metaheuristics techniques (1)
DESCRIPTION
Tabu searchTRANSCRIPT
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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 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
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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.
