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== Reference ==
E. Grabska, B. Strug, G. Ślusarczyk: [[Hypergraph-based Evolutionary Design System]]. In: [[Generative Art 2007]].

== DOI ==

== Abstract ==
This paper deals with applying evolutionary methods in computer aided design. The
design process is an iterative one consisting of several steps. It starts with a preliminary
or conceptual design, which is then analyzed or tested in order to find out which of its
elements must be redesigned or refined. The process of evaluation and optimization is
repeated until an acceptable solution is found. Since designing can be treated in
computer science as a search process, where all possible designs form a search space,
it is possible to use search techniques such as evolutionary ones.

As evolutionary search consists in evaluating and refining possible solutions, it can be
seen as analogous to a human design iterative process of analysis, testing and
optimization. Similarly to the refinement step in human design, in evolutionary search
designs to be transformed are determined according to their evaluation (fitness). The
refinement step is often performed not on actual solutions (phenotypes) but on their
coded equivalents (genotypes).

Since in design problems genotypes in the form of binary strings are very often
insufficient we propose to use a graph-based representation of genotypes which enables
us not only to express geometrical properties of an object but also its attributes (like
color, material etc.) and relations between object components.

In this paper we adopt hierarchical hypergraphs as they can represent an artifact with
both multi-argument relations and hierarchical dependence which are impossible to
express by other structures. The greatest advantage of this representation is its ability to
describe in a uniform way all types of relations and objects and to produce highly fitted
individuals.

Using hypergraphs in an evolutionary search requires the adaptation of traditional
evolutionary operators like cross-over and mutation. As the hypergraphs selected to be
transformed by the evolutionary operators at the subsequent stage of the evolution and
their structures are not known a priori the operator must be defined in a way which
allows for an "online" computation of new hypergraphs. Genetic operators working on
hypergraphs and the structure of an evolutionary design system is presented.
The method is illustrated by examples of floor-layouts generated by a house design
system, where structures of floor-layouts are represented by hypergraphs. In our
approach a cross-over operation exchanges subgraphs representing the functional
areas with different internal arrangements, while mutation affects local and global
attributes as well as the graph structure (by adding or deleting subgraphs)

== Extended Abstract ==

== Bibtex ==

== Used References ==
[1] P. J. Bentley, Generic Evolutionary Design of Solid Objects using a Genetic Algorithm, PhD thesis,
UCL London 1), 3-38, (1997).

[2] Borkowski A., Grabska E., Nikodem P, and Strug B., Searching for Innovative Structural Layouts by
Means of Graph Grammars and Evolutionary Optimization,, Proc. 2nd Int. Structural Eng. And Constr.
Conf, Rome, (2003).

[3] De Jong K, Arciszewski T, and Vyas H, An Overview of Evolutionary Computation and its Applications,
in. Artificial Intelligence in Engineerig,9-22, Warsaw, (1999).

[4] D.E.Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Reading, MA,
Addison-Wesley, (1989).

[5] E. Grabska. A. Lachwa, G. Slusarczyk, K. Grzesiak-Kopec and J. Lembas; Hierarchical Layout
Hypergraph Operations and Diagrammatic Reasoning, Machine GRAPHICS and VISION, (in print)

[6] E.Grabska,Theoretical Concepts of Graphical Modelling. Part one: Realization of CP-graphs. Machine
GRAPHICS and VISION, 2(1993).

[7] Grabska, E.. Graphs and designing. Lecture Notes in Computer Science, 776 (1994).

[8] E.Grabska, W. Palacz, Hierarchical graphs in creative design. Machine GRAPHICS and VISION,
9(1/2), 115-123. (2000).

[9] Hajela P. and Lee, J, Genetic Algorith in Truss Topological OpJournal of Solids and Structures vol.32,
no 22 , 3341-3357, (1995).

[10] Hoffman, C. M.,Geometric and Solid Modeling: An Introduction, Morgan Kaufmann, San Francisco,
CA, (1989).

[11]Holland, J. H. Adaptation in Natural and Artificial Systems, Ann Arbor, (1975).

[12] Mantyla, M.,An Introduction To Solid Modeling, Computer Science Press, Rockville,MD,vol.87,
(1988).

[13] Martin, R R and Stephenson, P C Sweeping of Three-dimensional Objects? Computer Aided Design
Vol 22(4) (1990), pp. 223-234.

[14] Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin
Heidelberg New York (1996).

[15] Michalewicz, Z. Fogel, D. B.: How to Solve It: Modern Heuristics.. Springer-Verlag, Berlin Heidelberg
New York (2000).

[16] P. Nikodem and B. Strug. Graph Transformations in Evolutionary Design, Lecture Notes in Computer
Science,vol 3070, pp. 456-461, Springer, 2004.

[17] Rozenberg, G. Handbook of Graph Grammars and Computing by Graph. Transformations, vol.1
Fundations, World Scientific London (1997)

[18] B. Strug. Hierarchical Representation and Operators in Evolutionary Design, Parallel Processing and
Applied Mathematics (PPAM 2005), LNCS vol 3911, pp. 447-454 Springer 2006.

== Links ==
=== Full Text ===
http://www.generativeart.com/on/cic/papersGA2007/04.pdf

[[intern file]]

=== Sonstige Links ===

@@ Zeile 98: / Zeile 98: @@
 Fundations, World Scientific London (1997)
-[18] B. Strug. Hierarchical Representation and Operators in Evolutionary Design, Parallel Processing and
+[18] Barbara Strug: Hierarchical Representation and Operators in Evolutionary Design. Parallel Processing and
-Applied Mathematics (PPAM 2005), LNCS vol 3911, pp. 447-454 Springer 2006.
+Applied Mathematics (PPAM 2005), LNCS vol 3911, pp. 447-454 Springer 2006. http://link.springer.com/chapter/10.1007%2F11752578_54
 == Links ==

@@ Zeile 92: / Zeile 92: @@
 New York (2000).
-[16] P. Nikodem and B. Strug. Graph Transformations in Evolutionary Design, Lecture Notes in Computer
+[16] P. Nikodem and B. Strug: Graph Transformations in Evolutionary Design. Artificial Intelligence and Soft Computing - ICAISC 2004 Lecture Notes in Computer
-Science,vol 3070, pp. 456-461, Springer, 2004.
+Science,vol 3070, pp. 456-461, Springer, 2004. http://link.springer.com/chapter/10.1007%2F978-3-540-24844-6_67
 [17] Rozenberg, G. Handbook of Graph Grammars and Computing by Graph. Transformations, vol.1
@@ Zeile 100: / Zeile 100: @@
 [18] B. Strug. Hierarchical Representation and Operators in Evolutionary Design, Parallel Processing and
 Applied Mathematics (PPAM 2005), LNCS vol 3911, pp. 447-454 Springer 2006.
 == Links ==

Hypergraph-based Evolutionary Design System - Versionsgeschichte

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