Variable neighborhood search
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Company LOGO Scientific Research Group in Egypt (SRGE) Meta-heuristics techniques (III) Variable neighborhood 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
Transcript of Variable neighborhood search
CompanyLOGO
Scientific Research Group in Egypt (SRGE) Meta-heuristics techniques
(III)Variable neighborhood searchDr. Ahmed Fouad Ali
Suez Canal University, Dept. of Computer Science, Faculty of Computers and informatics
Member of the Scientific Research Group in Egypt
CompanyLOGO Meta-heuristics
techniques
CompanyLOGO Outline
2. Variable neighborhood search(VNS)(Background)
3. VNS (main concepts)
5. VNS applications
4. VNS algorithm
1. Motivation
CompanyLOGO Motivation
startingpoint
descenddirection
local minima
global minima
barrier to local search?
CompanyLOGO 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.
CompanyLOGO 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.
CompanyLOGO VNS (main concepts)
NeighborhoodN1
NeighborhoodN2
NeighborhoodNmax
Initial solution
Shaking
MovingNon improving
neighbor
Movingimproving neighbor
CompanyLOGO VNS algorithm
CompanyLOGO 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
CompanyLOGO 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
CompanyLOGO SA ApplicationsScheduling Quadratic
assignment
Frequency assignmen
t
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 Satisfact
ion Problems
Network design
Telecomunication Network
Global Optimizati
on
CompanyLOGO 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, .
