1. Scientific Research Group in Egypt (SRGE)
Meta-heuristics techniques (III)
Variable neighborhood search
Scientific Research Group in Egypt (SRGE)
Dr. Ahmed Fouad Ali
Suez Canal University,
Dept. of Computer Science, Faculty of Computers and informatics
Member of the Scientific Research Group in Egypt

2. Scientific Research Group in Egypt

3. Meta-heuristics techniques

4. Outline 1. Motivation 2. Variable neighborhood search(VNS)(Background)
3. VNS (main concepts)
4. VNS algorithm
5. VNS applications

5. Motivation ? barrier to local search starting point descend direction
local minima
global minima

6. 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. 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.

8. Non improving neighbor
VNS (main concepts)
Moving
Non improving neighbor
Shaking
Neighborhood N1
Neighborhood N2
Neighborhood
Nmax
Moving
improving neighbor
Initial solution

9. VNS algorithm

10. 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. 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

12. SA Applications Scheduling 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 Constraint Satisfaction Problems
Network design
Telecomunication Network
Global Optimization

13. 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), , .

14. Thank you