1. How defuse combinatorial explosions By Dr Simon Martin Computational Heuristics, Operational Research and Decision Support Group University of Stirling

2. 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 14/02/15http://en.wikipedia.org/wiki/Operations_research

3. 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) Employees154,100 (December 2014) In Scotland: Dunfermline Fulfilment Centre, Scotland Edinburgh research facility – AI techniques, mathematics *http://en.wikipedia.org/wiki/Amazon.com -17/02/15

4. Objectives Complex explosive problems Algorithms  Exact algorithms  Heuristics Practical Problems In this talk we will find out about:

5. Task 2713? x

6. Answer Method 2 27 13 x 1 2 8 072 + 351 1 Method 1 200 70 60 21 + 15 3 207 10 3 20070 6021

7. OR… Use the calculator on your mobile ! But.. 1.Get smartphone out of pocket 2.Go to calculator app 3.Type numbers 4.Press equals 5.Call out answer This is also an algorithm!!

8. 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

9. Task Get from A to B Blindfolded!

10. Computers execute algorithms 97000 0.... R1R1 R2R2 R3R3 R4R4 R5R5 98100 0 R1R1 R2R2 R3R3 R4R4 R5R5 9900 0 R1R1 R2R2 R3R3 R4R4 R5R5 99200 0 R1R1 R2R2 R3R3 R4R4 R5R5 29200 0 R1R1 R2R2 R3R3 R4R4 R5R5 start stop r 1 = r 2 ? r 3 → R 1 r 2 = r 2 +1 r 3 = r 3 +1 2 Solve 9-7? Yes No Yes No

11. Can you find the shortest route round? G F E D C B A

12. Find the shortest Circuit G F E D C B A 7 cities or vertices 21 connections or Edges 360 Possible Routes!

13. Find the short test Circuit G F E D C B A 8 cities or vertices 28 connections or Edges 2520 Possible Routes! Find the shortest Circuit H

14. Find the short test Circuit G F E D C B A 9 cities or vertices 36 connections or Edges 20160 Possible Routes! Find the shortest Circuit H J

15. Combinatorial Explosion No. of Cities No. of Tours 31 43 512 660 7360 82520 920160 10181440 1004.66631 07722e +155 Boom!

16. Amazon's product delivery problem is worse!

17. ????????????? What do we do?

18. Answer We Cheat! We use Heuristics

19. 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

20. Nearest Neighbour Heuristic G F E D C B A

21. G F E D C B A

22. G F E D C B A

23. G F E D C B A

24. G F E D C B A

25. G F E D C B A

26. G F E D C B A

27. G F E D C B A

28. 2-opt (edge sapper) G F E D C B A

29. 2-opt (break 2 edges) G F E D C B A

30. 2-opt (Add 2 Edges) G F E D C B A

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

32. 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 ……

33. 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!

34. Thank you