Using Python to Solve Computationally Hard Problems

Transcription

1 Using Python to Solve Computationally Hard Problems

2 Using Python to Solve Computationally Hard Problems Rachael Madsen Optimal Design Software LLC BS in Mathematics Software Engineer & Architect Python programmer

3 NP-Complete Problems

4 NP-Complete Problems An individual solution can be checked for correctness in polynomial time, but.. A solution cannot be derived in polynomial time

5 NP-Complete Problems Nodes Polynomial (n 2 ) Exponential (2 n ) x Factorial (n!) x x 10 89

6 NP-Complete Problems Sequencing tasks or objects for any optimization Database design & normalization Games

7 The Traveling Salesman Problem

8 Traveling Salesman Problem Given a list of cities and their pairwise distances, find the shortest possible route that visits each city exactly once and returns to the origin city.

9 Algorithms

10 Algorithms Changing data may change which algorithm is best

11 Algorithms Searching available software implementations may yield the best results

12 Algorithms Considerations

13 Algorithms > Considerations Ease of Implementation

14 Algorithms > Considerations Quality of Solution

15 Algorithms > Considerations > Quality of Solution You are looking for a solution, not the solution

16 Algorithms > Considerations > Quality of Solution π = k= k 8k k k k + 6

17 Algorithms > Considerations > Quality of Solution Will this algorithm generate valleys?

18 Algorithms > Considerations Complexity

19 Algorithms > Considerations > Complexity Simple 50 lines of code Complex 100,000+ lines of code

20 Algorithms > Considerations Parallelization

21 Algorithms > Considerations Processing Power

22 Starting From Scratch

23 Starting From Scratch (it s a bad idea)

24 Python Options

25 Python Options Where to Look

26 Python Options > Where to Look Google code Git Forums Technical books

27 Python Options Licenses

28 Python Options Evaluation

29 Python Options > Evaluation Operations Research Tools Developed at Google browse/trunk/python/tsp.py?r=303

30 Python Options > Evaluation > or-tools Runtime Lines of code: 132 Hardware availability

31 Python Options > Evaluation > or-tools Quality of Solution

32 Python Options > Evaluation Github user trevlovett Python Ant Colony TSP Solver Python-Ant-Colony-TSP-Solver

33 Python Options > Evaluation > Ant Colony TSP Solver Runtime Lines of code: 132 Hardware availability

34 Python Options > Evaluation > Ant Colony TSP Solver Quality of Solution

35 Optimization

36 Optimization Confirm implementation of algorithm as written Check for most efficient coding practices

37 Optimization Use scientific package such as SciPy to rewrite code for speed Break out select code into C routine

38 Optimization Parallelize GPU CPU

39 Optimization Beware of fencepost errors and differences in hardware

40 Web Resources

41 Web Resources The Stony Brook Code Repository, Concorde TSP Solver plement.shtml TSP, github user denlunev, Operations Research Tools, Google, Ant Colony TSP Solver, github user trevlovett

42 Bibliography

43 Bibliography Introduction to Graph Theory, 2 nd Edition, Douglas Brent West, Prentice Hall, 2000 The Traveling Salesman Problem: A Computational Study, Applegate, Bixby, Chvátal & Cook, Princeton U. Press, 2007 The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Lawler, Lenstra, Kan & Shmoys, Wiley, 1985 The Traveling Salesman Problem and its Variations, Gutin & Punnen, Springer, 2002

44 Bibliography Combinatorial Optimization: Theory and Algorithms, 2 nd Edition, Korte & Vygen, Springer, 2002 Combinatorial Optimization, Cook, Cunningham, Pulleyblank & Schrijver, Wiley-Interscience, 1997 Local Search in Combinatorial Optimization, Aarts & Lenstra, Wiley, 1997 Combinatorial Algorithms: Generation, Enumeration, and Search, Kreher & Stinson,CRC Press, 1998

45 Bibliography Counting: The Art of Enumerative Combinatorics, Martin, Springer, 2001 Counting and Configurations, Herman, Kucera & Simsa, Springer, 2003 Abstract Algebra, 3 rd Edition, Dummit & Foote, Wiley, 2003

46 Thank You!