A heuristic is the study of search, the art and science of steering your attention fruitfully when confronted with an unresolved problem. The word heuristic comes from the same Greek root as Eureka, which means "I am in a state of having found it."
The most basic, though usually least efficient, heuristic is the brute-force search, also known as exhaustive search, which involved checking every single point in the search space.
Hill-climbing is a heuristic in which one searches for the optimum combination within a set of variables by changing one at a time until the results cease to improve.
According to this method, once you are no longer able to climb any higher then you've arrived at the top of the hill. When searching for a summit (the optimum), you should continue climbing (changing variables) until you are no longer going up. That's how you know you've reached the peak: any further movement can only bring you back down.
For example, we use hill-climbing to search for the optimal settings of volume, treble, and bass on a boombox. By individually adjusting each knob until you arrive at the point where any further fiddling would only worsen the audio quality, then you've reached the optimal setting.The Expand To Contract heuristic says that often you can find a solution by adding some new, arbitrary element to the problem. That is, make the problem more complicated, and it will often simplify itself.
Plopping down an arbitrary element increases the number of possible connections. Think of your start point and your end point as little squids with tentacles writhing about, looking to latch onto something. They only have a certain number of tentacles, and there's a small chance they'll ever connect. So put another squid down in between them. Now there are a lot more tentacles flapping about, an infrastructure of wormholes, which leads to a much greater probability of forging a link. This is the essence of brainstorming.
The opposite heuristic approach is Contract to Expand. Problems that appear difficult because of the vastness of possibility are actually hard because of unconscious constraints introduced by the problem solver. Form is liberating. Composition constrained by form, such as a sonnet or Oulipo, is actually much more conducive to creativity than a blank sheet of paper.
The underlying descriptive principle behind Contract To Expand is that only some goals are accessible to you right now. Pick something that you can do right now, and do it right now. It doesn't matter that it's not your ultimate goal and you can't quite see how the step right now will lead to the ultimate goal. Focusing on just one thing will open up new possibilities. A single, decisive success drives a spike into the unknown space
"Heuristics don’t guarantee you’ll find the optimal solution, nor do they generally guarantee a solution at all. But they do a good enough job of solving certain types of problems to be useful. Their strength is that they break the deadlock of indecision and get you into action.
As you take action you begin to explore the solution space, which deepens your understanding of the problem. As you gain knowledge about the problem, you can make course corrections along the way, gradually improving your chances of finding a solution. If you try to solve a problem you don’t initially know how to solve, you’ll often figure out a solution as you go, one you never could have imagined until you started moving." Steve Pavlina
