Solver Tutorial - Interpreting Solutions

Interpreting Solutions

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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