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An evolutionary graph transformation system as a modelling framework for evolutionary algorithms
 KI 2009: Advances in Artificial Intelligence. Lecture Notes in Computer Science
, 2009
"... Abstract. In this paper an heuristic method for the solving of complex optimization problems is presented which is inspired equally by genetic algorithms and graph transformation. In short it can be described as a genetic algorithm where the individuals (encoding solutions of the given problem) are ..."
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Abstract. In this paper an heuristic method for the solving of complex optimization problems is presented which is inspired equally by genetic algorithms and graph transformation. In short it can be described as a genetic algorithm where the individuals (encoding solutions of the given problem) are always graphs and the operators to create new individuals are provided by graph transformation. As a case study this method is used to solve the independent set problem. 1
Graph Transformation Units Guided by a SAT Solver
, 2010
"... Graph transformation units are rulebased devices to model graph algorithms, graph processes, and the dynamics of systems the states of which are represented by graphs. Given a graph, various rules are applicable at various matches in general, but not any choice leads to a proper result so that one ..."
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Graph transformation units are rulebased devices to model graph algorithms, graph processes, and the dynamics of systems the states of which are represented by graphs. Given a graph, various rules are applicable at various matches in general, but not any choice leads to a proper result so that one faces the problem of nondeterminism. As countermeasure, graph transformation units provide the generic concept of control conditions which allow one to cut down the nondeterminism and to choose the proper rule applications out of all possible ones. In this paper, we propose an alternative approach. For a special type of graph transformation units including the solution of many NPcomplete and NPhard problems, the successful derivations from initial to terminal graphs are described by propositional formulas. In this way, it becomes possible to use a SAT solver to find out whether there is a successful derivation for some initial graph or not and how it is built up in the positive case.
Graph Tuple Transformation
, 2013
"... Graph transformation units are rulebased devices to model and compute relations between initial and terminal graphs. In this paper, they are generalized to graph tuple transformation units that allow one to combine different kinds of graphs into tuples and to process the component graphs simultan ..."
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Graph transformation units are rulebased devices to model and compute relations between initial and terminal graphs. In this paper, they are generalized to graph tuple transformation units that allow one to combine different kinds of graphs into tuples and to process the component graphs simultaneously and interrelated with each other. Moreover, one may choose some of the working components as inputs and some as outputs such that a graph tuple transformation unit computes a relation between input and output tuples of potentially different kinds of graphs rather than a binary relation on a single kind of graphs.
Stepping from Graph Transformation Units to Model Transformation Units
"... Abstract: Graph transformation units are rulebased entities that allow to transform source graphs into target graphs via sets of graph transformation rules according to a control condition. The graphs and rules are taken from an underlying graph transformation approach. Graph transformation units s ..."
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Abstract: Graph transformation units are rulebased entities that allow to transform source graphs into target graphs via sets of graph transformation rules according to a control condition. The graphs and rules are taken from an underlying graph transformation approach. Graph transformation units specify model transformations whenever the transformed graphs represent models. This paper is based on the observation that in general models are not always suitably represented as single graphs, but they may be specified as the composition of a variety of different formal structures such as sets, tuples, graphs, etc., which should be transformed by compositions of different types of rules and operations instead of single graph transformation rules. Consequently, in this paper, graph transformation units are generalized to model transformation units that allow to transform such kind of composed models in a rulebased and controlled way. Moreover, two compositions of model transformation units are presented.
A Graph Transformational View on Reductions in NP
"... Abstract: Many decision problems in the famous and challenging complexity class NP are graph problems and can be adequately specified by polynomial graph transformation units. In this paper, we propose to model the reductions in NP by means of a special type of polynomial graph transformation units ..."
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Abstract: Many decision problems in the famous and challenging complexity class NP are graph problems and can be adequately specified by polynomial graph transformation units. In this paper, we propose to model the reductions in NP by means of a special type of polynomial graph transformation units, too. Moreover, we present some first ideas how the semantic requirements of reductions including their correctness can be proved in a systematic way.