Dynamic evacuation location choice model with risk-responsive
survival of alternatives
A. Kondoa , J. Urataa,∗ and E. Hatoa
a Department of Civil Engineering, University of Tokyo, Japankondo@bin.t.u-tokyo.ac.jp, urata@bin.t.u-tokyo.ac.jp, hato@bin.t.u-tokyo.ac.jp∗ Corresponding author
Extended abstract submitted for presentation at the 11th Triennial Symposium on
Transportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

January 15, 2022
Keywords: dynamic discrete choice, choice set formation, evacuation behavior, risk perception

1INTRODUCTION

Location choice in disaster situation follows a dynamic mechanism, where agents consider expected utilities of each location in their choices. However, when the future risks rise, alternatives
may easily drop out from agents’ choice set. Manski (1977) proposed a semi-compensatory framework which assumes alternatives are reduced to a feasible choice set, and a choice is made fromthe reduced choice set. Models for choice set formation applying Manski’s framework exist in
static context, for example in Kaplan et al. (2011).
Survival probability is a concept addressed by Rust (2016), which captures the probability
that the problem will continue. The concept aligns with the aforementioned mechanism oflocation choice during a disaster. Utilities brought by a risky candidate which may not survive
as a choice must be reduced when they are perceived.
We propose a dynamic location choice model in a heavy rain disaster, which considers realistic
choice set formation according to risk. Since choice set formation is probabilistic, dropping outof risky candidates are incorporated as the probability of candidate’s survival. Our proposedmodels are applied to real evacuation behavior data.

2METHODOLOGY

2.1

Dynamic evacuation location choice model

We formulate a dynamic evacuation location choice model using a time-structured network, basedon the discounted recursive logit model presented by Oyama & Hato (2017). The instant utilityof state st+1 from state st is expressed as:u(st+1 |st ) = ρ(st+1 |st ) v(st+1 |st ) + εst ,st+1 ,(1)where ρ(st+1 |st ) is the probability that st+1 survives as a choice of st , v(st+1 |st ) is the utility oftransition from st to st+1 , and εst ,st+1 is the error term. The expected utility V (st ) at state st is
expressed using a discount factor β:V (st ) = Emaxρ(st+1 |st ){v(st+1 |st ) + βV (st+1 )} + εst ,st+1 ,(2)st+1 ∈C(st )TRISTAN XI Symposium

Original abstract submittal

A. Kondo, J. Urata and E. Hato2

where C(st ) indicates all alternatives from state st , from which a realistic choice set is formed.
Assuming εst ,st+1 are i.i.d. extreme value type I error terms, Eq.(2) is reformulated as a logsum:X
exp ρ(st+1 |st ){v(st+1 |st ) + βV (st+1 )} st ̸= sT
log(3)V (st ) =st+1 ∈C(st )0
st = sT ,where T is the terminal time considered in the model. The proposed formulation is equivalent
to a traditional dynamic model when ρ = 1 for all alternatives.

2.2

Examplet=0

Settings
T=2

t=1

v(C2|Y1)=3v(D2|Y1)=4

risk

risk

v(A1|A0)=3v(B1|A0)=2

potential locationsat t=1location
at t=0AB
candidatesdeterministic
choices at t=0CDA

locationprobabilistic
choices at t=1

transition startingfrom A→ABCD
candidates

transition startingfrom A→B

locationcandidates at tFigure 1 – Example NetworkTo describe what is expressed by incorporating probabilistic choice set formation, we present an
example with a simple network shown in Figure 1. Consider a location choice problem at time
t = 0 in A. Let U (Yt+1 |Xt ) denote the utility of transition from X to Y at time t, expressed as:
U (Yt |Xt ) = ρ(Yt+1 |Xt ){v(Yt+1 |Xt ) + βV (Yt+1 )}.

(4)

The utilities are as shown in Figure 1 and the discount factor β = 0.9. At t = 0, alternatives
A and B are considered as next locations. The risk rises at t = 1 eliminating A and B, making
the safer locations C and D next candidates. A trip to C/D from A is however difficult due
to route risk. Moving to B1 in advance would make them more accessible. Table 1 shows theprobabilities of candidates’ survival and the utilities of transition to A1 and B1 , reflecting suchconditions.
Table 1 – Difference in preference when risk-responsive survival probability is consideredYZ

ρ(Z|Y )U (Y |A0 )A1C2D2116.88

B1C2D2115.88

A1C2
D2

0.4
0.2

4.54

B1C2
D2

0.8
0.6

4.78

Traditional

ProposedIn the traditional model, A1 with higher instant utility is more preferred, where as in theproposed model, B1 that broadens future choices are favored.
TRISTAN XI Symposium

Original abstract submittal

A. Kondo, J. Urata and E. Hato

2.3

3

Model for choice set formation

To determine ρ(st+1 |st ) exogenously, we propose a model for choice set formation with observed
choice set, based on Kaplan et al. (2011). Two criteria are assumed: (i)Location Risk and(ii)Route Risk. As risk is an unobserved latent variable, both risk and threshold are structured.
Threshold θkqt and risk Rkt of household q, time t, criterion k for an alternative is expressed:
θkqt = α′k Zkqt + ξkqt ,(5)

Rk = βk′ Gk + σkq ,(6)where α, β are parameters to be estimated, Z is household characteristics or time-dependent
rainfall, G is spatial characteristics of location or route, ξ and σ are random terms. When therisk exceeds its threshold, the alternative is considered risky and is eliminated from the choiceset. Assuming the random term σ − ξ are i.i.d. standard normally distributed, the probability
that an alternative will survive in criterion k is:
P (Rkt < θkqt ) = P (σkt − ξkqt < θkqt − Rk ) = Φ (θkqt − Rk ) ,(7)where Φ is the cumulative distribution function of the standard normal distribution. An alternative remains in the choice set when it is rejected by neither of the criteria. Thus the probability:Yρ(st+1 |st ) =Φ (θkqt (st+1 |st ) − Rk (st+1 |st )) .
(8)k∈{location,route}

2.4

Alternatives enumeration algorithm

Since full enumeration of alternatives is computationally demanding, we adopt an enumeration
algorithm to efficiently sample alternatives using the risk perception modeled in the previoussubsection 2.3. Each household will choose one node ji,k as the corresponding destination ofxi,k , the k-th alternative for origin node i. xi,k holds multiple nodes that have similar spatial
characteristics as seen from i. Below is the enumeration algorithm for a household:
1. Pick an origin node i and an alternative xi,k
2. Extract Ji,k , the set of nodes that are included in xi,k
3. Calculate the sampling probability for each node j in the set Ji,k
4. Generate a random number of uniform distribution, and choose node ji,k
5. Repeat steps for all k and i
The sampling probability Psample,i,k (j) in step 3 is normalized by ρ(st+1 |st ):ρ(j|i).
j∈Ji,k ρ(j|i)(9)

Psample,i,k (j) = P

3RESULTS

3.1

Evacuation behaviors in the 2018 heavy rain disaster

Kure, Hiroshima was one of the hardest hit in the 2018 heavy rain disaster in western Japan.
The heavy rain in early July caused floods and landslides in Hiroshima prefecture, which ranked
first in its casualties of 150. Kure had the highest number in the prefecture with 29 deaths.
A survey was conducted among the residents of Kure about their evacuation behaviors andhousehold characteristics. Their choice sets of evacuation location were included in the survey.
The results revealed many stayed in their houses instead of sheltering in evacuation sites, andthose who evacuated often left their homes when the rainfall was hardest.
The proposed model is implemented on survey data of Tenno, Kure. A zonal network thattakes into account spatial barriers such as rivers and elevation difference is used. Zones are
smaller when closer to the place of stay, and larger when they are farther away.
TRISTAN XI Symposium

Original abstract submittal

A. Kondo, J. Urata and E. Hato3.24Parameter estimation

Estimation results of the choice set formation model indicated that more the rainfall and higher
the elevation of origin, lower the threshold. A lower threshold means small risks will be perceived
risky. Higher the elevation of destination and closer the destination from river, higher the location
risk will be. Crossing the river and a trip of long distance were considered a route risk. The
results align with the fact that damage was caused by flood and landslides.
Table 2 presents estimation results of two dynamic location choice models. Model 1 assumes
deterministic choice sets and model 2 is the proposed model. All attributes were significant andhad the expected signs. Staying in the same location brings positive utility and staying home
was better than staying elsewhere. A transition to relatives’ or friends’ houses were positive
too, though smaller than staying. Evacuation sites with larger capacity were more likely to bechosen, and a long distance was avoided. The two models compared, distance is more importantin model 1, because unrealistic options are not dropped out. A likelihood ratio test of the twomodels proved that the proposed model had better predictive power, where the improvement
was significant at 1%, shedding light on the significance of considering choice set formation.
Table 2 – Estimation result: Dynamic location choice
1. Traditional
Attributes
Stay: homea
Stay: not homea
Not stay: relatives/friendsa
Capacity of evacuation shelter(persons, ln/10)
Distance: owns car (m, ln)
Distance: no car (m, ln)
Discount Factor

2. Proposed

Param.

t-Stat.

Param.

t-Stat.

2.47
1.92
1.52
0.38
-0.37
-0.40
0.74

3.10**
2.33*
3.48**
2.14*-3.36**-3.50**
9.20**

3.08
2.67
1.67
0.26
-0.23
-0.20
0.82

3.72**
2.98**
3.75**
1.70†-1.93†-1.65†
8.10**

Observations
1651
1651
LL(0)
-2859.91-2069.44
LL(C)b-312.55-283.06
Final LL
-248.17-229.78*significant at 5%, **significant at 1%
a Included as a dummy variableb A model with only a stay-dummy, discount factor is fixed to estimated value

4DISCUSSION

Extending the works of Rust (2016) and Kaplan et al. (2011), we proposed a dynamic evacuation
location choice model that incorporates choice set formation by introducing the ρ, the probabilityof evacuation location candidate’s survival. Our simple example demonstrated the update inchoice preference when ρ is considered. We collected actual evacuation data that surveys requiredcomponents in our proposed model, such as households’ choice sets, which is rarely surveyed.
Estimation results proved that our methodology is superior to traditional models, which does
not consider choice set formation.

References
Kaplan, Sigal, Bekhor, Shlomo, & Shiftan, Yoram. 2011. Development and estimation of a semicompensatory residential choice model based on explicit choice protocols. The Annals of RegionalScience, 47(8), 51–80.
Manski, Charles F. 1977. The structure of random utility models. Theory and Decision, 8(7), 229–254.
Oyama, Yuki, & Hato, Eiji. 2017. A discounted recursive logit model for dynamic gridlock network
analysis. Transportation Research Part C: Emerging Technologies, 85(12), 509–527.
Rust, John. 2016. Dynamic Programming. The New Palgrave Dictionary of Economics, 1–26.

TRISTAN XI Symposium

Original abstract submittal