STMTS_SOS

Special ordered sets and piecewise linear functions

• $SOS1{...};
• $SOS2{...};
• $PWL[...]{...};
• Return to the index

SOS1

Usage: $SOS1{varl, ub=1};

Description: creates a special ordered set of type 1 (SOS1) for a set of variables. At most one variable in a SOS1 can take a strictly positive value.

Parameters:

• Python:
  • varl: list of variable names;
  • ub: largest possible value if non-zero (default 1).

Creates:

• AMPL:
  • creates a variables and constraints to model the special ordered set.

Example:

var x{1..3}, >= 0;
$SOS1{["x[1]", "x[2]", "x[3]"]};

SOS2

Usage: $SOS2{varl, ub=1};

Description: creates a special ordered set of type 2 (SOS2) for a set of variables. At most two variables in a SOS2 can take a strictly positive value, and if two are non-zero these must be consecutive in their ordering.

Parameters:

• Python:
  • varl: list of variable names;
  • ub: largest possible value if non-zero (default 1).

Creates:

• AMPL:
  • creates a variables and constraints to model the special ordered set.

Example:

$PARAM[X{I}]{[0, 10, 15, 25, 30, 35, 40, 45, 50, 55, 60, 70]};
$PARAM[Y{^I}]{[0, 20, 15, 10, 0, 50, 18, 0, 15, 24, 10, 15]};
# Model a piecewise linear function
var x;
var y;
# Model a piecewise linear function using a special ordered set of type 2:
var z{I}, >= 0;
s.t. fix_x: x = sum{i in I} X[i] * z[i];
s.t. fix_y: y = sum{i in I} Y[i] * z[i];
s.t. convexity: sum{i in I} z[i] = 1;
$SOS2{["z[{}]".format(i) for i in _sets['I']]};

PWL

Usage: $PWL[var_x, var_y]{xyvalues};

Description: models a piecewise linear function given a list of pairs (x, y=f(x)).

Parameters:

• AMPL:
  • 'var_x': name for the first variable;
  • 'var_y': name for the second variable.
• Python:
  • 'xyvalues': list of pairs (x, y=f(x)) for the piecewise linear function f(x).

Creates:

• AMPL:
  • creates variables 'var_x' and 'var_y';
  • creates a variables and constraints to model the piecewise linear function ('var_y' = f('var_x')).

Examples:

$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]
};
$PWL[x,y]{zip(xvalues, yvalues)};

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Copyright © 2015-2016 Filipe Brandão < fdabrandao@dcc.fc.up.pt >. All rights reserved.