Title page for ETD etd-07042001-165926


Type of Document Dissertation
Author Aytemiz, Tevfik
Author's Email Address taytemiz@vt.edu
URN etd-07042001-165926
Title A Probabilistic Study of 3-SATISFIABILITY
Degree PhD
Department Industrial and Systems Engineering
Advisory Committee
Advisor Name Title
Jacobson, Sheldon H. Committee Co-Chair
Koelling, Charles Patrick Committee Co-Chair
Bish, Ebru K. Committee Member
Meller, Russell D. Committee Member
Ye, Keying Committee Member
Keywords
  • 3-Satisfiability
  • Satisfiability
  • Probabilistic Analysis of Max 3-Satisfiability
  • Tabu Search
  • Threshold Conjecture
  • Max 3-Satisfiability
Date of Defense 2001-06-28
Availability unrestricted
Abstract
Discrete optimization problems are defined by a finite set of solutions together with an objective function value assigned to each solution. Local search algorithms provide useful tools for addressing a wide variety of intractable discrete optimization problems. Each such algorithm offers a distinct set of rules to intelligently exploit the solution space with the hope of finding an optimal/near optimal solution using a reasonable amount of computing time.

This research studies and analyses randomly generated instances of 3-SATISFIABILITY to gain insights into the structure of the underlying solution space. Two random variables are defined and analyzed to assess the probability that a fixed solution will be assigned a particular objective function value in a randomly generated instance of 3-SATISFIABILITY. Then, a random vector is defined and analyzed to investigate how the solutions in the solution space are distributed over their objective function values. These results are then used to define a stopping criterion for local search algorithms applied to MAX 3-SATISFIABILITY.

This research also analyses and compares the effectiveness of two local search algorithms, tabu search and random restart local search, on MAX 3-SATISFIABILITY. Computational results with tabu search and random restart local search on randomly generated instances of 3-SATISFIABILITY are reported. These results suggest that, given a limited computing budget, tabu search offers an effective alternative to random restart local search. On the other hand, these two algorithms yield similar results in terms of the best solution found. The computational results also suggest that for randomly generated instances of 3-SATISFIABILITY (of the same size), the globally optimal solution objective function values are typically concentrated over a narrow range.

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