On Problem Solving XVII: Heuristics

"Devising the plan of the solution, we should not be too afraid of merely plausible, heuristic reasoning. Anything is right that leads to the right idea. But we have to change this standpoint when we start carrying out the plan and then we should accept only conclusive, strict arguments." (George Pólya, "How to solve it", 1945)

"Heuristic reasoning is reasoning not regarded as final and strict but as provisional and plausible only, whose purpose is to discover the solution of the present problem. We are often obliged to use heuristic reasoning. We shall attain complete certainty when we shall have obtained the complete solution, but before obtaining certainty we must often be satisfied with a more or less plausible guess. We may need the provisional before we attain the final. We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building." (George Pólya, "How to solve it", 1945)

"Fast and frugal heuristics employ a minimum of time, knowledge, and computation to make adaptive choices in real environments. They can be used to solve problems of sequential search through objects or options, as in satisficing. They can also be used to make choices between simultaneously available objects, where the search for information (in the form of cues, features, consequences, etc.) about the possible options must be limited, rather than the search for the options themselves. Fast and frugal heuristics limit their search of objects or information using easily computable stopping rules, and they make their choices with easily computable decision rules." (Gerd Gigerenzer & Peter M Todd, "Fast and Frugal Heuristics: The Adaptive Toolbox" [in "Simple Heuristics That Make Us Smart"], 1999)

"Heuristics are rules of thumb that help constrain the problem in certain ways (in other words they help you to avoid falling back on blind trial and error), but they don't guarantee that you will find a solution. Heuristics are often contrasted with algorithms that will guarantee that you find a solution - it may take forever, but if the problem is algorithmic you will get there. However, heuristics are also algorithms." (S Ian Robertson, "Problem Solving", 2001)

"Heuristics are needed in situations where the world does not permit optimization. For many real-world problems (as opposed to optimization-tuned textbook problems), optimal solutions are unknown because the problems are computationally intractable or poorly defined." (Christoph Engel & Gerd Gigerenzer, "Law and Heuristics: An interdisciplinary venture" [in "Heuristics and the Law", 2006)

"Less apparent is that qualitatively different problem-solving techniques are required at high levels of complexity than at low ones. Purely analytical techniques, powerful for the lower levels, can be overwhelmed at the higher ones. At higher levels, architecting methods, experience-based heuristics, abstraction, and integrated modeling must be called into play."  (Mark W Maier, "The Art Systems of Architecting" 3rd Ed., 2009)

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