A feasible solution is one that satisfies all defined constraints and requirements. A solution is infeasible when no combination of decision variable values can satisfy the entire set of requirements and constraints. Notice that a solution (i.e., a single set of values for the decision variables) can be infeasible by failing to satisfy the problem requirements or constraints, but this doesn’t imply that the problem or model itself is infeasible.
However, constraints and requirements can be defined in such a way that the entire model is infeasible. For example, suppose that in the Portfolio Allocation problem in Chapter 1, the investor insists on finding an optimal investment portfolio with the following constraints:
Income fund + Aggressive growth fund <= 10000
Income fund + Aggressive growth fund >= 12000
Clearly, no combination of investments exists that will make the sum of the income fund and aggressive growth fund no more than $10,000 and at the same time greater than or equal to $12,000.
Or, for this same example, suppose the bounds for a decision variable were:
$15,000 <= Income fund <= $25,000
This also results in an infeasible problem.
You can make infeasible problems feasible by fixing the inconsistencies of the relationships modeled by the constraints. OptQuest detects optimization models that are constraint-infeasible and reports them to you.
If a model is constraint-feasible, OptQuest will always find a feasible solution and search for the optimal solution (that is, the best solution that satisfies all constraints).
When an optimization model includes requirements, a solution that is constraint-feasible may be infeasible with respect to one or more requirements.
After first satisfying constraint feasibility, OptQuest assumes that the user's next highest priority is to find a solution that is requirement-feasible. Therefore, it concentrates on finding a requirement-feasible solution and then on improving this solution, driven by the objective in the model.