Piece of Pie Search: Confidently Exploiting Heuristics.

Search is not a direct path to a solution. While searching for a solution to a problem, heuristics consult us to avoid paths with dead ends, but they are not infallible. Many popular search methodologies \"disobey\" them during critical points of the search. In this work, we found an efficient stochastic methods framework that smoothly combines randomness with normal heuristics. We consider a factor of disobedience to the heuristics and we fine-tune it each time, according to our estimation of heuristic-reliability. We prove mathematically that while the disobedience factor falls, the stochastic methods approximate deterministic methods. Our algebraic evidence is supported by empirical evaluations on real life problems, such as course scheduling and frequency assignment. In this context, we exploit our proposed heuristic-reliability semantics in order to produce a piece of pie search (PoPS) method that can outperform other known constructive search processes in hard optimization problems.