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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)

A simple, graph-oriented database model, supporting object-identity, is presented. For this model, a transformation language based on elementary graph operations is defined. This transformation language is suitable for both querying and updates. It is shown that the transformation language supports both set-operations (except for the powerset operator) and… (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)

In reflective programming languages it is possible for a program to generate code that is integrated into the program's own execution. We introduce a reflective version of the relational algebra. Reflection is achieved by storing and manipulating relational algebra programs as relations in the database. We then study the expressibility and complexity of the… (More)