Constraints in AMPL

1. Description
2. Defining a Constraint
3. Bounded Constraints
4. Examining Constraints
5. Changing Constraints

Description

Mathematical programmes use constraints to describe the relationships that define a feasible set of decision variables.

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Defining a Constraint

Constraints are defined using the subject to keywords, a label and possibly and indexing set, the : operator, two expressions and a relational operator:

subject to <conname> [{conset}] :
  <lhs_expression> <relational operator> <rhs_expression>;

Examples

subject to LimitedResin:
  sum {s in SURFBOARDS} Resin[s] * Production[s] <= TotalResin;

# Must conserve flow in the network (steel cannot disappear!)
subject to ConserveFlow {n in NODES}:
  sum {m in NODES: (m, n) in ARCS} Shipment[m, n] + Supply[n] =
  sum {p in NODES: (n, p) in ARCS} Shipment[n, p] + Demand[n] + Storage[n];

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Bounded Constraints

AMPL also allows bounded constraints to be defined. These constraints consist of an expression and a lower and upper bound. The lower and upper bounds may also be expressions, but may only involve parameters. (Note Regular constraints may have variables in either the left- or right-hand-side expressions.)

subject to MeetRequirement {r in REQUIREMENTS}:
  Min[r] <= sum {i in INGREDIENTS} Contributes[i, r] * Amount[i] <= Max[r];

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Examining Constraints

We have already seen how to observe the value of variables using display <varname>;. For constraints, we can look at the value of the expression involving the variables (known as the body) by using

display <conname>.body;

For bound constraints this represents the expression in the middle, for other constraints this represents the value of the constraint expression with all variables shifted to the left-hand side. You can see the constraints in modified form by using

expand <conname>;

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Changing Constraints

Once constraints have been added to a model you cannot remove them. However, you can drop a given constraint from the model. To drop a constraint, use the drop keyword and the constraint name.

drop <conname>;

If you decide to reinstate the constraint, you can restore it. To restore a constraint, use the restore keyword and the constraint name.

restore <conname>;

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-- MichaelOSullivan - 02 Mar 2008