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In this thesis we are going to introduce the notion of k-SAT problem as one of the NP-complete problems and illustrate its importance of investigation. To study and seperate the hard and easy samples of this problem, we are going to explain the satisfiability threshold conjecture and some theorems in the infinity limit cases for the phase transition threshold. At last we are going to define the notion of sharp threshold and state a fundamental theorem which gives a necessary and sufficient condition for a threshold to be coarse  

Many problems in the field of 0-1 integer programming are NP-Complete. Execution time for exact solving these problems is very high due to many constraints and decision variables. Hence, scientists use Fast algorithms, for example, the Greedy algorithms, in the approximated solution of these problems.A classic greedy approach may not search the whole solution space for better choices. However, other methods with a greedy approach, such as meta heuristic and hyper heuristic, in addition to local search, consider the more search space. These methods search randomly, so it does not provide a good guarantee for finding the proper solutions. Finding suitable solutions in this category of...