1. 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
Company
LOGO
6. Company
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.
7. Company
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.
10. Company
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
11. Company
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
13. Company
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), 10971100, .