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Simulated Annealing

Simulated Annealing

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Simulated Annealing

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

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

  3. 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

  4. 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

  5. Spatially Explicit Models Advantages • Maximum clear-cut size • Wildlife habitat requirements. • Dynamic corridors • Minimum patch size • Incorporation of road building

  6. Spatially Explicit Model Xij is binary Singularity Adjacency Return Harvest target

  7. 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

  8. 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 Heuristic Solution Techniques

  9. Advantages and Disadvantages Advantage Disadvantages Faster solutions Sub-optimality Constraints by penalty functions Infeasibility

  10. Random Search Algorithm Go to Model New Current

  11. Disadvantage

  12. The Simulated Annealing Algorithm • Analogy of the annealing process Allows nonlinear and discontinuous constraints and objectives

  13. The Physical Annealing Process High temperature Elements move freely Slow cooling(Annealing) System crystallizes into a state of minimal energy

  14. Stop Start With an initial solution Improvement? Stop criteria? P(delta)>rand? 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

  15. 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

  16. ++ ++ +++ + ++ ++ ++ +++ + ++ ++ ++ +++ + ++ ++ ++ +++ + ++ CPLEX solution + simulated annealing (SA) 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

  17. Thank You Time for Questions