FORS 8450 • Advanced Forest Planning
Lecture 11
Tabu Search
Tabu Search
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.
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.
Tabu Search
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
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 develop
an initial solution
Tabu Search
Calculate 1-opt
neighborhood
Basic Process
Choose a candidate move
Is
candidate
tabu?
Yes
Yes
No
Update solution by
incorporating the
candidate move, set z value
No
Will
solution be
the absolute
best?
Have we
reached the
stopping
criteria?
Yes
Stop and report
the best solution
found during search
No
Reject candidate move,
adjust the neighborhood
Tabu Search
A Specific Forest
Planning Process
Read data
Step 1
Clear arrays
Step 2
Develop
initial random
solution
Step 3
Calculate
solution
value
Step 4
Schedule
activities
Four broad steps.
Step 4 is
described in
more detail
next.
Done?
Report best
solution
Tabu Search
A Specific Forest
Planning Process
Step 4
Schedule
activities
Assess
contribution
of units
Check
adjacency
constraints
Develop
neighborhood
Make a choice
Adjust tabu
states
Best?
No
(Return)
Yes
Save as best
solution
(Return)
Random feasible
solution
Tabu Search
A Specific Forest
Planning Process
1-opt and
2-opt
neighborhoods
Develop 1-opt
neighborhood
Develop 2-opt
neighborhood
Select candidate
move
Select candidate
move
No
Tabu ?
Yes
No
No
Best
solution
?
Tabu ?
No
Yes
Update
solution
No
1-opt
iterations
complete?
Yes
Yes
Update
solution
2-opt
iterations
complete?
Yes
Yes
Yes
Do
another
loop?
No
Report best
solution
Best
solution
?
No
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
Tabu Search
Cycling of solution values over about 1,000 iterations for a specific
forest planning problem with a minimization objective.
Tabu state = 75 iterations
Tabu Search
Cycling of solution values over about 1,000 iterations for a specific
forest planning problem with a minimization objective.
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