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Simulated annealing
A heuristic method for optimisation
Ferdinand Diermanse, Deltares
Simulated Annealing (SA)
o Named after the chemical process
of “annealing”
o It is a ‘heuristic’ method which
means it loo...
Applications
1. Generate (lengthy) synthetic time series for improved drought risk
analysis
 Netherlands
 California
2. ...
Objective
Look for a “solution vector” X that minimizes a cost function
4
12 107 38 82 47 5
x1 x2 x3 x4 xn-1 xn
…
X
Exampl...
Concept of simulated annealing
5
Data
Generate initial
Solution for X
Objective function
input
Modify X
Objective function...
Historical
records
Extended
synthetic
time series
Derive stochastic
model
Frequency
analysis of
droughts
Drought impact
si...
Case study 1 – drought risk analysis time series
7
Case study 1 – drought risk analysis time series
8
Case study 1 – drought risk analysis time series
9
lag (months)
autocorrelation
Cherry Valley
0 2 4 6 8 10 12 14 16 18 20
...
Case study 1 – drought risk analysis time series
10
ARMA
SA
CASE STUDY 2: OPTIMAL DIKE DESIGN
Investment costs
Expected damages
Total costs
Costs
Level of protection
- Cost: construc...
Complex: multiple flood defences; time dependence
1
2
Protectionlevel
time
Lake system – even more complex
Benchmark: discrete linear optimisation problem
February
903,000 variables
32,000 constraints
Solved with CPLEX (IBM)
Results
15
t
veiligheidsniveau
IJsselmeer
2050 2100 2150 2200 2250
0
1
2
3
4
5
6
7
8
9
10
zwf
nop
nfl
wfn
wie
t
veiligheid...
Case study 3 – flood risk analysis South East Asia
16
o The World Bank
o Lao PDR, Cambodia and Myanmar
o Objective: increa...
The “compound event challenge”
17
90 92 94 96 98 100 102 104 106 108 110
10
15
20
25
30
35
Cambodia
Lao
Myanmar
Simulate j...
Joint occurrence – joint probabilities
1.00 0.69 0.69 0.46 0.26 0.40 0.06
0.69 1.00 0.66 0.43 0.26 0.40 0.06
0.69 0.66 1.0...
Joint occurrence probabilities - Lao
synthetic series
observeddata
percentage joint occurrences for each location pair; La...
Joint occurrence probabilities - Myanmar
Population affected
21
empirical frequency of exceedance (per year)
Populationaffected
population affected; Country: Cambo...
Generic conclusions on SA
+
 Extremely flexible method, as you can define the cost function (with
multiple sub-functions ...
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DSD-INT 2018 Simulated annealing - Diermanse

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Presentation by Ferdinand Diermanse (Deltares) at the Data Science Symposium 2018, during Delft Software Days - Edition 2018. Thursday 15 November 2018, Delft.

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DSD-INT 2018 Simulated annealing - Diermanse

  1. 1. Simulated annealing A heuristic method for optimisation Ferdinand Diermanse, Deltares
  2. 2. Simulated Annealing (SA) o Named after the chemical process of “annealing” o It is a ‘heuristic’ method which means it looks for “good” solutions, not necessarily the optimum o Therefore useful in applications where finding the optimal solution is practically infeasible 2
  3. 3. Applications 1. Generate (lengthy) synthetic time series for improved drought risk analysis  Netherlands  California 2. Optimal dike design (timing and magnitude) 3. Simulation of joint occurrence of flood events in South East Asia 3
  4. 4. Objective Look for a “solution vector” X that minimizes a cost function 4 12 107 38 82 47 5 x1 x2 x3 x4 xn-1 xn … X Example: X: a synthetic time series Cost function: difference between X and observed time series (e.g. differences in mean, standard deviation, autocorrelation, etc)
  5. 5. Concept of simulated annealing 5 Data Generate initial Solution for X Objective function input Modify X Objective function improved? Accept new synthetic series yes Accept new synthetic series with probability p* no Stop? no Final solution X yes output
  6. 6. Historical records Extended synthetic time series Derive stochastic model Frequency analysis of droughts Drought impact simulation Case study 1 – drought risk analysis time series SA
  7. 7. Case study 1 – drought risk analysis time series 7
  8. 8. Case study 1 – drought risk analysis time series 8
  9. 9. Case study 1 – drought risk analysis time series 9 lag (months) autocorrelation Cherry Valley 0 2 4 6 8 10 12 14 16 18 20 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 observed generated lag (months) autocorrelation variable: discharge 0 2 4 6 8 10 12 14 16 18 20 -0.2 0 0.2 0.4 0.6 0.8 1 observed generated Rhine, discharge Rain, Cherry valley Cal. USA
  10. 10. Case study 1 – drought risk analysis time series 10 ARMA SA
  11. 11. CASE STUDY 2: OPTIMAL DIKE DESIGN Investment costs Expected damages Total costs Costs Level of protection - Cost: construction and maintenance - Benefit: reduction of flood risk
  12. 12. Complex: multiple flood defences; time dependence 1 2 Protectionlevel time
  13. 13. Lake system – even more complex
  14. 14. Benchmark: discrete linear optimisation problem February 903,000 variables 32,000 constraints Solved with CPLEX (IBM)
  15. 15. Results 15 t veiligheidsniveau IJsselmeer 2050 2100 2150 2200 2250 0 1 2 3 4 5 6 7 8 9 10 zwf nop nfl wfn wie t veiligheidsniveau IJsselmeer 2050 2100 2150 2200 2250 0 1 2 3 4 5 6 7 8 9 ijd mas vol sal ovl Solution with simulated annealing 0.2% higher costs than the global optimum (CPLEX)
  16. 16. Case study 3 – flood risk analysis South East Asia 16 o The World Bank o Lao PDR, Cambodia and Myanmar o Objective: increase financial resilience against flood events, o Rapid response financing if an event has more than X number of population affected
  17. 17. The “compound event challenge” 17 90 92 94 96 98 100 102 104 106 108 110 10 15 20 25 30 35 Cambodia Lao Myanmar Simulate joint occurrence of flood events at 130 locations. Joint occurrence probabilities have to be in accordance with observations
  18. 18. Joint occurrence – joint probabilities 1.00 0.69 0.69 0.46 0.26 0.40 0.06 0.69 1.00 0.66 0.43 0.26 0.40 0.06 0.69 0.66 1.00 0.57 0.37 0.51 0.06 0.46 0.43 0.57 1.00 0.43 0.51 0.00 0.26 0.26 0.37 0.43 1.00 0.43 0.00 0.40 0.40 0.51 0.51 0.43 1.00 0.00 0.06 0.06 0.06 0.00 0.00 0.00 1.00 90 95 100 105 110 10 15 20 25 30 35 year: 1981 03-Jul - 09-Jul 30-Apr - 06-May 26-Jul - 01-Aug 01-Sep - 07-Sep 09-Aug - 15-Aug Joint occurrence probability (130*129)/2 = 8385 joint probabilities
  19. 19. Joint occurrence probabilities - Lao synthetic series observeddata percentage joint occurrences for each location pair; Lao max abs diff: 0.001 mean abs diff: 0.000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
  20. 20. Joint occurrence probabilities - Myanmar
  21. 21. Population affected 21 empirical frequency of exceedance (per year) Populationaffected population affected; Country: Cambodia 10 -2 10 -1 10 0 10 1 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10 5 observed synthetic empirical frequency of exceedance (per year) Populationaffected population affected; Country: Cambodia 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 0 1 2 3 4 5 6 7 8 x 10 5 observed synthetic
  22. 22. Generic conclusions on SA +  Extremely flexible method, as you can define the cost function (with multiple sub-functions if desired)  Broadly applicable  Relatively straightforward, so easy to understand _  Computation times can be large, especially if the evaluation of the cost function is time consuming 22

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