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PyMPL is a python extension to the AMPL modelling language that adds new statements for evaluating python code within AMPL models. PyMPL also includes, among others, procedures for modelling piecewise linear functions, arc-flow graphs for vector packing, and sub-tour elimination constraints for TSP.

Table of Contents

• Useful links
• Examples
• PyMPL Parser
• PyMPL Statements

Useful links

• GiHub repository: https://github.com/fdabrandao/pympl
• BitBucket repository: https://bitbucket.org/fdabrandao/pympl

Examples

piecewise_linear.mod

# Evaluate python code:
$EXEC{
xvalues = [0, 10, 15, 25, 30, 35, 40, 45, 50, 55, 60, 70]
yvalues = [0, 20, 15, 10, 0, 50, 18, 0, 15, 24, 10, 15]
};

var u >= 0;
# Model a piecewise linear function given a list of pairs (x, y=f(x)):
$PWL[x,y]{zip(xvalues, yvalues)};

maximize obj: 2*x + 15*y;
s.t. A: 3*x + 4*y <= 250;
s.t. B: 7*x - 2*y + 3*u <= 170;

solve;
display x, y, u;
display "Objective:", 2*x + 15*y;
end;

vector_packing.mod:

# Load a vector packing instance from a file:
$VBP_LOAD[instance1{I,D}]{"instance1.vbp", i0=1};

var x{I}, >= 0;

# Generate an arc-flow model for instance1:
$VBP_FLOW[Z]{_instance1.W, _instance1.w, ["x[%d]"%i for i in _sets['I']]};
# Variable declarations and flow conservation constraints will be created here

minimize obj: Z;
s.t. demand{i in I}: x[i] >= instance1_b[i]; # demand constraints

solve;
display Z;
end;

variable_size_bin_packing.mod:

# Evaluate python code:
$EXEC{
# Bin capacities:
W1 = [100]
W2 = [120]
W3 = [150]

# Bin costs:
Costs = [100, 120, 150]

# Item weights:
ws = [[10], [14], [17], [19], [24], [29], [32], [33], [36],
      [38], [40], [50], [54], [55], [63], [66], [71], [77],
      [79], [83], [92], [95], [99]]

# Item demands:
b = [1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1]
};

# Generate a parameter 'b' for the demand:
$PARAM[b{I}]{b, i0=1};

# Generate a parameter 'C' for the cost:
$PARAM[C{T}]{Costs, i0=1};

# Feedback arcs for each graph:
var Z{T}, integer, >= 0;
# Assignment variables:
var x{T, I}, integer, >= 0;
# Generate an arc-flow graph for each bin type:
$VBP_FLOW[^Z[1]]{W1, ws, ["x[1, %d]"%i for i in _sets['I']]};
$VBP_FLOW[^Z[2]]{W2, ws, ["x[2, %d]"%i for i in _sets['I']]};
$VBP_FLOW[^Z[3]]{W3, ws, ["x[3, %d]"%i for i in _sets['I']]};
# Note: the ^prefix is used to avoid the redefinition of Z

minimize obj: sum{t in T} C[t] * Z[t];
s.t. demand{i in I}: sum{t in T} x[t, i] >= b[i];

solve;
display{t in T} Z[t]; # number of bins of type t used
display sum{t in T} C[t] * Z[t]; # cost
end;

PyMPL Parser

import os
from pympl import PyMPL  # import the parser

# Create a parser and pass local and global variables to the model:
parser = PyMPL(locals_=locals(), globals_=globals())`

# Parse a file with PyMPL statements and produce a valid AMPL model:
parser.parse("pympl_model.mod", "ampl_model.mod")

# Call GLPK to solve the model (if the original model uses only valid GMPL statements):
os.system("glpsol --math ampl_model.mod")

# Call AMPL to solve the model:
os.system("ampl ampl_model.mod")

[Folder with examples]

Advanced features:

• Given a function f(varname) that given a variable name returns its value:

  • If any command used implements solution extraction you can use parser[command_name].extract(f) to extract the solution;
  • If any command used implements cut generation you can use parser[command_name].separate(f) to generate cutting planes.

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Copyright © Filipe Brandão. All rights reserved.
E-mail: [email protected]. [Homepage]