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A solution (set of values for the decision variables) for which all
of the constraints in the Solver model are satisfied is called a feasible
solution. Most solution algorithms first try to find a feasible
solution, and then try to improve it by finding another feasible
solution that increases the value of the objective function (when
maximizing, or decreases it when minimizing). An
optimal solution is a feasible solution where the objective
function reaches a maximum (or minimum) value.
A globally optimal solution is one where
there are no other feasible solutions with better objective function
values. A locally optimal solution is one where there are no
other feasible solutions "in the vicinity" with better
objective function values -- you can picture this as a point at the
top of a "peak" or at the bottom of a "valley"
which may be formed by the objective function and/or the
constraints. The Solver is designed to find optimal solutions --
ideally the global optimum -- but this is not always possible. In
many cases, though, you may be happy to find a good solution
-- one that is better than the solution you are using now.
Whether the Solver can find a globally optimal
solution, a locally optimal solution, or a good solution depends on
the nature of the mathematical relationship between the variables
and the objective function and constraints (and the solution
algorithm used). For more information, click on the link "What
Makes a Model Hard to Solve?"
Next: What Makes a Model Hard to Solve?
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