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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  (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

H EURISTIC S OLVER 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

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT 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

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 5.0 ac cluster area ? Clustered area No 5.0 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 4.5 ac cluster area ? Clustered area No 9.5 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 5.8 ac cluster area ? Clustered area No 15.3 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 6.1 ac cluster area ? Clustered area No 21.4 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 5.2 ac cluster area ? Clustered area No 26.6 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 7.2 ac cluster area ? Clustered area No 33.8 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 8.1 ac cluster area ? Clustered area No 41.9 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 8.8 ac cluster area ? Clustered area No 50.7 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 7.7 ac cluster area ? Clustered area No 58.4 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 7.8 ac cluster area ? Clustered area No 74.0 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 8.9 ac cluster area ? Clustered area No 82.9 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 8.2 ac cluster area ? Clustered area No 91.1 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Adjacent Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Selected polygon area > minimum 7.8 ac cluster area ? Clustered area No 98.9 ac Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon No action Selected Clustered Update cluster area Minimum cluster 100.0 ac Is current cluster Yes Selected polygon area > minimum 7.8 ac cluster area ? Clustered area No Stop clustering 106.8 ac polygons Identify adjacent polygons Select random adjacent polygon

B UILDING C LUSTERS OF P OLYGONS FOR T REATMENT Clustering adjacent stand polygons  Select random polygon Update cluster area Minimum cluster 100.0 ac Is current cluster Yes Selected polygon area > minimum 7.8 ac cluster area ? Clustered area No Stop clustering 106.8 ac polygons Identify adjacent polygons Select random adjacent polygon

H EURISTIC S OLVER Objective is to minimize expected loss  ∑∑ × Minimize Loss P c t c t , , ∈ ∈ t T c C where : c : Index of grid cells (pixels) t : Index of time period Loss c,t : Expected loss value for grid cell c for period t , based on the flame length predicted by MTT P c,t : Probability of cell c being burned in period t, based on the fire arrival time predicted by MTT

S TEPS IN Data passed to Solver: EACH I TERATION • Landscape fuel parameters • Fire scenario • Objective Function • Constraints • Adjacent Polygons • topography Build or modify a solution (timing and placement of treatments) Update the landscape fuel parameters for each period Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) No Calculate Is SA stopping Report Best Found objective function value criteria met ? Solution (total expected loss value) Yes

S TEPS IN Data passed to Solver: EACH I TERATION • Landscape fuel parameters • Fire scenario • Objective Function • Constraints • Adjacent Polygons • topography Build or modify a solution (timing and placement of treatments) Update the landscape fuel parameters for each period Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) No Calculate Is SA stopping Report Best Found objective function value criteria met ? Solution (total expected loss value) Yes

S TEPS IN Data passed to Solver: EACH I TERATION • Landscape fuel parameters • Fire scenario • Objective Function • Constraints • Adjacent Polygons • topography Build or modify a solution (timing and placement of treatments) Update the landscape fuel parameters for each period Run MTT for each planning period and retrieve results by pixel ( flame length , arrival time) No Calculate Is SA stopping Report Best Found objective function value criteria met ? Solution (total expected loss value) Yes