A Personal Navigation System with a Schedule Planning Facility Based on Multi-Objective Criteria

Takayuki Shiraishi, Munenobu Nagata, Naoki Shibata*, Yoshihiro Murata, Keiichi Yasumoto, and Minoru Ito

Nara Institute of Science and Technology (NAIST)*Shiga University

Background

Navigation systems have become popular Car navigation systems EZ Naviwalk (pedestrian navigation by KDDI)

• can compute the “best” route between two locations and navigate though map

• insufficient for sightseeing tours• tourists want to travel multiple destinations

within restricted time

P-Tour: Personal navigation system for sightseeing tour (see [7] for details)

Multiple destinations with•Relative importance•Time Restrictions

Schedule•order of visiting•arrival/departure time at each destination•detailed route

Start(9:00)and

Goal(20:30)

Horyujitemple

The ruins of Heijopalace 10:30

Yamato Koriyamacastle15:30

YakushijiTemple14:30

Kofukujitemple

Todaijitemple12:30

Nara park11:30

Kintetsu Nara Station

JR Nara station

Kasugataisyashrine

KintetsuGakuenmaestation 18:30

dinner

NAIST

lunch

Saidaijitemple 10:35

Snapshots of P-TourCalculation/display of schedule

Current position

Navigation

Time tableRouteUser input

at each destroute to next dest

System structure of P-Tour

Criteria for sightseeing tours

A: As many destinations as possible B: Minimizing walking distance C: Minimizing total travel expense etc

tradeoff

Optimized for criterion Bvarious compromises

when we consider multiple criteria, many candidate solutions worth

considering.

Optimized for criterion A

Need for temporal guidance

Users may not follow the schedule due to traffic jam/accident staying more/less time at a destination intentional change of destinations, and so on

Mechanism to detect following situations should be provided user is on time, behind, or ahead of schedule user entered wrong route

warns user to hurry, show modified schedule, etc

Our proposal

We propose following new functions

Multi-objective schedule planning: allow users to obtain best tour schedules

under multiple conflicting criteria

Temporal guidance: checks whether the user is behind/ahead of

the schedule, and warns the user if necessary

Outline

Schedule planning facility with multi-objective criteria

Warning mechanism for user to follow the schedule

Experimental results Conclusion

Tradeoff among conflicting criteria

Existing systems use one objective function multiple objectives unify into one function

Criterion A: total expense Criterion B: total distance...

f ＝ （ eval. on A ） + （ eval. on B ） + ...

find solutions which maximize f for given , ,...

• How to determine appropriate coefficients?coefficients

How to adjust coefficients

Users can find best coefficients by following steps

new coefficients(=-0.2, =0.8)

serversearch engine

coefficients(=-0.5, =0.5)

I want to go to

National museum.

schedule

new schedule

New

It takes a long way to get there... I won’t go.

× This kind of trial-and-error interaction may take a lot of time

Our approach

compute multiple solutions with various proportions of multiple criteria at one time

let user choose best one intuitively

Schedule with minimum expense

Schedule traveling important sight spots

Other candidates

model as multi-objective optimization problem

What is “multi-objective optimization problem”?

ex. go to Nagoya with public transportation Multiple criteria

travel expense time to get there

Many schedules

Osaka

NagoyaShinkansen

express

time: 1hr, expense: $60

normal train

time:3hr, expense:$30

Airplane and normal train (via Tokyo)

time:6hr? expense:

$200?

multi-objective optimization problem is to extract only worthy candidates from many possible solutions

not worthy

Dominant solutions

Normal train

Shinkansen

time: 1hr, expense: $60

time: 3hr, expense: $30

Airplane and normal train

time: 6hr, expense:

$200

cost

time

dominate

dominateNot dominate each other

Solutions which are not dominated by any other:

Pareto optimal solutions

Pareto optimal solutions

cost

time

Set of candidate solutions

Set of pareto optimal solutions

Multi-objective optimization problem

optimization

optimization

Pareto optimal solutions

We want to uniformly obtain various Pareto optimal solutions among multiple criteria

optimization

optimization

cost

time

Set of candidates+

optimized for time

+

optimized for expense

+compromises

worth considering

+

Searching Pareto optimal solutions

We use Genetic Algorithm (GA)

cost

time

Set of candidates

Set of Pareto optimal solutions

＋

＋＋＋＋

Evolution of candidates

Why GA?•GA can obtain semi-optimal solutions rather quickly.•Since GA evolves multiple candidate solutions simultaneously, it is easy to find various/multiple Pareto optimal solutions at one time.

How to obtain various solutions?

cost

time

＋＋＋＋

＋We want to uniformly obtain Pareto optimal solutions.

cost

time

＋＋＋＋＋

Only part of Pareto optimal solutions may be obtained.

＋＋＋＋＋

undesirable

Elite preservation strategy of GApreserve candidate solutions far from the nearest neighborfor next generation.

How to obtain high quality solutions with GA?

cost

time

Set of candidates＋

＋＋

＋ ： solutions by GA

Local searchsearch better solutions in the space around GA solutions

With local search, we can obtain high quality solutions difficult to find by GA

＋

＋＋

＋ ： solutions by local search

Outline

Schedule planning facility with multi-objective criteria

Warning mechanism for user to follow the schedule

Experimental results Conclusion

Warning mechanism for users to follow schedule System warns user when detecting the

following undesirable situations.

Ahead of schedule

Behind schedule

Wrong route

only show the fact

warn when the delay becomes large

warn immediately

Undesirable situations

How to detect?

calculate user’s expected location at time t departure time at previous dest route to next destination moving speed

road/street

node （ intersection ）

Expected location at time t

nodei

nodei+1

nodei+2

A

B

are known

How to detect? (Cont’d)

Expected location

User’s current location by GPS

perpendicular line

Errory

Errorx

Errorx > threshold Wrong routeErrory > threshold Behind or ahead of schedule

Outline

Schedule planning facility with multi-objective criteria

Warning mechanism for user to follow the schedule

Experimental results Conclusion

Experiments and evaluation

We have investigated whether the proposed method can obtain various solutions how good solutions can be obtained how fast solutions can be computed

Used two conflicting criteria travel expense (sum of admission fee) minimize satisfaction degree (sum of importance degree) maximize

User input moving speed ： 30km/hour (assuming car) start and goal ： NAIST, 9:00am － 8 ： 00pm Candidate destinations ： 30 in Northern Nara prefecture

Map Northern Nara Map 2500 by GSI (Geographical Survey Institute) Num of nodes: 29871

Variety of obtained schedules

Satisfaction (maximize)

Exp

en

se (

min

imiz

e)

Satisfaction253

Expense2620 yen

Satisfaction126

Expense0 yen

Satisfaction210

Expense1220 yen

Optimality of computed schedules

Satisfaction (maximize)

Exp

en

se

(min

imiz

e)

Number of destinations: 18

optimal solutionApproximate solutions(computation time: 15sec)

×

Time to calculate optimal solutions

Our proposed method

16 destinations 2,807 seconds = about 46 minutes17 destinations 9,861 seconds = about 2.7 hours18 destinations 29,587seconds = about 8.2 hours

Global optimization (branch and bound method)

•#candidate solutions=400•#Generations=400•With local search

About 14.5 seconds(independent of number

of destinations)

with j2sdk 1.4.2 on Athlon 2500+, 512Mbyte Memory, Debian GNU linux

Conclusion

We proposed two new functions for personal navigation systems function for planning best tour schedules with

multiple conflicting criteria warning mechanism which helps users to follow the

schedule We implemented and integrated the proposed

functions into P-Tour our GA-based algorithm can compute schedules

in practical time (around 15 seconds) precisely (close to optimal solutions)