Local Search Methods

swimlogisticsElectronics - Devices

Nov 26, 2013 (3 years and 6 months ago)

96 views

1

Local Search Methods


Applicable when seeking Goal State & don't care how to get
there. E.g.,



N
-
queens,


map coloring,


finding shortest/cheapest round trips
(TSP, VRP)


VLSI layout, planning, scheduling, time
-
tabling, . . .


resource allocation


protein structure prediction


genome sequence assembly


2

Local search


Key idea (surprisingly simple):


1.
Select (random) initial state
(
generate an initial guess
)


2.
Make local modification to
improve current state (evaluate
current state and
move to other
states
)


3.
Repeat Step 2 until goal state
found (or out of time)

8
-
queens

Example
:


Put N Queens on an
n
×

n

board with no two queens on the same row,
column, or diagonal



Initial state … Improve it … using local transformations (perturbations)

4

Traveling Salesman Person


A Solution: Exhaustive Search


(Generate and Test) !!



The number of all tours

is about (n
-
1)!/2


If n = 36 the number is about:


566573983193072464833325668761600000000


Not Viable Approach !!

5

Traveling Salesman Person


A Solution: Start from an initial solution and improve
using local transformations.

6

Example: Graph Coloring

1.
Start with random coloring of nodes

2.
Change color of one node to reduce # of
conflicts

3.
Repeat 2