A Discrete Lagrangian-Based Global-Search Method for Solving Satisfiability Problems (1998)
| Venue: | Journal of Global Optimization |
| Citations: | 54 - 7 self |
BibTeX
@ARTICLE{Shang98adiscrete,
author = {Yi Shang},
title = {A Discrete Lagrangian-Based Global-Search Method for Solving Satisfiability Problems},
journal = {Journal of Global Optimization},
year = {1998},
volume = {12},
pages = {61--99}
}
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Abstract
. Satisfiability is a class of NP-complete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method (DLM) for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Our method and analysis provides a theoretical foundation and generalization of local search schemes that optimize the objective alone and penalty-based schemes that optimize the constraints alone. In contrast to local search methods that restart from a new starting point when a search reaches a local trap, the Lagrange multipliers in DLM provide a force to le...
