Integer Linear Programming and the Google Optimization Toolset

GDG Reading & Thames Valley DevFest 2015

Transcript

1. Integer Linear Programming & The Google Optimization Toolset By Selma Ardelean
2. > whoami • Junior Software Developer @ NewVoiceMedia • Interested in machine learning, artificial intelligence and optimization techniques @matah @s_ardelean selma.ardelean@gmail.com
3. Lınear Optımızatıon or lınear programıng is the name given to computing the best solution to a problem modeled as a set of linear relationships.
4. A bit of history • Developed during World War 2 • Released to the public in 1947 • Active work going on • Still quite a few open problems George Bernard Dantzig Leonid Kantorovich John von Neumann
5. Ok..ok.. but how does it look like?
6. Canonical Form Constants Variables
7. Variables: x, y Objective function: 3*x + 4*y Constraints: x + 2*y <= 14 3*x - y >= 0 x - y <= 2 Basic Example
8. Simplex Algorithm Let’s just call it magic • Proposed by George Bernard Dantzig in 1947 • average case polynomial complexity • worst case exponential complexity • used widely in practice
9. Procedure 1. Simplify constraints 2. Represent constraints geometrically 3. Get coordinates of all vertices and replace into the objective function
10. Applications • Transportation problem • Minimization of production costs • Maximization of profit • Telecommunications networks • Cellular networks • Scheduling • Travelling Salesman
11. Let’s get real
12. Google Optimization Toolset • Open Source under the Apache License ◦ https://github.com/google/or-tools • Written in C++ • Used internally at Google • Provides an APIs for various languages: C++, Java, Python and C# • Can be used with other solvers • Does provide its own open source linear solver: GLOP • Actively being developed • Documentation has come a long way
13. NumVar - define the limits of our variables Setup the constraints
14. Print out your results and enjoy!
15. A bit more real
16. The Problem: Stigler diet, named for economics Nobel laureate George Stigler, who computed an inexpensive way to fulfill basic nutritional needs given a set of foods The Constraints: The Variables: The Objective: minimize cost
19. Resources • Discrete Optimization Course ◦ https://class.coursera.org/optimization-003 • https://en.wikipedia.org/wiki/Integer_programming • Scheduling problem ◦ https://github.com/evilqubit/lpSolve • lp_solve API reference ◦ http://lpsolve.sourceforge.net/5.5/ • Online example of simplex algorithm ◦ http://www.zweigmedia.com/RealWorld/simplex.html • Gurobi solver reference ◦ http://www.gurobi.com/
20. Conclusion I am by no means an expert in anything Linear programming is applicable to a variety of problems The Google Optimization toolset is easy to use and understand And provides much more than just a linear solver Math is fun!
21. Thanks for listening! Questions?