1. FORS 8450 Advanced Forest Planning Lecture 5 Relatively Straightforward Stochastic Approach

2. Monte Carlo Simulation or Random Search

3. Background A class of algorithms that rely on repeated random sampling to locate a solution to a problem. These are often used to simulate systems that have stochastic elements, but in forest planning they are mainly used to simulate systems randomly (even if no stochastic element is recognized). "Optimization" in this sense is based on a random allocation of activities to decision variables (e.g., random scheduling of harvests). In essence, the process moves randomly through a solution space, preferring the development of better plans of action, yet allowing severely sub-optimal choices to be assessed.

4. Monte Carlo Simulation or Random Search Advantages: They are more easily developed than other heuristics. They are fast. Disadvantages: Unless given some intelligence, they produce the worst quality forest plans. The best solution produced with simple random search may be worse than the lowest quality solution generated with other methods.  Our intent is not to discourage the use of this method, we are simply pointing out that the most basic implementation of a Monte Carlo technique for scheduling activities incorporates no information about the problem to help guide the search process, and simply randomly assigns harvest timing choices to management units.

5. Necessary parameters 1) The number of random solutions to be assessed. Other assumptions 1) When building a solution randomly, is information about previously scheduled activities used to influence the schedule? If so, then one assured themselves that each solution generated will likely be feasible. If not, many of the solutions generated are likely to be infeasible if either wood flow or spatial constraints are part of the planning problem. Monte Carlo Simulation or Random Search

6. Basic Process Randomly develop a solution Evaluate goals Stop and report the best solution found during search Have we reached the stopping criteria? Yes No Monte Carlo Simulation or Random Search

7. Alternatives Randomly develop a solution and evaluate some goals as it is being developed Stop and report the best solution found during search Have we reached the stopping criteria? Yes No Monte Carlo Simulation or Random Search Randomly develop a solution by selecting randomly from a set of feasible actions that may address goals Stop and report the best solution found during search Have we reached the stopping criteria? Yes No A)B)

8. Alternatives Monte Carlo Simulation or Random Search C) Like binary search, develop a schedule of activities period-by-period using random assignment of activities to management units. D) Use Random Ascent: Randomly define an initial solution Select at random a stand and treatment schedule not in the current solution Assess the impact of the proposed change Keep the proposed change if the objective function value improves Otherwise, discard the proposed change and try again

9. A Specific Forest Planning Process Four broad steps. Step 2 is described in more detail next. Monte Carlo Simulation or Random Search Clear arrays Develop a solution Calculate solution value Best? Save solution Done? Report best solution Read data Step 1 Step 2 Step 3 Step 4 Yes No

10. A Specific Forest Planning Process Step 2 Monte Carlo Simulation or Random Search Develop set of unscheduled units Randomly select unit and time period to cut Develop a solution Check for adjacency violation Violated? No Yes (Return) Schedule more? No Yes

11. Monte Carlo Simulation or Random Search Change in solution value over about 10,000 iterations for a specific forest planning problem with a minimization objective.