Solving 3-SAT Using Adaptive Sampling

A framework is brieey introduced, which supports the comparison of Neural Networks and Evolutionary Algorithms. This framework, called \Adaptive Sampling", was used for the design of two incomplete 3-SAT methods. The rst one is based on the Neural Network approach, and the second method mixes general features of Neural Networks and Evolutionary Algorithms (EAs). These methods have been tested against the best currently known incomplete 3-SAT algorithm, the SAWing EA. Perhaps contradicting conventional intuition, the Neural method needs less evaluations to reach a higher success rate than the SAWing EA, but its oating point representation consumes much more time. However, the mixed approaches, called Lamarkian SEA-SAW, outperforms the SAWing EA in success rate, in number of evaluations and in runtime, on all test sets. This suggest that it is ben-eecial to study Evolutionary Computing and Neurocomputing in the new unifying Adaptive Sampling framework. The Adaptive Sampling framework is a model, in which problems and methods can be deened for optimization and learning. The principles of sampling and adaptation are its central concepts. Sampling refers to what could be called the \black box approach". Evolutionary Algorithms use this approach with respect to the representation of the problem that is to be solved: a tness function is sampled, i.e., speciic combinations of inputs and outputs of this function are all that is used in the investigation of a problem. Neural Networks also use the black box approach, but with respect to candidate solutions: the transfer function of the network is sampled, i.e., speciic combinations of inputs and outputs are used for the investigation of a problem. Adaptation refers to what is often called iterative improvement. This means that candidate solutions are maintained, and improved iteratively. For Neural Networks, there is only one candidate solution, whereas for Evolutionary Algorithms, there is a population of several candidate solutions. These solutions are improved in every cycle of the algorithm, taking into account new information that is gathered by sampling.