We can use labeling/2
to minimize or maximize the value of a CLP(FD) expression, and generate
solutions in increasing or decreasing order of the value. See the
labeling options min(Expr) and max(Expr),
respectively.
Again, to easily try different labeling options in connection with optimisation, we recommend to introduce a dedicated predicate for posting constraints, and to use labeling/2 in a separate goal. This way, we can observe properties of the core relation in isolation, and try different labeling options without recompiling our code.
If necessary, we can use once/1 to commit to the first optimal solution. However, it is often very valuable to see alternative solutions that are also optimal, so that we can choose among optimal solutions by other criteria. For the sake of purity and completeness, we recommend to avoid once/1 and other constructs that lead to impurities in CLP(FD) programs.
Related to optimisation with CLP(FD) constraints are
library(simplex)
and CLP(Q) which reason about linear constraints over rational
numbers.