This document discusses the meta-heuristic technique of Tabu Search (TS). It begins with an outline that covers the motivation for TS, background information, main concepts, algorithms, examples, and applications. TS was proposed by Glover in 1986 as a local search algorithm that uses memory to avoid getting stuck in local optima. The key feature of TS is the use of memory, in the form of a tabu list, to record previously visited solutions and avoid cycling. The tabu list is updated each iteration on a first-in, first-out basis. TS guides the search towards unexplored regions of the solution space, even if it means accepting non-improving moves, in order to escape local optima. Example

1. Scientific Research Group in Egypt (SRGE)
Meta-heuristics techniques (I)
Tabu search
Dr. Ahmed Fouad Ali
Suez Canal University,
Dept. of Computer Science, Faculty of Computers and informatics
Member of the Scientific Research Group in Egypt
Company
LOGO

2. Company
LOGO
Scientific Research Group in Egypt
www.egyptscience.net

3. Company
LOGO
Meta-heuristics techniques

4. Company
LOGO
Outline
1. Motivation
2. Tabu search (TS)(Background)
3. TS (main concepts)
4. TS algorithm
5. TS examples
6. TS applications

5. ?
Company
LOGO
Motivation
?
barrier to local search
starting
point
descend
direction
local minima
global minima

6. Company
LOGO
Tabu search (TS)(Background)
• Tabu search (TS) algorithm was proposed
by Glover (1986).
•In the 1990s, the tabu search algorithm
became very popular in solving
optimization problems.
•Nowadays, it is one of the most wide
spread (single ) S-metaheuristics.
•The use of memory represents the
particular feature of tabu search.
•TS behaves like a steepest LS algorithm, but it
accepts nonimproving solutions to escape from
local optima.

7. Company
LOGO
Tabu search (main concepts)
• The key feature of TS method is the use
of memory, which records information
related of the search process.
•TS generates a neighborhood solution
from the current solution and accepts the
best solution even if is not improving the
current solution.
This strategy may lead to cycles
i.e the previous visited solutions could
be selected again.

8. Company
LOGO
Tabu search (main concepts)
• In order to avoid cycles, TS discards the
solution that have been previously visited
by using memory which is called tabu list.
•The length of the memory (tabu list)
control the search process.
•A high length of the tabu list is high the
search will explore larger regions and
forbids revisiting high number of solution.
•A low length of the tabu list concentrates
the search on a small area of the search
space.

9. Company
LOGO
Tabu search (main concepts)
• At each iteration the tabu list is
updated (first in – first out queue).
•The tabu list contains a constant
number of tabu moves called tabu
tenure, which is the length of time for
which a move is forbidden.
•If a move is good and can improve the
search process but it is in tabu list, there
is no need to be prohibited and the
solution is accepted in a process called
aspiration criteria.

10. Company
LOGO
Tabu search algorithm

11. Company
Tabu search examples
LOGO
N(x0)
X0 Neighborhood
trail solutions
N(x1)
x0
x1
x2
x3
x4
x14
x15
x16

12. Company
TS examples
LOGO
1||SwjTj
Jobs
1
2
3
4
wj
4
5
3
5
pj
12
8
15
9
dj
16
26
25
27


Determine Sc by the best schedule in the
neighborhood that is not tabu
Use tabu-list length = 2
– The tabu list is denoted by L

13. Company
LOGO
TS examples
Iteration 1

Step 1: S0=S1=(1,3,2,4). G(S1)=136. Set L={}.

Step 2. N(S1)= {(3,1,2,4), (1,2,3,4), (1,3,4,2)}
with respective cost = {174, 115, 141} =>
Sc=S0=S2=(1,2,3,4).
Set L={(3,2)}, i.e., swapping 3 and 2 is not
allowed (Tabu)

Step 3: Let k=2

14. Company
TS examples
LOGO
Iteration 2

Step 2.
– N(S2)= {(2,1,3,4), (1,3,2,4), (1,2,4,3)}
X
– with respective costs = {131, - , 67}
–
=> Sc=S3=(1,2,4,3)
– Set S0=Sc
– Set L={(3,4),(3,2)}

Step 3: Let k=3

15. Company
TS examples
LOGO
Iteration 3

Step 2
– N(S3)= {(2,1,4,3), (1,4,2,3), (1,2,3,4)}
X
– with respective costs = {83, 72, -}
–
=> Sc=S4=(1,4,2,3)
– Set L={(2,4),(3,4)}

Step 3: Let k=4

16. Company
TS examples
LOGO
Iteration 4

Step 2
– N(S4)= {(4,1,2,3), (1,2,4,3), (1,4,3,2)}
X
– with respective costs = {92, -, 123}
–
=> Sc=S5=(4,1,2,3)
– Set L={(1,4),(2,4)}

Step 3: Let k=5

17. Company
TS examples
LOGO
Iteration 5

Step 2
– N(S5)= {(1,4,2,3), (4,2,1,3), (4,1,3,2)}
X
– with respective costs = {-, 109, 143}
–
=> Sc=S6=(4,2,1,3)
– Set L={(2,1),(4,1)}

Step 3: Let k=6

18. Company
LOGO
TS Applications
Scheduling
Quadratic
assignment
Frequency
assignment
Car pooling
Capacitated
p-median,
Resource
constrained project
scheduling (RCPSP)
Vehicle
routing
problems
Graph
coloring
Retrieval
Layout
Problem
Maximum
Clique
Problem,
Traveling Salesman
Problems
Database
systems
Nurse
Rostering
Problem
Neural Nets
Grammatical
inference,
Knapsack problems
SAT
Constraint
Satisfaction
Problems
Network
design
Telecomunicati
Global
Optimization
on Network

19. Company
LOGO
References
Metaheuristics From design to implementation, El-Ghazali
Talbi, University of Lille – CNRS – INRIA.
F. Glover, Future paths for integer programming and links to
artificial intelligence, Computers and Operations Research 13
(1986), 533-549.

20. Company
LOGO
Thank you
Ahmed_fouad@ci.suez.edu.eg
http://www.egyptscience.net