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Modifiable Attribute Cell Problem in Population Synthesis for Land-Use Microsimulation

Noriko Otani (Tokyo City University)

Nao Sugiki (Docon Co., Ltd.)

Kazuaki Miyamoto (Tokyo City University)

Land-Use Microsimulation

A popular approach to describe detailed changes in land use and transportation

Micro-level modeling of a dataset of individuals

Micro-data

Require micro-data for the base year

Synthesize data based on

Iterative Proportional Fitting (IPF) method

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IPF Method

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1 2 j Σ

1 Z11 Z12 Z1j Σ

2 Z21 Z22 Z2j Σ

Σ

i Zi1 Zi2 Zij Σ

Σ

Σ

Σ Σ Σ Σ Σ Σ Σ

Control TotalAttribute 2

Att

rib

ute

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Cell-based Synthesis

Control Total

Pre-defined categories

Generate the number

of agents

given by the census data 　 etc.

Analogy : Modifiable Area Unit Problem

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Spatial analysis The results vary according to the spatial

zoning model Two factors

Scale of unitsType of units

Cell Organization

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1 2 3 Σ

1 Σ

2 Σ

3 Σ

Σ Σ Σ Σ

1 2 3 Σ

1 Σ

2 Σ

3 Σ

Σ Σ Σ Σ

1 2 3 4 5 6 Σ

1 Σ

2 Σ

3 Σ

4 Σ

5 Σ

6 Σ

Σ Σ Σ Σ Σ Σ Σ

Elemental set of cells

Combine categories

Which is better?What is the best?

Modifiable Attribute Cell Problem (MACP)

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Optimization problem for microsimulation

Target output : “key output variable”

Base of decision makingCondition

Benchmark : Elemental set of cells

(pre-defined categories)

Constraint : No significant difference of the key output variable from the benchmark

Goal : Minimize the number of cells

Computational Complexity of MACP

Possible number of cell organization Continuous-valued attribute

16 for 5 categories512 for 10 categories524,288 for 20 categories

Categorical attribute52 for 5 categories115,975 for 10

categories51,724,158,235,372 for 20

categories7

Apply Symbiotic Evolution

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Symbiotic Evolution

One kind of “Genetic Algorithm”

Optimization algorithm Imitates biological evolution process Applicable to various problems

Parallel evolution of two population Whole-solution = Combination of partial

solutions Partial-solution

Avoid local minimum and find good solution

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Flowchart of Symbiotic Evolution

Initialization

Evolution

Evaluation

G generation?No

Yes

End

Start

Partial-solution population

Whole-solution populationBest whole-solution

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For continuous-valued attributes Bit string

Length : the number of categories the adjoining same bits = a combination of

some categories

Partial-solution (1)

000111011110000000

① ④③② ⑤Serial numbers for combination of categories

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For categorical attributes String of binary numbers

Partial-solution (2)

101011110110101110

① ①③② ③Serial numbers for combination of categories

③↓5 563 66

↓ ↓ ↓ ↓ ↓Decimal numbers

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Combination of pointers for partial solution

Partial-solution population

Whole-solution

011100000111100001

011110000110011000000001111100110001

001111010000111100

000111110001100000

001111110001110001

1st attribute

2nd attribute3rd attribute

For a whole-solution Iw Difference of the key output value

Fitness value

Fitness Value (1)

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)keyv(

|)keyv()keyv(|)diff(

element

IelementI ww

otherwiseMAX_VALUE

)diff()diff(10000)cellnum()fit(

RIIII wwww

Elemental set of cells

Key output variable

Constraint

For a Partial-solution Ipthe best fitness value in whole-solutions that are pointed by the partial-solution

Fitness Value (2)

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)fit(max)fit( wII

p IIpw

Case Study (1)

Data obtained from the person-trip-survey for the

Sapporo metropolitan area in Japan 5,000 persons

Attribute Age

18 categories (0-9, 10-14, 15-19, ..., 85-89, >90)

Work status

5 categories (primary industry, secondary industry, tertiary industry, student, housewife or other)

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Case Study (2)

Microsimulation model Aging Death Birth Monte Carlo

simulation Work status change

Key output value Trip generation number after 5 years

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Categories of work status => one categoryCategories of age => five categories

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Results

Category of agediff(Iw)0

-9

10-

14

14-

19

20-

24

25-

29

30-

34

35-

39

40-

44

45-

49

50-

54

55-

59

60-

64

65-

69

70-

74

75-

79

80-

84

85-

89

90-

1 8.5×e-9

2 1.1×e-6

3 1.3×e-6

Baby, Kindergartener, Elementary school student, Junior high school student

High school student, College student, Young worker

Very busy workerPeople who enjoy their life after retirementPeople who enjoy their life in their house

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Conclusion

Addressed the modifiable attribute cell problem in cell-based population synthesis for microsimulation

Proposed a method for the cell organization

Proved the usefulness by simple case study

Please ask questions in easy English...19

Genetic Algorithm

Optimization algorithm Chromosome = Solution of a problem

１０ ０ １０ １ ０１ ０ １０ ０

１０ １ ００ １ １０ ０ ０１ ０

１０ ０ １０ ０ ０１ ０ １０ １・・・

Population

１０ ０ １０ １ ０１ ０ １０ ０

１０ １ ００ １ １０ ０ ０１ ０Parents

１０ ０ １０ １ １

１ ０ ０１ ０

Children１０ ０ １０ １ １ １ ０ ０１ ０

Crossover

Mutation

１０ ０ 1０ １ １０ ０ ０１ ０

１０ １ ００ １ ０

０ ０ １０ ０

１０ １ ００ １ ０ ０ ０ １０ ０

１０ １ ００ １ ０ ０ １０ ００

Cannot keep good partial solutionsConverge on a local minimum