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9.3. Solutions to planning problems

A planning problem has a number of solutions.

Several categories of solutions are:

Possible solution
A possible solution is any solution, whether or not it breaks any number of constraints. Planning problems often have an incredibly large number of possible solutions. Many of those solutions are not useful.
Feasible solution
A feasible solution is a solution that does not break any (negative) hard constraints. The number of feasible solutions are relative to the number of possible solutions. Sometimes there are no feasible solutions. Every feasible solution is a possible solution.
Optimal solution
An optimal solution is a solution with the highest score. Planning problems usually have a few optimal solutions. They always have at least one optimal solution, even in the case that there are no feasible solutions and the optimal solution is not feasible.
Best solution found
The best solution is the solution with the highest score found by an implementation in a given amount of time. The best solution found is likely to be feasible and, given enough time, it’s an optimal solution.

Counterintuitively, the number of possible solutions is huge (if calculated correctly), even with a small data set.

In the examples provided in the planner-engine distribution folder, most instances have a large number of possible solutions. As there is no guaranteed way to find the optimal solution, any implementation is forced to evaluate at least a subset of all those possible solutions.

Business Optimizer supports several optimization algorithms to efficiently wade through that incredibly large number of possible solutions.

Depending on the use case, some optimization algorithms perform better than others, but it is impossible to know in advance. Using Business Optimizer, you can switch the optimization algorithm by changing the solver configuration in a few lines of XML or code.

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