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This paper is a survey of genetic algorithms for the traveling salesman problem. Genetic algorithms are randomized search techniques that simulate some of the processes observed in natural evolution. In this paper, a simple genetic algorithm is introduced, and various extensions are presented to solve the traveling salesman problem. Computational results(More)
We investigate properties of finite relational structures over the reals expressed by first-order sentences whose predicates are the relations of the structure plus arbitrary polynomial inequalities, and whose quantifiers can range over the whole set of reals. In constraint programming terminology, this corresponds to Boolean real polynomial constraint(More)
In this paper, we discuss augmentations of the nested relational algebra with programming constructs, such as while-loops and for-loops. We show that the algebras obtained in this way are equivalent to a slight extension of the powerset algebra, thus emphasizing both the strength and the naturalness of the powerset algebra as a tool to manipulate nested(More)
—We give a language-independent characterization of the expressive power of the relational algebra on finite sets of source-target relation instance pairs. The associated decision problem is shown to be co-graph-isomorphism hard and in coNP. The main result is also applied in providing a new characterization of the generic relational queries.