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

1. Simulated annealing
A heuristic method for optimisation
Ferdinand Diermanse, Deltares

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. 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. 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. 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. 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. Case study 1 – drought risk analysis time series
7

8. Case study 1 – drought risk analysis time series
8

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. Case study 1 – drought risk analysis time series
10
ARMA
SA

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. Complex: multiple flood defences; time dependence
1
2
Protectionlevel
time

13. Lake system – even more complex

14. Benchmark: discrete linear optimisation problem
February
903,000 variables
32,000 constraints
Solved with CPLEX (IBM)

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. 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. 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. 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. 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. Joint occurrence probabilities - Myanmar

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. 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