Problem Solving

Problem Solving

Well-defined problems

In a well-defined problem, it is clear what the problem is and the solution is clearly specified as well. That is, the solution can be recognized clearly when arrived at. Well defined problems often have generally known solutions.

They are solved using standard methods, methods of similar problems, or methods of analogous problems Problem → Analogous standard problem → Analogous standard solution → Solution

Examples: puzzles, simple games, and lower level mathematics, science, and engineering.

The class of well-defined problems include computationally intractable problems, the solution requires more time and/or space that is available. Therefore, an alternative solution must be found which involves the use of heuristics and approximations.

Ill-defined problems

In an ill-defined problem, it is not clear from the beginning what theproblem is and thus, what a solution is. Therefore, finding a solution requires in addition, finding out what the real problem is. Solving and specifying the problem develop in parallel and drive each other. Ill-defined problems usually have unknown solutions. The solutions found are often such that they still could be improved and it is up to the problem solver to decide when enough is enough. Ill-defined problems include:
[i]Computationally intractable problems which require heuristic solutions.
[ii]Approximate solutions
[iii]Unexplored problem domains

Wicked problems

Wicked problems are similar to ill-defined problems, just much worse. Furthermore solutions are very difficult, if at all, to recognize as such. In other words, stating the problem is the problem.
[i]often contain contradictory requirements
[ii]often the problem changes over time
[iii]there is uncertainty if the offered solution is the best solution or is even a solution requires an inventive/creative solution Problem → Inventive insight → Solution