Simulated Annealing

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Simulated Annealing
An Alternative Solution Technique for Spatially
Explicit Forest Planning Models
Sonney George
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Acknowledgement

• Dr. Marc E. McDill
• PA DCNR Bureau of Forestry

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Introduction
LP based Models
Xij acres allotted to the prescription from age
class i in period j and Cij, the corresponding
contribution to objective function
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Disadvantage

• Solution will not give the geographic location.

• E.g. harvest 350 acres from initial age class
  60-70 in Period 1

• Violate clear cut restrictions

• Spatial constraints are difficult to model

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Spatially Explicit Models
Advantages

• Maximum clear-cut size
• Wildlife habitat requirements.
• Dynamic corridors
• Minimum patch size
• Incorporation of road building

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Spatially Explicit Model
Xij is binary
Adjacency
Singularity
Return
Harvest target
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Disadvantage

• Standard solution method is by using branch and
  bound algorithm

• Solution time is too long

• Ranges from a few hours to infinity even on the
  fastest computer

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Heuristic Solution Techniques

• Random search.
• Simulated annealing
• Great deluge algorithm
• Threshold accepting
• Tabu search with 1-opt moves
• Tabu search with 1-opt and 2-opt moves
• Genetic algorithm
• Hybrid tabu search / genetic algorithm

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Advantages and Disadvantages

• Advantage

Disadvantages

• Faster solutions

• Sub-optimality
• Constraints by penalty functions
• Infeasibility

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Random Search Algorithm
Go to Model
New
Current
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Disadvantage
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The Simulated Annealing Algorithm

• Analogy of the annealing process

• Allows nonlinear and discontinuous constraints
  and objectives

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The Physical Annealing Process
High temperature
Elements move freely
Slow cooling(Annealing)
System crystallizes into a state of minimal
energy
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Flow Chart
Add new random stand at random period
no
yes
no
yes
Accept new Solution
P(delta) ? 1 when c is very high. P(delta) ? 0
when c is very small rand ?(0,1)
no
yes
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Basis for future research

• Spatially explicit modeling is a promising
  technique for modeling non-timber objectives and
  constraints

• Finding real time solutions to spatially explicit
  models is a challenging task

• Simulated annealing is a promising heuristic
  solution technique

• Comparison between simulated annealing and CPLEX?
  results not been reported

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Comparing With CPLEX?
Drawback Comparison of feasible solution from
CPLEX? with infeasible one from SA
Deviation from optimum
Solution Make CPLEX? solutions compatible with SA
by using penalty functions in both
Solution time
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Time for Questions