Building Applications with Python & Gurobi · } Call Model.update()once to process pending model...
23
Building Applications with Python & Gurobi Kostja Siefen
Transcript of Building Applications with Python & Gurobi · } Call Model.update()once to process pending model...
Building Applications with Python & Gurobi
Kostja Siefen
© 2015 Gurobi Optimization2
Building optimization models with Gurobi
} Option 1 – use a modeling language◦ Very easy to build models
� Optimization modeling constructs built into language◦ Attractive choice for non-programmers◦ Alternatives: AMPL, GAMS, Pyomo, …
} Option 2 – use a full programming language◦ Much more powerful and flexible development environment
� Complete access to solver functionality� Richer set of language features
◦ Natural choice when deploying models and/or integrating them into applications for others to use
◦ Alternatives: C, C++, C#, Java, MATLAB, Python, R, VB
} But what if users didn't have to choose between easy and powerful?
© 2015 Gurobi Optimization3
Gurobi Python Environment
} High-level optimization modeling constructs embedded in Python programming language◦ Combines expressiveness of a modeling language with the power and
flexibility of a programming language
} Design goals:◦ Require minimal programming skills to get started◦ Bring "feel" of a modeling language to the Python interface◦ Allow for code that is easy to write and maintain◦ Maintain unified design across all of our interfaces◦ Remain lightweight and efficient (memory & CPU) when compared with
solver alone◦ Support all solver and programming needs
} Consistently earns high praise from our users
© 2015 Gurobi Optimization4
Why Python?
} Fast, powerful and easy-to-use
} Extendible with vast library of prewritten modules (over 50,000)◦ Statistical analysis, visualization, GUIs, web development, web services,
data connections, file compression, data encryption, …
} One of top-10 most popular programming languages, according to TIOBE Programming Community Index◦ http://www.tiobe.com/index.php/content/paperinfo/tpci/index.html◦ Large and rapidly growing Python community with great training resources
} Interactive shell is useful for prototyping} Can be deployed to create full-featured optimization applications◦ GUI, server, web, …
} Free and open source with license that's business-friendly
© 2015 Gurobi Optimization5
Getting started with Python} Don't need to be an expert to start modeling in Python
} Nothing extra to buy or install◦ Gurobi distribution includes Python interpreter and basic modules
} Gurobi Interactive Shell is Python shell with Gurobi extensions◦ Powerful environment for interacting with existing models
} To launch the shell:◦ Windows
� Double-click the Gurobi icon on the desktop� Or run gurobi from a Command Prompt window
◦ Linux� Run the gurobi.sh command from a terminal
◦ Mac� Click on the Gurobi icon in the Launchpad � Or run the gurobi.sh command from a terminal
© 2015 Gurobi Optimization6
Programming in Python} Python is a cross-platform, high-level programming language◦ Object-oriented◦ Interpreted◦ Dynamically typed◦ Automatic memory management◦ Includes a large standard library◦ Documentation tightly integrated with the code
} Python programs are typically stored in text files with .py extension
} Most functionality in Python is provided by modules◦ To use a module in Python programs, include an import statement
} To use the Gurobi interface, import the gurobipy module:from gurobipy import *
© 2015 Gurobi Optimization7
Editing and running Python programs
} Any text editor can be used to work with .py files◦ Most programming editors have Python mode with syntax highlighting,
etc.
} To run a program:◦ Windows
� At a Command Prompt window, entergurobi [program_name]
◦ Linux/Mac� At a terminal, enter
gurobi.sh [program_name]
} Many IDEs available◦ https://wiki.python.org/moin/IntegratedDevelopmentEnvironments◦ Easy to install Gurobi in other Python distributions
© 2015 Gurobi Optimization8
Gurobi recommends Anaconda
} Windows, Mac, Linux; 32/64-bit
} Python 2.x, 3.x — your choice} ~150 packages in the default installation
} conda package and environment management◦ ~350 packages available with a simple conda install
◦ Create isolated “silos” for multiple projects
} Gurobi provides/maintains Anaconda packages
© 2015 Gurobi Optimization9
Essential Gurobi modeling constructs
} Model a model} Var a decision variable} Constr a constraint
} Overloaded operators◦ Basic arithmetic (+, -, ×, ÷)◦ Constraint (≤, =, ≥)
} Aggregate sum operator (quicksum)
} Python provides the rest!
© 2015 Gurobi Optimization10
Typical steps for building a model
} Create empty Model object with Model() constructor
} Add variables with Model.addVar()
} Call Model.update() once to process pending model updates◦ Gurobi provides efficient "lazy updates"◦ Only call Model.update()when necessary to reference new elements
} Call Model.setObjective() to set objective function
} Add constraints with Model.addConstr()
} Solve the model with Model.optimize()◦ Will process any pending model updates
© 2015 Gurobi Optimization11
Example: simple model
# Create empty Model
m = Model()
# Add variables
x = m.addVar(vtype=GRB.BINARY)
y = m.addVar(vtype=GRB.BINARY)
z = m.addVar(vtype=GRB.BINARY)
# Process pending updates
m.update()
© 2015 Gurobi Optimization12
Example: simple model
# Set objective function
m.setObjective(x + y + 2*z, GRB.MAXIMIZE)
# Add constraints
m.addConstr(x + 2*y + 3*z <= 4)
m.addConstr(x + y >= 1)
# Solve model
m.optimize()
© 2015 Gurobi Optimization13
Indices and subscripts in Python
} List is a mutable sequence of elements◦ Useful when representing index sets◦ Elements of any type (integers, strings, …) indexed by integers (0 to n-1)◦ Ex: cities=['CHI', 'NYC', 'ATL']; cities.append('MIA'); cities[2]='BOS'; cities.remove('NYC'); cities.sort()
} Tuple is an immutable, compound grouping of elements◦ Ideal for representing multidimensional subscripts◦ Ex: arc=('CHI','NYC'); j=arc[1]
} Dictionary is a mutable mapping from keys to values◦ Useful when representing coefficients or variables indexed by subscripts◦ Keys must be immutable (integers, strings, tuples, …)◦ Ex: cost={('CHI','NYC'):100, ('ATL','MIA'):150}; cost[('NYC','MIA')]=200; c=cost['ATL','MIA']
© 2015 Gurobi Optimization14
Iterating in Python and aggregate sums} Loops iterate over collections of elements (list, dictionary, …)◦ Useful when representing the for-all modeling construct◦ Ex:
for c in cities:print c # must indent all statements in loop
} List comprehension efficiently builds lists via set notation◦ Ex: penaltyarcs=[a for a in arcs if cost[a]>1000]
} quicksum() is direct replacement for Python's sum() function◦ Gurobi feature that is more efficient when working with Var objects◦ Ex: obj=quicksum(cost[a]*x[a] for a in arcs)
} Combining loops with sums is ideal when building constraints
Ex: can be built with
for i in I:m.addConstr(quicksum(x[i,j] for j in J) <= 5)
xijj∈J∑ ≤ 5,∀i ∈ I
© 2015 Gurobi Optimization15
Building a Gurobi Model: Six Steps
Create a model m = Model()
Add variables x = m.addVar(...)
Commit changes m.update()
Set objective m.setObjective(...)
Add constraints m.addConstr(...)
Optimize m.optimize()
© 2015 Gurobi Optimization16
Spyder
} Scientific Python Development EnviRonment
} Familiar integrated development environment (IDE) for users of MATLAB, Visual Studio, etc.
} Built-in editor, file explorer, documentation browser} Graphical interface for debugging (ipdb)
} IPython console for interactive code execution
http://pythonhosted.org/spyder
© 2015 Gurobi Optimization17
Latest Python-related enhancements in v6.5} Interactive examples for commonly faced business problems◦ http://www.gurobi.com/resources/examples/example-models-overview
} Expression building is more than 4X faster
} Lazy update mode◦ Set new UpdateMode parameter to 1◦ Refer to new variables and constraints without calling Model.update()
} More control over when Gurobi environments are created/released◦ Default environment not created until first used◦ Released with new disposeDefaultEnv()method
} New Conda package simplifies installation for the Anaconda Python distribution$ conda config --add channels http://conda.anaconda.org/gurobi$ conda install gurobi
© 2015 Gurobi Optimization18
Interactive Examples
© 2015 Gurobi Optimization19
Jupyter (formerly IPython)
} A web application for interactive data analysis
} Create notebooks containing live code, text, equations, and visualizations
} A great way to prototype new algorithms, document experiments, share reproducible results
} Originally for Python, now there are kernels for over 50 different languages
http://www.jupyter.org
© 2015 Gurobi Optimization20
Pandas
} Fast and efficient DataFrame and Series objects
} Read/write CSV, HDF5, Excel, SQL, plain text} Missing data handling
} Slicing, fancy indexing, subsetting} Merges, joins
} Split-apply-combine operations (groupby)
http://pandas.pydata.org
© 2015 Gurobi Optimization21
Bokeh
} Interactive visualization for web browsers◦ High performance with streaming data and big data◦ In-browser interactivity on otherwise static pages◦ Bindings for Python, Scala, Julia, R
http://bokeh.pydata.org
© 2015 Gurobi Optimization22
Jupyter Demo
© 2015 Gurobi Optimization23
References} Visit http://www.gurobi.com/documentation/ for more information on
the Gurobi Python Interface◦ Quick Start Guide◦ Reference Manual
} Explore our functional code examples to learn more about advanced features◦ Working with sparse models: netflow, workforce◦ Accessing data sources (databases, spreadsheets, …): diet
} Visit https://docs.python.org/ learn more about Python ◦ Official Python website◦ Tutorials, documentation, examples, …
} Visit https://www.continuum.io to get started with the Anaconda Python distribution, which includes iPython and Jupyter
