fors 8450 advanced forest planning lecture 11 tabu search
TRANSCRIPT
FORS 8450 • Advanced Forest Planning
Lecture 11
Tabu Search
Tabu Search
Background
Tabu search was introduced by Glover (1989, 1990) as a deterministicmethod for efficiently searching a solution space.
It evolved from gradient search techniques, and aspects of the processdiversify 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.
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.
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
Tabu Search
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?
Randomly developan initial solution
Choose a candidate move
Calculate 1-optneighborhood
Update solution byincorporating the
candidate move, set z value
Stop and reportthe best solution
found during search
Is candidate tabu?
Have we reached the stopping criteria?
Yes
No
YesNo
Will solution bethe absolute best?
Reject candidate move,adjust the neighborhood
Yes No
Tabu Search
Basic Process
Clear arrays
Developinitial random
solution
Scheduleactivities
Calculatesolutionvalue
Done?Report best
solution
Read dataTabu Search
Step 1
Step 2
Step 3
Step 4
A Specific Forest Planning Process
Four broad steps.
Step 4 is described inmore detail next.
Assess contribution
of units
Checkadjacencyconstraints
Save as bestsolution
Developneighborhood
YesBest?
Make a choice
No
Adjust tabustates
(Return)(Return)
Scheduleactivities
Tabu Search
A Specific Forest Planning Process
Step 4
Random feasiblesolution
Develop 1-optneighborhood
Select candidatemove
Updatesolution
Tabu ?
1-optiterationscomplete?
Bestsolution
?
Develop 2-optneighborhood
Select candidatemove
Updatesolution
Tabu ?
2-optiterationscomplete?
Doanotherloop?
Report bestsolution
Bestsolution
?
Yes Yes
YesYes
Yes
Yes
No No
NoNo
No No
Yes
No
Tabu Search
A Specific Forest Planning Process
1-opt and2-opt neighborhoods
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
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
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
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
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