metaheuristics techniques (3)

Company

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

Company

LOGO Scientific Research Group in Egyptwww.egyptscience.net

Company

LOGO Meta-heuristics techniques

Company

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

Company

LOGO Motivation

startingpoint

descenddirection

local minima

global minima

barrier to local search

?

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.

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.

Company

LOGO VNS (main concepts)

NeighborhoodN1

NeighborhoodN2

NeighborhoodNmax

Initial solution

Shaking

MovingNon improving neighbor

Movingimproving neighbor

Company

LOGO VNS algorithm

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

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

Company

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

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), 1097-1100, .

Company

LOGO

Thank youThank you

http://www.egyptscience.net

Ahmed_fouad@ci.suez.edu.eg