selection by the roulette method, reproduction: elite count, two-point crossover,
mutation: constraint dependent default, both side migration.
Calculations were made for the following cases: 1. A population consisting exclusively of males
under thirty. The travel time from a public space to muster stations was 178 seconds. Figure 4 presents the distribution of population for this case.
Fig. 4. Population distribution for case 1 Rys. 4. Rozkład populacji dla przypadku 1
2. Uniform distribution of the population. The travel time from a public space to muster sta-tions was 268 seconds. Figure 5 presents the population distribution for this case.
Fig. 5. Population distribution for case 2 Rys. 5. Rozkład populacji dla przypadku 2
3. Majority of mobility impaired passengers. The travel time from a public space to muster stations was 280 seconds. Figure 6 shows the popu-lation distribution for this case.
Fig. 6. Population distribution for case 3 Rys. 6. Rozkład populacji dla przypadku 3
Number of variables (8) C ur re nt b est in di vi du al Number of variables (8) C ur re nt b est in di vi du al Number of variables (8) C ur re nt b est in di vi du al
Mean and best values of the fitness function in particular generations of the genetic algorithm for case 3 are shown in figure 7.
Fig. 7. Values of the fitness function in particular generation for case 3
Rys. 7. Wartości funkcji przystosowania genetycznego w po-szczególnych pokoleniach dla przypadku 3
Summary
This article presents theoretical assumptions of the method of searching for the most disadvan-tageously diversified population, i.e. one corres-ponding with the longest time of evacuation. The determination of the longest, i.e. most dis-advantageous time allows to verify the design of escape routes in new and existing ships. At present many solutions to such problems require time-consuming and costly calculations, if a satisfactory result is to be obtained. As genetic algorithms using simple methods of coding and reproduction prove to be a very effective tool, their range of applica-tions in solving complex issues is wide. Genetic algorithms can be used to solve problems where
functions assessing the given solution can be for-mulated. This justifies the use of this method for solving the formulated problem.
The example calculations were made for a very simple case of evacuating only 160 passengers, moving along geometrically uncomplicated escape routes. However, the differences in the calculated evacuation time depending on population diversifi-cation varied and reached 40%. It is a clear indica-tion of the fact that disadvantageous diversificaindica-tion of individuals in the population may significantly lengthen the actual time of evacuation, to the extent it will be longer than the time available for its execution. The developed method may be especial-ly useful in estimating the time of evacuation from very large cruise ships with complicated layout of escape routes and a few thousand passengers onboard. The influence of the human factor may be even stronger, if we additionally assume there will be other obstructions affecting the ordered move-ment of people to their muster stations, such as a fire or panic.
References
1. ŁOZOWICKA D.: Możliwości wykorzystania Genetic Algo-rithm and Direct Search Toolbox programu MATLAB w projektowaniu statków. Logistyka, 2009, 6.
2. International Maritime Organisation (IMO), Interim Guide-lines for evacuation analysis for new and existing passen-ger ships, MSC Circular n. MSC/Circ.1033, 26th June 2002. 3. SFPE Fire Protection Engineering Handbook, 2nd edition,
NFPA, 1995.
4. GALEA E.,GWYNNE S.,LAWRENCE P.,FILLIPIDES L.: Build-ing EXODUS user guidelines manual. University of Greenwich, 1998.
Recenzent: prof. dr hab. inż. Tadeusz Szelangiewicz Akademia Morska w Szczecinie Generation Fi tn ess va lu e Best: –280.4968 Mean: –280.4963
