This suggests that when the search space is very large and a complete search will take too long, then it can be worthwhile to give up any hope of ever doing a complete systematic search and instead use an algorithm that concentrates on first exploring a good selection of the most likely places.
Many such algorithms are based on some form of ``iterative repair.'' We propose a solution, look at its deficiencies and then try to repair one of these deficiencies, obtaining a new state that we hope is closer to an acceptable solution. This process is repeated many times until the state is acceptable, or we run out of patience. In order to save memory such algorithms cannot remember all the places that have already been searched. Hence, they often intentionally involve some degree of randomness: if decisions are made by tossing a coin then it is less likely that we will repeat exactly the same mistakes on each attempt to solve the problem.