Cyclone Solo did extensive damage to the forests which are home to many of our endemic species. We are particularly concerned about one region that can be roughly divided into nine sites, as shown in the map below:
Collectively, these sites are home to twenty significant species. The table below gives a list of the species that are found in each site:
Site
Species
0
12, 19
1
7, 11, 15, 18
2
3, 5, 6, 7, 12, 15
3
4, 14, 17
4
8, 10, 12, 18
5
1, 2
6
6, 8, 16
7
0, 12
8
8, 9, 12, 13, 18
At the moment our ecologists have assessed that each of these sites is in
a fragile state. Each month they can focus efforts on one of the fragile sites to turn it into a restored state, permanently saving all the species in that site from extinction.
Communication 12
Unfortunately, at the end of each month there is a probability 0.2 that a fragile site will have degraded into a lost state which can no longer be restored, losing all the associated species.
Based on the species data, our current plan is to prioritise restoring the sites in the following order:
2, 8, 4, 1, 6, 3, 7, 5, 0
We will definitely be able to restore Site 2 in the first month but, for example, if Site 8 is lost during the first month then in the second month we will work on restoring Site 4.
If we follow this plan, what is the expected number of species we will save? 14.24
Communication 13
Can you recommend a restoration strategy that would give a higher expected number of species saved? What would be the expected number of species saved?
14.90
Communication 14
In practice, once a site is lost it becomes more likely that neighbouring sites will also be lost. We think the probability of a site being lost in a given month can be quantified as 0.2 + 0.05 n, where n is the number of directly adjacent sites that have already been lost.
Taking this into account, what would the maximum expected number of species saved be now?
14.67
Communication 15
It has occurred to us that tourists really come to see species 1, 7, 10 and 12. Instead of maximising the expected number of species we save, what should we do if we wanted to maximise the probability of just saving all of these species? What would be the probability of being successful?
ÐèҪд communication 14 ºÍ 15 Óà dynamic programming
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