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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

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Scientific Research Group in Egypt
www.egyptscience.net
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Meta-heuristics techniques
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Outline
1. Motivation

2. Tabu search (TS)(Background)
3. TS (main concepts)

4. TS algorithm
5. TS examples
6. TS applications
?
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Motivation
?
barrier to local search

starting
point

descend
direction
local minima
global minima
Company

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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.
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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.
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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.
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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.
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Tabu search algorithm
Company

Tabu search examples

LOGO

N(x0)

X0 Neighborhood
trail solutions

N(x1)

x0
x1
x2

x3
x4
x14
x15
x16
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
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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
Company

TS examples

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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
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
Company

TS examples

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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
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
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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
Company

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

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