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Tutorial: Python, PuLP and GLPK

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A brief tutorial of Python, PuLP & GLPK.

A brief tutorial of Python, PuLP & GLPK.

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  • 1. Tutorial: Python, PuLP & GLPK  Sucha Supittayapornpong Twitter: @Sucha 5 Mar. 2010 Creative Commons Attribution 3.0.
  • 2. Architecture Programming Language: Python Interface: PuLP Optimization Solvers: GLPK, CPLEX, COIN, etc.
  • 3. Python  Python is a programming language.  Python runs on Windows, Linux/Unix, Mac OS X.  Python is free to use. From: http://www.python.org/
  • 4. Python: Features  High-level data structures  Ex: list, tuple, dictionary  Object-oriented  Interpreter  Standard library & Third party modules  Ex: pulp, numpy, matplotlib From: http://code.google.com/p/pulp-or/ , http://numpy.scipy.org/ , http://matplotlib.sourceforge.net/
  • 5. Python: Basic Data Type  Integer (int)  Ex: 1, 2, 3, 5, 8, 13, 21  Float (float)  Ex: 3.14, 2.71828  Boolean (bool)  Ex: True, False  String (str)  Ex: 'Python', ”Sucha”
  • 6. Python: High-Level Data Type  List (list): [ d1, d2, …, dn ]  Ex: [ 1, 3.14, True, 'a', [1], (2,3), {'B+':3.5} ]  Tuple (tuple): ( d1, d2, ..., dn, )  Ex: ( 1, 3.14, True, 'a', [1], (2,3), {'B+':3.5} )  Dictionary (dict): { k1:v1 , k2:v2 , ..., kn:vn }  Ex: { 'A':4 , 'B+':3.5 , 3:'B' }  Set (set): set([ d1, d2, ..., dn ])  Ex: set([ 4, 3.5, 'B'])
  • 7. Python: Flow Control - If  If statement if boolean: command elif boolean: command else: command
  • 8. Python: Loop - For, While  For loop for var in sequence: command  While loop while boolean: command
  • 9. Python: List Comprehensions  >>>[ i for i in range(5)] → [ 0, 1, 2, 3, 4 ]  >>>[ i for i in range(5) if i <> 3 ] → [ 0, 1, 2, 4 ]  >>>[ (i, j) for i in range(3) for j in range(i) ] → [ (1,0), (2,0), (2,1) ]
  • 10. PuLP & GLPK  PuLP is an LP modeler written in Python.  PuLP can generate LP files, and calls solvers to solve linear problems.  Supported solvers are GLPK, COIN, CPLEX, and GUROBI. http://code.google.com/p/pulp-or/  The GLPK (GNU Linear Programming Kit) package is intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. http://www.gnu.org/software/glpk/
  • 11. PuLP: Import Module  Import module  >>>import pulp >>>pulp.pulpTestAll()  >>>from pulp import * >>>pulpTestAll() Following slides assume the first import method.
  • 12. PuLP: Create Decision Variables  DV = pulp.LpVariable(name_str, lowbound, upbound, category)  For lowbound and upbound, No bound → None .  category ∈{ pulp.LpContinuous, pulp.LpInteger, pulp.LpBinary }  Ex: x ∈[0, ∞) x = pulp.LpVariable('Var X', 0, None, pulp.LpContinuous)
  • 13. PuLP: Formulate Problem  PB = pulp.LpProblem(name_str, sense)  sense ∈{ pulp.LpMinimize, pulp.LpMaximize }  Ex: maximization problem prob = pulp.LpProblem('Benefit', pulp.LpMaximize)
  • 14. PuLP: Add Objective Function  PB += linear_function, objective_name_str  linear_function is in the form of c1*DV1 + c2*DV2 + … + cn*DVn  Ex: Cost: 2*DV1 – 1.5*DV2 prob += 2*x1 – 1.5*x2, 'Cost'
  • 15. PuLP: Add Constraints  PB += linear_constraint , constraint_name_str  linear_constraint is in the form of a1*DV1 + a2*DV2 + … + an*DVn == a0 or a1*DV1 + a2*DV2 + … + an*DVn <= a0 or a1*DV1 + a2*DV2 + … + an*DVn >= a0  Ex: Con1: 5*DV1 + 6*DV2 <= 7 prob += 5*x1 + 6*x2 <= 7, 'Con1' or prob += 2*x1 + 6*x2 <= 7 – 3*x1, 'Con1'
  • 16. PuLP: Write .lp File  PB.writeLP(filename_str)  Ex: write to Benefit.lp prob.writeLP('Benefit.lp')
  • 17. PuLP: Solve  PB.solve() // Solved by COIN solver  Ex: prob.solve()  PB.solve(pulp.GLPK()) //Solved by GLPK solver  Ex: prob.solve(pulp.GLPK())
  • 18. PuLP: Results  Check status: pulp.LpStatus[PB.status]  Ex: pulp.LpStatus[prob.status]  Optimal cost: pulp.value(PB.objective)  Ex: pulp.value(prob.objective)  Optimal solution: DV.varValue  Ex: x1.varValue or pulp.value(x1)