How defuse combinatorial explosions By Dr Simon Martin Computational Heuristics, Operational...

How defuse combinatorial explosions

ByDr Simon Martin

Computational Heuristics, Operational Research and Decision Support Group

University of Stirling

What is Operational Research?

Operational research (OR) is a discipline that deals with the application of advanced analytical methods to help make better decisions*.

It is also known as management science or decision science .

*http://en.wikipedia.org/wiki/Operations_research 14/02/15

Amazon

Services* Online shopping, Web hosting, Content Distribution

Revenue US$ 88.988 billion (2014)

Operating income US$ 178 million (2014)

Net income US$ -241 million (2014)

Total assets US$ 54.505 billion (2014)

Total equity US$ 10.741 billion (2014)

Employees 154,100 (December 2014)

In Scotland:

•Dunfermline Fulfilment Centre, Scotland

•Edinburgh research facility – AI techniques, mathematics

*http://en.wikipedia.org/wiki/Amazon.com -17/02/15

Objectives

Complex explosive problems

Algorithms

Exact algorithms

Heuristics

Practical Problems

In this talk we will find out about:

Task

27 13?x

Answer

Method 22713

x

128

072 +351

1

Method 1200706021 +

153

20 7

10

3

200 70

60 21

OR…Use the calculator on your mobile!

But..

1.Get smartphone out of pocket2.Go to calculator app3.Type numbers4.Press equals5.Call out answer

This is also an algorithm!!

Algorithm

An algorithm is a procedure or formula for solving a problem. The word derives from the name of the mathematician, Mohammed ibn-Musa al-Khwarizmi, who was part of the royal court in Baghdad and who lived from about 780 to 850.*

*whatis.techtarget.com/definition/algorithm – 15/02/15

Task

Get from A to B Blindfolded!

Computers execute algorithms

9 7 0 0 0 0 ....R

1R

2R

3R

4R

5

9 8 1 0 0 0 ....R

1R

2R

3R

4R

5

9 9 0 0 0 ....R

1R

2R

3R

4R

5

9 9 2 0 0 0 ....R

1R

2R

3R

4R

5

2 9 2 0 0 0 ....R

1R

2R

3R

4R

5

start

stop

r1= r

2?

r1= r

2?

r3→ R

1

r2= r

2+1

r3= r

3+1 2

Solve 9-7?Yes

No

Yes

No

Can you find the shortest route round?

GF

E

DC

BA

Find the shortest Circuit

GF

E

DC

BA

7 cities or vertices21 connections or Edges360 Possible Routes!

Find the short test Circuit

GF

E

DC

BA



H

Find the short test Circuit

GF

E

DC

BA



H

J

Combinatorial Explosion

No. of Cities

No. of Tours

3 1

4 3

5 12

6 60

7 360

8 2520

9 20160

10 181440

100 4.6663107722e+155

Boom!

Amazon's product delivery problem is worse!

?????????????

What do we do?

Answer

We Cheat!

We use Heuristics

Heuristics

A heuristic technique is any approach to problem solving, learning, or discovery that employs a practical methodology not guaranteed to be optimal or perfect, but sufficient for the immediate goals.

Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution.

Heuristics employ common sense knowledge of “rules of thumb” to help solve a problem

Nearest Neighbour Heuristic

GF

E

DC

BA

2-opt (edge sapper)

GF

E

DC

BA

2-opt (break 2 edges)

GF

E

DC

BA

2-opt (Add 2 Edges)

GF

E

DC

BA

TSP Video

By poprythum https://www.youtube.com/watch?v=SC5CX8drAtU 17/02/15

Remember Amazon's delivery problem?

Millions of deliveries

Need many - trucks all different sizes

Drivers to drive

Millions of gallons of fuel

Not taking into account warehouse staff, web staff, etc etc ……

Operational Research

Gives practical solutions to explosive problems

Helps companies make complex operational decisions

We use heuristic techniques

We employ computer science and mathematical techniques

We save companies millions of pounds!

Thank you

How defuse combinatorial explosions By Dr Simon Martin Computational Heuristics, Operational...

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