1. Modifiable Attribute Cell Problem and a Method of Solution for Population Synthesis in Land-Use Microsimulation
Noriko Otani (Tokyo City University)
Nao Sugiki (Docon Co., Ltd.)
Varameth Vichiensan (Kasetsart University)
Kazuaki Miyamoto (Tokyo City University)

2. 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

3. Generate the number of cells
IPF Method
Cell-based Synthesis
Control Total
Pre-defined categories
Attribute 2 1 2 j Σ
Z11
Z12
Z1j
Z21
Z22
Z2j i
Zi1
Zi2
Zij
Generate the number of cells
Result of a simulation depends on the pre-defined categories
given by the census data　etc.
Attribute 1
Control Total

4. Analogy : Modifiable Area Unit Problem
Spatial analysis
The results vary according to the spatial zoning model
Two factors
Scale of units
Type of units

5. Modifiable Attribute Cell ProblemΣ
xij Σ
xij

6. Cell Organization Elemental set of cells Combine categories1 2 3 Σ 1 2 3 4 5 6 Σ
Combine categories 1 2 3 Σ
Which is better?
What is the best?

7. Position of Cell Organization in Microsimulation
Full-scale IPF estimation and simulation
The best organized cell set
Cell organization
Entire study area
a few zones

8. A method to solve MACP Optimization problem for microsimulation
Target output : “key output variable”
Base for decision making
Condition
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

9. Stochastic Test of Key Output Variable
Key output variable is a stochastic variable.
For it is obtained by Microsimulation.
The distribution is obtained by conducting plural simulations.
No Significant difference
Significant difference
Significant difference
Candidate
Microsimulations
Elemental set of cells

10. The procedure to find the best organized cell set
Several cases of cell organization that generate large are found by aggregating the elemental cell set.
Cell-based estimation of the base-year data is conducted by using a representative IPF method for those cases.
Forecasting is performed using a simple microsimulation model.
Comparison is made based on the variations in the key output variable, using a Student’s T-test. If no significant difference is noted between the distributions of the key output value of the elemental cell set and of the organized cell set to be compared, the former cell set is accepted.
The case with the minimum number of cells is considered to be the best cell organization, subject to the condition described earlier.

11. Flowchart of Naive Method
c ← the elemental cell set
bestc ← c
Make base-year data using c and execute microsimulation M times
Make the other organized cell set c’
|bestc| < |c’|
Make base-year data using c’ and execute microsimulation M times
Significant difference?
bestc ← c’
Other organized cell set?
bestc
|c| : number of cells in c
yes no
Student’s T-test of the key output value between c and c’

12. Computational Complexity of MACP (1)
Possible number of cell organization
Continuous-valued attributes
16 for 5 categories
512 for 10 categories
524,288 for 20 categories

13. Computational Complexity of MACP (2)
Possible number of cell organization
Categorical attributes
52 for 5 categories
115,975 for 10 categories
51,724,158,235,372 for 20 categories

14. Computational Complexity of MACP (3)
Possible number of cell organization
The number of organized cell sets is a product of the numbers of combinations of categories for all attributes.
This can become a huge number.

15. Flowchart of Naive Method
c ← the elemental cell set
bestc ← c
Make base-year data using c and execute microsimulation M times
Make the other organized cell set c’
|bestc| < |c’|
Make base-year data using c’ and execute microsimulation M times
Significant difference?
bestc ← c’
Other organized cell set?
bestc
|c| : number of cells in c
yes no
Student’s T-test of the key output value between c and c’

16. Computational Complexity of MACP (3)
Possible number of cell organization
The number of organized cell sets is a product of the numbers of combinations of categories for all attributes.
This can become a huge number.
Apply Symbiotic Evolution

17. 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

18. Flowchart of Symbiotic Evolution
Start
Initialization
Evaluation
Partial-solution population
Evolution
G generation? No
Whole-solution population
Yes
Best whole-solution
End

19. 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)

20. Case Study (2) Microsimulation model Aging Death
Birth Monte Carlo simulation
Work status change
Key output variable
Trip generation number after 5 years

21. Trip Generation Rate

22. Parameters Parameter Name Value Whole-solution population size 500
Partial-solution population size
Mutation rate Pm
0.01
Rejection rate in T-test
0.05
Microsimulation frequency M 10
Maximum generation G

23. Combinations of Age Categories
Test No.
Age Categories - 9 10 14 15 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 A B C D E F 2 3 4 5 6 7 8

24. Best Organized Cell Set
Numerical Results
Test No.
Number of Cells
T-value
Best Organized Cell Set
Elemental Cell Set
Mean
Variance 1 12 2 3 14 4 5 6 7 16 8 9 10 18

25. Results Work status => 2 categories
(“housewives and others” and the others)
Age => 6-9 categories
students, workers
housewives, others
Category of age
tvl(Iw) - 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-
7.6×e-6
Children,
High school student
College student, Young worker
Very busy worker,
active housewives
People who enjoy their life in their house
People who enjoy their life actively
Young parents

26. 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
Appropriate set of cells for microsimulation
Characteristics of attributes for the key output variable

28. Genetic Algorithm Optimization algorithm
Chromosome = Solution of a problem １ ０
・・・
Population １ ０ １ ０ ０ １
Parents １ ０ １ ０ １ ０
Crossover
Children １ ０ １ ０ １ ０ ０ １
Cannot keep good partial solutions
Converge on a local minimum
Mutation １ ０ 1 １ ０

29. 000111011110000000 ① ② ③ ④ ⑤ Partial-solution (1)
For continuous-valued attributes
Bit string
Length : the number of categories
the adjoining same bits = a combination of some categories ① ② ③ ④ ⑤
Serial numbers for combination of categories

30. Partial-solution (2)
For categorical attributes
String of binary numbers 5 3 6 6 5 6
Decimal numbers ↓ ↓ ↓ ↓ ↓ ↓ ① ② ③ ③ ① ③
Serial numbers for combination of categories

31. Whole-solution Combination of pointers for partial solution
2nd attribute
1st attribute
3rd attribute
Partial-solution population

32. Fitness Value For a whole-solution Iw T-value
For a Partial-solution Ip
the best fitness value in whole-solutions that are pointed by the partial-solution
T-value
Number of cells