2

4

3

1 3

2

4

6

5

7

9

8

10

7

46

32

4

6 1

5 3

3

3

6

4

1

3

4

9

8

10

3

4

6

5

7

9

8

10

3

3

3

6

4

1

3

4

6

5

7

9

8

10

3+4

3+3

3+4

6+3

4+4

1+3

3

4

6

5

7

9

8

10

3+3

3+4

1+3

3

4

3

2

4

6

5

7

9

8

10

7

46

32

4

6 1

5

6

7

4

3

2

4

6

5

7

9

8

10

11

11

7

86

7

4

2

4

3

1 3

2

4

6

5

7

9

8

10

11

11

7

8

s f*4(s) x*4

8 3 10

9 4 10

Stage=4

s 8 9 f*3(s) x*3

5 4 8 4 8

6 9 7 7 9

7 6 7 6 8

Stage=3

s 5 6 7 f*2(s) x*2

2 11 11 12 11 5 or 6

3 7 9 10 7 5

4 8 8 11 8 5 or 6

Stage=2

s 2 3 4 f*1(s) x*1

1 13 11 11 11 3 or 4

Stage=1

Problem: The World Health Council has 5 additional medical teams that it can allocate among three different countries. The goal is to maximize the number of additional person-years of life. Estimates are available on how many additional person-years of life would result from the allocation of medical teams to each country.

Data for World Health Council

Thousands of additonal person-years of life

Number ofMedicalTeams Country 1 Country 2 Country 30 0 0 01 45 20 502 70 45 703 90 75 804 105 110 1005 120 150 130

5

Stage 3 (where stage is country)

s (state is remainingnumber of teams toallocate)

f*3(s)(benefits)

x*3best choice atthis stage

0 0 01 50 12 70 23 80 34 100 45 130 5

Stage 2 (where stage is country)

Number of teams to allocate to country 2

s 0 1 2 3 4 5 f*2 x*2 0 0 0 0 1 50 20 50 0 2 70 70 45 70 0 1 3 80 90 95 75 95 2 4 100 100 115 125 110 125 3 5 130 120 125 145 160 150 160 4

Stage 1 (where stage is country)

s 0 1 2 3 4 5 f*1 x*15 160 170 165 160 155 120 170 1

Best choice at stage 1 (when we have 5 teams to allocate)is to put one team to country 1. We then back up to countrytwo (where we now have 4 remaining teams), and allocate 3teams to country 2. We go back to stage 3 where we have 1remaining team, and allocate that to country 3.

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Age 1 Age 2 Age 3 Age 4 Age 5

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25gramsA 25 gram fish can contain 50 eggs at mostA 50 gram fish can contain 100 eggs at most75 g 150…

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25grams 50 eggs

0 eggs

A 25 gram fish gains enoughenergy to either grow to 75 gramsand not reproduce, or produce 50eggs and grow to 50 grams

225 grams

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400 eggs

0 eggs

A 100 gram fish gains enoughenergy to either grow to 200 gramsand not reproduce, or produce 400eggs and grow to 150 grams

225 grams

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Iterate process until get to 1st stage (age 1)

Accumulate fitness at each stage (in this case,fitness may depend on number of eggs produced, and survivalrate, which may differ depending on whether a fishreproduces or not

225 grams

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