Optimization in Julia

Transcript

1. Optimization in Julia Philip I. Thomas, philipithomas.com
2. Goal Give an understanding of how to formulate and express an optimization problem in JuMP (Julia for Mathematical Programming)
3. About Me • philipithomas.com • Engineer, OpenDNS • Education - Systems Engineering and Physics • For fun - Workforce Scheduling
4. Agenda • Optimization and Operations Research • Julia • JuliaOpt • Examples
5. Optimization and OR
6. Optimization Minimize or maximize a function subject to constraints. • Linear Programming • Nonlinear Programming • Dynamic Programming • Constraint Programming
7. Minimize x Subject to x >= 0
8. Minimize x Subject to x >= 0 Min 0
9. Minimize x - y Subject to x <= 0 y >= -4 x - 2y = -2
10. Minimize x - y Subject to x <= 0 y >= -4 x - 2y = -2 Substitute x - y = -2 + y Min -6 (x = -2, y = 4)
11. Minimize -2x - 3y - 3z Subject to 3x + 2y + z = 10 3x + 5y +3z = 15 x, y, z > 0 Source: Wikipedia
12. Minimize -2x - 3y - 3z Subject to 3x + 2y + z = 10 3x + 5y +3z = 15 x, y, z > 0 Min -130/7 Source: Wikipedia
13. Simplex Algorithm Source: Wikipedia
14. Minimize -2x - 3y - 3z Subject to 3x + 2y + z = 10 3x + 5y +3z = 15 x, y, z > 0 x, y, z ∈ Z
15. Minimize -2x - 3y - 3z^2 Subject to 3x + 2y + z = 10 3x + 5y +3z = 15 x, y, z > 0
16. Minimize -2x - 3y*z Subject to 3x + 2y + z = 10 3x + 5y +3z = 15 x, y, z > 0
17. Complexity Notation • Nondeterministic-Polynomial Time • Some of the hardest problems in computer science
18. Operations Research Optimization and Applied Mathematics in Business • Military • Workforce scheduling • Routing • Factories • Sports Games
19. Julia
21. About Julia • Fast • JIT Compiler • Dynamic Dispatch • Package Manager • Parallel and Distributed • Call C and Python functions • Open Source (JuliaLang.org)
22. http://learnxinyminutes.com/docs/julia/
23. JuMP
24. Julia for Mathematical Programming • Modeling language written in Julia • Supports a variety of solvers • LP, IP, Convex Programming, Constraint Programming
25. Solvers • Commercial / Open Source • Parallelism / Stability Source: JuliaOpt.org
26. Why JuMP • High-Level • Portable • Extensible
27. Examples
28. Examples Online github.com/philipithomas/jump-examples Need Julia with JuMP package and CBC Solver.
29. macklemore.jl We’re going to the thriftshop and need 99 cents. Coins are heavy - minimize the mass needed to carry 99 cents. Source: ProjectEuler.net
30. sudoku.jl Constraint Satisfaction - Not Optimization http://www.dailysudoku.com/sudoku/today.shtml
31. salesman.jl https://forio.com/app/showcase/route-optimizer/
32. Scheduling • 20 employees • not available all the time • varying demand throughout a day • some part time, some full time • minimum shift length, maximum shift length • time between shifts
33. Conclusion
34. Agenda • Optimization and OR • Julia • JuliaOpt • Applications
35. Goal Give an understanding of how to formulate and express an optimization problem in JuMP (Julia for Mathematical Programming)
36. Further Reading • In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William Cook • Data Smart (Chapter 4) by John Foreman • Intro to Operations Research by Hillier
37. Optimization in Julia Philip I. Thomas, philipithomas.com