Metaheuristic methods for the 3-SAT problem

stemswedishΤεχνίτη Νοημοσύνη και Ρομποτική

15 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

85 εμφανίσεις

Metaheuristic methods for the 3
-
SAT problem


Stochastic search algorithms have been successfully applied to solve hard optimization
problems, as they allow finding solutions in reasonable times. Among them, metaheuristics

are generic strategies that define algorithmic frameworks for techniques able to efficiently and
accurately find approximate solutions for search, optimization, and machine learning
problems (Glover, 1986).

In practice, many optimization/search/machine le
arning problems are NP
-
hard, intrinsically
complex, and a lot of computing effort is demanded to solve them. The classical exact
resolution methods (i.e. enumerative, branch & bound, dynamic/linear/integer programming)
allow computing optimal solutions, bu
t are often useless in practice as they are extremely
time
-
consuming when solving real
-
world large
-
dimension problems. In opposition,
metaheuristics allow computing sub
-
optimal (even optimal, sometimes) solutions in a
reasonable execution time for a wide c
lass of problems. Metaheuristic methods usually allow
researchers to meet the resolution delays imposed in scientific, industrial, and commercial
fields (Talbi 2009).

Many proposals have been presented for metaheuristic methods, including well
-
known
techni
ques like Evolutionary Computation, Particle Swarm Optimization, Simulated
Annealing, Tabu Search, and others. These techniques differ in the search pattern, but all of
them are conceived to provide accurate and balanced methods for diversification (explor
ation
of the search space) and intensification (exploitation of already found accurate solutions).
Although originally proposed to solve combinatorial optimization problems, nowadays
metaheuristics are useful tools to tackle real
-
life problems arising in m
any application areas.

The 3
-
SAT is a case of the Boolean satisfiability problem (with 3 variables in each clause), a
classical optimization problem in the field of computing theory, with important applications in
many research fields, including electronic

design, verification planning, scheduling,
cryptography, and others.

The 3
-
SAT is NP
-
hard (Cook 1971), since no polynomial
-
time algorithm is known to solve.
In fact, 3
-
SAT was the first problem proved to be NP
-
Complete, and many others NP
-
complete problem
s have been proved so, by reducing them to an instance of 3
-
SAT. However,
no efficient algorithm to solve the 3
-
SAT is known. Among several other stochastic methods
to solve the 3
-
SAT, metaheuristics have been applied to find accurate solutions for the
pro
blem.

This talk will provide a general overview of metaheuristic methods and a review of previous
works on applying metaheuristics to solve the 3
-
SAT problem. The application of high
performance computing techniques in distributed computing platforms to sp
eed up the search
will also be commented.