1. FORS 8450 Advanced Forest Planning Lecture 11 Tabu Search

2. Background Tabu search was introduced by Glover (1989, 1990) as a deterministic method for efficiently searching a solution space. It evolved from gradient search techniques, and aspects of the process diversify and intensify the search for good solutions. The key to Tabu search is that it remembers the choices it makes, thereby avoiding becoming trapped in local optima, a feature not common to traditional gradient search algorithms. This forces the Tabu search process to explore other areas of the solution space, thus increasing the chance of locating a good solution. While Tabu search cannot guarantee an optimal solution, it should provide a number of good, feasible solutions to a fully specified problem.

3. Tabu Search Characteristics of the algorithm 1) A solution is improved upon as the algorithm operates. 2) When the full "neighborhood" is developed, all potential changes to the current solution are assessed. In general, Tabu search operates by selecting "candidate" decision choices from a "neighborhood". Therefore, a neighborhood must be defined, and it must consist of a set of candidate decision choices. One of these candidates is selected. If unacceptable, another choice from the neighborhood is selected. 3) Candidate choices that lead to higher quality solutions are always welcome. 4) Candidate choices that lead to lower quality solutions are acceptable as well, as long as they are not tabu. 5) The acceptance of one choice into the solution is one iteration. 6) The algorithm stops and reports the best solution when the total number of iterations have been performed.

4. Advantages: It is intuitive, since it generally does not include random elements. It is deterministic, and chooses the best option available to improve a solution. Disadvantages: It is relatively slow, since a number of choices must be assessed before one is chosen. It may "cycle," or get in a rut, during the search for a good solution. Unless given some enhancements, it is an "average" heuristic. These enhancements may include: 2-opt neighborhoods Adjustments to the neighborhood based on frequency of choices Strategic oscillation Tabu Search

5. Necessary parameters 1) The length of the tabu state (number of iterations of the model). 2) A total number of iterations to run the model. Other assumptions 1) Does the tabu state remain fixed, or is it variable? 2) Is the entire neighborhood developed with each iteration of the model? 3) Is the "aspiration criteria" employed? This allows further consideration of Tabu candidate choices when the inclusion of the choice into the current solution will result in a solution that has an objective function value which is better than any previously observed objective function value. 4) Is a "frequency list" created and used?

6. Randomly develop an initial solution Choose a candidate move Calculate 1-opt neighborhood Update solution by incorporating the candidate move, set z value Stop and report the best solution found during search Is candidate tabu? Have we reached the stopping criteria? Yes No Yes No Will solution be the absolute best? Reject candidate move, adjust the neighborhood Yes No Tabu Search Basic Process

7. Clear arrays Develop initial random solution Schedule activities Calculate solution value Done? Report best solution Read data Tabu Search Step 1 Step 2 Step 3 Step 4 A Specific Forest Planning Process Four broad steps. Step 4 is described in more detail next.

8. Assess contribution of units Check adjacency constraints Save as best solution Develop neighborhood Yes Best? Make a choice No Adjust tabu states (Return) Schedule activities Tabu Search A Specific Forest Planning Process Step 4

9. Random feasible solution Develop 1-opt neighborhood Select candidate move Update solution Tabu ? 1-opt iterations complete? Best solution ? Develop 2-opt neighborhood Select candidate move Update solution Tabu ? 2-opt iterations complete? Do another loop? Report best solution Best solution ? Yes No Yes No Tabu Search A Specific Forest Planning Process 1-opt and 2-opt neighborhoods

10. Tabu Search Cycling of solution values over about 1,000 iterations for a specific forest planning problem with a minimization objective. Tabu state = 25 iterations

11. Tabu Search Cycling of solution values over about 1,000 iterations for a specific forest planning problem with a minimization objective. Tabu state = 50 iterations

12. Cycling of solution values over about 1,000 iterations for a specific forest planning problem with a minimization objective. Tabu Search Tabu state = 75 iterations

13. Cycling of solution values over about 1,000 iterations for a specific forest planning problem with a minimization objective. Tabu Search Tabu state = 100 iterations

14. Tabu Search Typical non-cycling of solution values over about 2,500 iterations for a specific forest planning problem with a minimization objective. Tabu state = 125 iterations