metaheuristics techniques (3)
DESCRIPTION
Variable neighborhood searchTRANSCRIPT
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LOGO
Scientific Research Group in Egypt (SRGE)
Meta-heuristics techniques (III)Variable neighborhood search
Dr. Ahmed Fouad AliSuez 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. Variable neighborhood search(VNS)(Background)2. Variable neighborhood search(VNS)(Background)
3. VNS (main concepts)3. VNS (main concepts)
5. VNS applications5. VNS applications
4. VNS algorithm4. VNS algorithm
1. Motivation1. Motivation
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LOGO Motivation
startingpoint
descenddirection
local minima
global minima
barrier to local search
?
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LOGO Variable neighborhood search (VNS)(Background)
• Variable neighborhood search (VNS) has been proposed by P. Hansen and N. Mladenovic in 1997.
• The basic idea of VNS is to successively explore a set of predefined neighborhoods to provide a better solution.
• It explores either at random or systematically a set of neighborhoods to get different local optima and to escape from local optima.
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LOGO VNS (main concepts)
• VNS is a stochastic algorithm in which, first, a set of neighborhood structures Nk (k = 1, . . . , n) are defined.
• Then, each iteration of the algorithm is composed of three steps: shaking, local search, and move.
• VNS explores a set of neighborhoods to get different local optima and escape from local optima.
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LOGO VNS (main concepts)
NeighborhoodN1
NeighborhoodN2
NeighborhoodNmax
Initial solution
Shaking
MovingNon improving neighbor
Movingimproving neighbor
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LOGO VNS algorithm
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LOGO VNS algorithm• A set of neighborhood structure
Nk are defined where k = 1, 2,…, n.
• At each iteration, an initial solution x is generated randomly.
• A random neighbor solution x' is generated in the current neighborhood Nk.
• The local search procedure is applied to the solution x' to generate the solution x".
Shaking
Local search
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LOGO VNS algorithm• If the solution x" is better than
the x solution then the solution x" becomes the new current solution and the search starts from the current solution.
• If the solution x" is not better than x solution, the search moves to the next neighborhood Nk+1, generates a new solution in this neighborhood and try to improve it.
• These operations are repeated until a termination criteria satisfied.
Moving
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LOGO SA Applications
Scheduling Quadratic assignme
nt
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.
M. Mladenovic and P. Hansen, Variable neighborhood search. Computers and Operations Research, 24:(1997), 1097-1100, .
