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H EURISTIC S OLVER Greg Jones , Jody Bramel, and Kurt Krueger , USDA Forest Service RMRS Woodam Chung , Edward Butler, Marco Contreras-Salgado , The University of Montana H EURISTIC S OLVER Builds and tests alternative fuel treatment schedules

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SLIDE 1

Greg Jones, Jody Bramel, and Kurt Krueger, USDA Forest Service RMRS Woodam Chung, Edward Butler, Marco Contreras-Salgado, The University of Montana

HEURISTIC SOLVER

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SLIDE 2

HEURISTIC SOLVER

Builds and tests alternative fuel treatment schedules (solutions) at each iteration

In each iteration:

Evaluates the effects of each alternative schedule on the constraints

Evaluates the expected loss over time

Selects the fuel treatment schedule that provides the minimum overall expected loss over time while satisfying the constraints

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SLIDE 3

HEURISTIC SOLVER

Uses Simulated Annealing (SA) Algorithm to select treatments

The SA algorithm is based on simulating cooling of materials in a bath (annealing)

Heuristic optimization technique widely used to solve large combinatorial problems in various fields

Assignment/scheduling problems

Transportation network problems

Manufacturing problems

Monte Carlo approach that uses a local search

A subset of all possible solutions is explored by moving to through neighbor solutions

Some lower quality solutions are accepted to avoid solutions stagnation at local optimum

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SLIDE 4

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

Assigns fuel treatments to stand polygons (GIS layer)

Treating individual stands is generally not effective at changing fire behavior at the landscape level (Finney 2006)

Solver builds clusters of adjacent polygons to form larger treatment units

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SLIDE 5

Clustering adjacent stand polygons

No action

Select random polygon

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 6

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 5.0 ac Clustered area 5.0 ac

No action Selected Adjacent

Select random polygon Update cluster area Is current cluster area > minimum cluster area ? Identify adjacent polygons No Select random adjacent polygon

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 7

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 4.5 ac Clustered area 9.5 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 8

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 5.8 ac Clustered area 15.3 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 9

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 6.1 ac Clustered area 21.4 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 10

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 5.2 ac Clustered area 26.6 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 11

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 7.2 ac Clustered area 33.8 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 12

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 8.1 ac Clustered area 41.9 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 13

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 8.8 ac Clustered area 50.7 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 14

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 7.7 ac Clustered area 58.4 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 15

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 7.8 ac Clustered area 74.0 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 16

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 8.9 ac Clustered area 82.9 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 17

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 8.2 ac Clustered area 91.1 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 18

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 7.8 ac Clustered area 98.9 ac

No action Selected Adjacent Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 19

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 7.8 ac Clustered area 106.8 ac

No action Selected Clustered

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No Stop clustering polygons Yes

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 20

Clustering adjacent stand polygons

Minimum cluster 100.0 ac Selected polygon 7.8 ac Clustered area 106.8 ac

Select random polygon Identify adjacent polygons Select random adjacent polygon Update cluster area Is current cluster area > minimum cluster area ? No Stop clustering polygons Yes

BUILDING CLUSTERS OF POLYGONS FOR TREATMENT

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SLIDE 21

HEURISTIC SOLVER

Objective is to minimize expected loss

t c t c T t C c

P Loss Minimize

, ,

×

∑∑

∈ ∈

where : c : Index of grid cells (pixels) t : Index of time period Lossc,t : Expected loss value for grid cell c for period t, based

  • n the flame length predicted by MTT

Pc,t : Probability of cell c being burned in period t, based

  • n the fire arrival time predicted by MTT
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SLIDE 22

STEPS IN

EACH ITERATION

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

slide-23
SLIDE 23

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

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SLIDE 24

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

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SLIDE 25

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

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SLIDE 26

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

slide-27
SLIDE 27

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

slide-28
SLIDE 28

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

slide-29
SLIDE 29

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

slide-30
SLIDE 30

Build or modify a solution (timing and placement of treatments) Is SA stopping criteria met ? No Data passed to Solver:

  • Landscape fuel

parameters

  • Fire scenario
  • Objective Function
  • Constraints
  • Adjacent Polygons
  • topography

Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) Calculate

  • bjective function value

(total expected loss value) Report Best Found Solution Yes Update the landscape fuel parameters for each period

STEPS IN

EACH ITERATION

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SLIDE 31

TREATMENT SELECTION

Selection of treatments and location of clusters to develop alternative schedules (solutions) is conducted in two phases

Phase I: Add clusters until the maximum area feasible to treat is reached in each period

Iteration zero – “no action”

Following iterations – randomly locate and add feasible clusters over the landscape

Phase II: Replace clusters with new clusters to find the best allocation and timing of fuel treatments

At each iteration – randomly select a new cluster and remove a previously selected cluster

Continues until stopping rule is reached

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SLIDE 32

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

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SLIDE 33

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

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SLIDE 34

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

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SLIDE 35

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-36
SLIDE 36

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-37
SLIDE 37

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-38
SLIDE 38

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-39
SLIDE 39

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

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SLIDE 40

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-41
SLIDE 41

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-42
SLIDE 42

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-43
SLIDE 43

Lower bound Upper bound

400 650 P1 P2

Phase I – add a cluster

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

Numerous tries found no addition clusters could be added without exceeding the 650–ac Upper Bound ===> Go to Phase II

TREATMENT SELECTION

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SLIDE 44

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-45
SLIDE 45

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-46
SLIDE 46

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-47
SLIDE 47

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-48
SLIDE 48

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-49
SLIDE 49

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-50
SLIDE 50

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-51
SLIDE 51

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-52
SLIDE 52

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-53
SLIDE 53

Lower bound Upper bound

400 650 P1 P2

Phase II – change cluster locations and timing

  • Evaluate feasibility
  • Run MTT algorithm

arrival time

flame length

  • Calculate expected loss

Period 1 Period 2

Area constraints Period 1  400 – 650 acres Period 2  400 – 650 acres

TREATMENT SELECTION

slide-54
SLIDE 54

SOLVER PERFORMANCE

Algorithm performance

Phase I Phase II “no action”

Expected Loss Iteration Number

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SLIDE 55

HARDWARE REQUIREMENTS

AND SOLUTION TIMES

OptFuels has parallel computing capabilities that use all available processors in a machine

For an area of 34,600 acres with 2 treatment period the solver takes:

Computer Type (Processor ) Number of processor/Th reads Processor Speed Iterations per minute Solution times Risk Assessment Run Low Intensity Run (~400 iterations) Regular desktop (Intel Core 2 4300) 2 1.8 GHz 0.4 Several minutes 18 hrs Multi-processor Laptop (Intel i7-2720QM) 8 2.33 GHz 2.5 Seconds 2.5 hrs Multi-processor workstation (Intel Xeon X5570) 8 2.93 GHz 3.5 Seconds 2 hrs

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SLIDE 56

HEURISTIC SOLVER ENHANCEMENTS

Adding selection of individual stands for treatments in the latter stages of Phase II.

This selects individual stands for treatment that lie between treatment clusters where the area is too small to generate another cluster

Adding the ability to schedule treatments to minimize expected loss from two or more fire scenarios.

Different ignition points

Different wind direction and speed

Integrating OptFuels into IFT-DSS

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SLIDE 57

RESULTS AVAILABLE FROM OPTFUELS

Spatial and temporal treatment schedule that can be mapped in GIS

Expected loss

Effects functions evaluated for the treatment schedule could include:

Treatment costs, treatment acres, volumes of treatment products (if any), treatment revenues (if any), sediment yields, resource effects (eg. acres of aspen)

Outputs produced by FlamMap MTT for both the treated and untreated landscapes:

GIS display of flame length and arrival time.

LCP files that could be used for additional FlamMap analyses.

FVS stand parameters for the projected stands for both the treated and untreated landscapes:

Tree species, stand size, stand volume, etc.

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SLIDE 58

THANK YOU!

Questions?