metaheuristics techniques (1)

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LOGO

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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LOGO Scientific Research Group in Egyptwww.egyptscience.net

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LOGO Meta-heuristics techniques

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LOGO Outline

2. Tabu search (TS)(Background)

3. TS (main concepts)

5. TS examples

4. TS algorithm

6. TS applications

1. Motivation

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LOGO Motivation

startingpoint

descenddirection

local minima

global minima

barrier to local search

?

?

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LOGOTabu 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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LOGOTabu 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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LOGOTabu 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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LOGOTabu 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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LOGO Tabu search algorithm

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LOGO Tabu search examples

x0

N(x0) X0 Neighborhood trail solutions

x1

N(x1)

x2

x3

x4

x14

x15

x16

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LOGO TS examples1||SwjTj

Jobs 1 2 3 4wj 4 5 3 5pj 12 8 15 9dj 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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LOGO TS examples

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

Iteration 1

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LOGO TS examples

Step 2. – N(S2)= {(2,1,3,4), (1,3,2,4), (1,2,4,3)} – 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

Iteration 2

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LOGO TS examples

Step 2– N(S3)= {(2,1,4,3), (1,4,2,3), (1,2,3,4)} – with respective costs = {83, 72, -} – => Sc=S4=(1,4,2,3)– Set L={(2,4),(3,4)}

Step 3: Let k=4

Iteration 3

X

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LOGO TS examples

Step 2– N(S4)= {(4,1,2,3), (1,2,4,3), (1,4,3,2)} – with respective costs = {92, -, 123} – => Sc=S5=(4,1,2,3)– Set L={(1,4),(2,4)}

Step 3: Let k=5

Iteration 4

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LOGO TS examples

Step 2– N(S5)= {(1,4,2,3), (4,2,1,3), (4,1,3,2)} – with respective costs = {-, 109, 143} – => Sc=S6=(4,2,1,3)– Set L={(2,1),(4,1)}

Step 3: Let k=6

Iteration 5X

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LOGO TS ApplicationsScheduling 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 Constrain

t Satisfacti

on Problems

Network design

Telecomunication

Network

Global Optimizati

on

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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.

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LOGO

Thank you

http://www.egyptscience.net

Ahmed_fouad@ci.suez.edu.eg