FICO Xpress Optimization

Xpress Python examples

Examples of using Xpress from Python

This directory contains examples of usage of the Xpress Python interface. If you installed the Xpress Suite installation, please note that it does not contain the Xpress Python module. You can install our Python module from the Python Package Index (PyPI) or from the Conda repository by running

or, if you have a Conda install,

Either way, please verify that the XPAUTH_PATH environment variable is set to the full path to the license file, xpauth.xpr. If you do not have an Xpress license, the Xpress Community license is provided with the Python module and is automatically detected by the module provided that the XPAUTH_PATH variable is not set.

If you have any question or want to file a bug report, please email support@fico.com.

API examples

Using NumPy arrays to create variables: Using NumPy arrays

Visualize the BB tree: Using the newnode callback

Irreducible Infeasible Sets: Using Irreducible Infeasible Sets

Loading a problem: Loading a problem directly

Using Python model objects to build a problem: Modeling using Python objects

Changing the optimization problem: Modifying a problem

Extending a problem: Extending a problem

Using NumPy and Xpress: Using NumPy and Xpress


Type:	Programming
Rating:	2 (easy-medium)
Description:	An example of printing a matrix of random numbers and a problem formulation that uses the xpress.Dot() operator to formulate constraints simply. Note that the NumPy dot operator is not suitable here as the result is an expression in the Xpress variables.
File(s):	numpy1.py, numpy2.py

Finding an LP subsystem with as many constraints as possible: Infeasibility detection, infeasibility reporting

Basis and Stability: Basis handling and sensitivity methods


Type:	Programming
Rating:	2 (easy-medium)
Description:	We solve a simple 2x2 LP problem to optimality, which serves as a showcase for basis handling methods and sensitivity analysis.
File(s):	basis_sensitivity.py

Solving a quadratic problem: Building quadratic expressions

Repeatedly solving a problem: Solving a problem multiple times

Using indicators: Model with indicators

Using special ordered sets: Model with special ordered sets

Writing and reading problem matrix files: Writing and reading a problem


Type:	Programming
Rating:	2 (easy-medium)
Description:	The file write_read.py creates a few variables, then builds a problem and saves it to a file before re-reading that file into a new problem. The file getmatrix.py shows how to retrieve the coefficient matrix, objective coefficients, and constraints' right-hand sides for a given problem.
File(s):	write_read.py, getmatrix.py

Comparing Matrices: Compare two optimization problems

Create a problem with piecewise linear functions: Piecewise linear, low-level API

Create a problem with general constraints that use operator abs: General constraints, operators, low-level functions


Type:	Programming
Rating:	2 (easy-medium)
Description:	Create a simple problem using the modeling methods abs, And and max, as well as their corresponding modeling constructs using the API method problem.addgencons, for creating general constraints.
File(s):	general_constraints_abs.py, general_constraints_logic.py, general_constraints_max.py

Solving a quadratically constrained problem: Solve a nonlinear problem

Solve a polynomial optimization problem: Modeling a polynomial optimization problem

Modeling with user functions: Modeling with user functions

Implementing a branching rule using branch objects: Demonstrate the Xpress change branch object callback

Re-solving problem using the Barrier method's warm start:

Using the tuner functions in the Python interface:

Solution enumeration: Using callbacks, customizing the branch and bound search

Modeling examples

The travelling salesman problem: Using Xpress callbacks


Type:	Programming
Rating:	2 (easy-medium)
Description:	The file tsp.py retrieves a problem instance from https://www.math.uwaterloo.ca/tsp/world/countries.html and creates a corresponding TSP instance, then solves it using the Xpress Optimizer library with the appropriate callback. In tsp_numpy.py, a randomly generated TSP problem is modeled using NumPy vectors and matrices and solved using the Optimizer's libraries and callback functions.
File(s):	tsp.py, tsp_numpy.py

The feasiblity pump:

The n-queens problem: Puzzle modeling

Min-cost-flow problem : Modeling a graph problem

Solving Sudoku: Puzzle modeling

Multicommodity flow problem: Solve a multicommodity flow minimum cost optimization problem on a randomly created graph

Find largest-area inscribed polygon: Nonlinear programming, trigonometric functions

Solve a simple MIP using Benders decomposition: Benders decomposition, callbacks

Create an iterative algorithm cutting stock problem:

Maximize the sum of logistic curves subject to linear and piecewise linear constraints:

Transportation problem with piecewise-linear costs:

Modeling Satisfiability and PseudoBoolean problems with MIP:


Type:	Programming
Rating:	4 (medium-difficult)
Description:	The file gencons_sat.py provides a rudimentary SAT solver that translates a Satisfiability (SAT) problem into a MIP and solves it, and gencons_pbo.py includes a basic solver of PseudoBoolean optimization problems (PBO) that translates a problem into a MIP before solving it.
File(s):	gencons_sat.py, gencons_pbo.py

Multi-objective knapsack problem: Multi-objective MIP problem with binary variables

Goal programming: Lexicographic goal programming using the Xpress multi-objective API

Markowitz portfolio optimization: Multi-objective quadratic optimization


Type:	Portfolio optimization
Rating:	3 (intermediate)
Description:	In Markowitz portfolio optimization there are two objectives: to maximize reward while minimizing risk (i.e. variance). This example plots several points on the optimal frontier using a blended multi-objective approach, and shows that a point computed using a lexicographic approach also lies on this frontier.
File(s):	markowitz.py

Basic LP tasks: problem statement and solving; solution analysis: LP solving, modeling variables and constraints, printing the solution

Network problem: transport from depots to customers: LP solving, modeling variables and constraints

Blend: A model for mineral blending: simple LP problem, formulation of blending constraints


Type:	Blending
Rating:	1 (simple)
Description:	Several ores are blended to a final product that must have a certain quality ('grade'). We wish to determine the quantity of every ore to be used in the blend with the objective to maximize the total profit (calculated as sales revenues - raw material cost).
File(s):	blend.py, blend2.py
Data file(s):	blend_data.py

Basic MIP tasks: binary variables; logic constraints: MIP solving, binary variables, index set types, logic constraints

Coco: The Coco productional planning problem: LP problem, formulation of resource constraints and material balance constraints, formatted solution printing


Type:	Production planning
Rating:	2 (easy-medium)
Description:	The company Coco has two plants that can produce two types of cocoa powder. The plant capacities are limited. It is possible to store raw materials and finished product from one time period to the next. Raw material prices, sales revenues, and the maximum amount that may be sold depend on the time period. Raw material storage capacity is limited. Storing product between time periods incurs storage costs. Some product is held in stock at the beginning of the planning period. The objective function of maximizing the total profit is to maximize the sales revenues, minus the cost of production, buying raw material, and storing finished products and raw material.
File(s):	coco.py

Catenary: Determine chain shape: QCQP problem

Pplan: A project planning problem: Formulation of resource use profiles


Type:	Project planning
Rating:	3 (intermediate)
Description:	Over the next 6 months we have three projects which can be done. Each of these projects has a profile of manpower requirements over its lifetime, and a benefit which accrues each month when the project has been completed. Our problem is to determine when each project is to start, subject to the constraint that in no month can we try to use more manpower than is available.
File(s):	pplan.py

Firestns: A set-covering model for emergency service provision: Solve a MIP problem

Solve a nonconvex nonlinear problem from MINLPlib with a local or global solver: Solving with local or global solvers

Pooling example for nonlinear solving: Nonlinear solving

Firestation location problem using SciPy sparse arrays: Sparse arrays, Dot product

Facility location problem using Pandas data frames: Pandas data frames

Getting started guide - Python examples

Folio - Introductory examples from 'Getting Started': LP, MIP and QP models, explicit initialization, index sets, heuristic solution


Type:	Portfolio optimization
Rating:	2 (easy-medium)
Description:	Simple tasks for formulating and solving a portfolio optimization problem: inputting an LP problem from data arrays (Folio.py) inputting a MIP problem - binary variables (FolioMIP1.py) inputting a MIP problem - semicontinuous variables (FolioMIP2.py) inputting a QC problem (FolioQC.py) inputting a QP problem (FolioQP.py) inputting a problem using heuristics (FolioHeuristic.py)
File(s):	Folio.py, FolioMIP1.py, FolioMIP2.py, FolioQC.py, FolioQP.py, FolioHeuristic.py
Data file(s):	foliocppqp.csv

Comments or suggestions about the examples? Please e-mail support@fico.com