Reactive Dynamic Local Search algorithms for the Satisfiability Problem CPSC 532D Course Project Proposal

Stochastic Local Search (SLS) algorithms are of interest to a large number of research areas as well as business applications because they constitute some of the current best approaches to efficiently solve hard (NP-complete) combinatorial problems approximatively [1]. Satisfiability (SAT) problems, forming one of the most prominent type of NP-complete problems, are especially suitable for the study of SLS algorithms because they are easy to understand, and can represent a wide variety of problems. Numerous algorithms are available to solve SAT problems, and they often have varied results, depending on the type, characteristics and the source of the problem [2]. One promising family of SLS algorithms is known as Dynamic Local Search (DLS) [2]. While all SLS approaches have an evaluation function to guide the local search, DLS approaches are generally characterized as having dynamic evaluation functions that can change over time. When a DLS algorithm is trapped in a local optima (and possibly in the process of getting stuck), it can escape by changing the evaluation function such that improvement is possible. For SAT solving DLS algorithms, the evaluation function typically uses weights or penalties assigned to the clauses. Some recent DLS algorithms have been very successful, and are considered amongst the current state of the art, such as the Exponentiated Subgradient Algorithm (ESG) [3]. It would appear that there are opportunities to explore and analyze existing DLS algorithms, and to research the effects of combining some successful DLS techniques with traditionally non-dynamic approaches. Furthermore, many of the DLS techniques are very sensitive with respect to their tunable parameters. There is potential for a reactive DLS approach that could eliminate this dependency on tuned parameters.