## The Tree-String Problem: An Artificial Domain for Structure and Content Search (2005)

Venue: | Genetic Programming, Proceedings of the 6th European Conference, volume 3447 of LNCS |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Gustafson05thetree-string,

author = {Steven Gustafson and Edmund K. Burke and Natalio Krasnogor},

title = {The Tree-String Problem: An Artificial Domain for Structure and Content Search},

booktitle = {Genetic Programming, Proceedings of the 6th European Conference, volume 3447 of LNCS},

year = {2005},

pages = {215--226},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

This paper introduces the Tree-String problem for genetic programming and related search and optimisation methods. To improve the understanding of optimisation and search methods, we aim to capture the complex dynamic created by the interdependencies of solution structure and content. Thus, we created an artificial domain that is amenable for analysis, yet representative of a wide-range of real-world applications.

### Citations

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Citation Context ...location. Higher level nodes typically encode more important features, while lower level nodes are used to make finer class distinctions. A classic example of such a method is Quinlan’s ID3 algorithm =-=[3]-=-. Finally, structure and content issues can be found in the induction of mathematical expressions from data. In this case we look for both a functional form and its ideal operators and coefficients. T... |

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Citation Context ...s problem, using a canonical representation and operator, werestunably difficult and allowed a more direct examination of structure mechanisms and representation issues during search. The Max problem =-=[9, 10]-=- and the Royal Tree problem [11] were created to contain a singular goal state to allow analysis of how structure acquires appropriate content. These problems define an ideal solution that requires sp... |

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Citation Context ...oscillate between states and become trapped in local optimum. The fixed points of heuristics are usually hard to determine, making their run time average and worst case complexity difficult to assess =-=[1]-=-. Consequently, the design and application of heuristic methods for real-world problems typically proceeds by trial-and-error. However, artificial domains can provide insight into the search abilities... |

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Citation Context ... decision trees and symbolic regression. Planning typically requires hierarchical solutions that encapsulate key low-level behaviours. An example in mobile robot planning is the issue of localisation =-=[2]-=-: robots have a difficult time maintaining a good approximation of their locationsduring moving and sensing. Localisation is a key low-level behaviour that needs to be carried out during a high-level ... |

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Citation Context ...o create the set of tree shapes on which to place random content, forming an instance, we generate a tree shape using the iterative tree growth method from [8], similar to the hill-climbing method in =-=[16]-=-. The method iteratively adds two child nodes to a probabilistically chosen leaf node, starting with the root. The probability of selecting leaf nodes can be altered to restrict trees to be less than ... |

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Citation Context ...entation and operator, werestunably difficult and allowed a more direct examination of structure mechanisms and representation issues during search. The Max problem [9, 10] and the Royal Tree problem =-=[11]-=- were created to contain a singular goal state to allow analysis of how structure acquires appropriate content. These problems define an ideal solution that requires specific primitives at specific st... |

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Citation Context ...sis. To further illustrate the Tree-String problem, we report preliminary work toward furthering the understanding of problem difficulty in genetic programming. 3 A Preliminary Study of Difficulty In =-=[15]-=-, the Tree-String problem was used to represent key properties of other common testbed domains (Artificial Ant, Parity, Regression) to study dissimilarity. A single instance of the problem using a bin... |

18 | What Makes a Problem GP-Hard? Validating a Hypothesis of Structural Causes
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Citation Context ...e aforementioned problems place emphasis on solution content, which is not independent from solution structure. The following problems direct attention back toward solution structure. The Lid problem =-=[8]-=- focused only on the search for structure by using fixed arity primitives with no meaning themselves, other than for creating tree shapes. Instances in this problem, using a canonical representation a... |

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Citation Context ...e regression domain, tunably difficult random polynomials were created by considering the increased precision required by an approximation using the same search space (i.e. primitive constant ranges) =-=[7]-=-. This allowed the study of code growth under varied levels of difficulty for genetic programming. The aforementioned problems place emphasis on solution content, which is not independent from solutio... |

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Citation Context ...ake it harder to improve either objective in proportion to the size (right column of Figure 3). A similar behaviour was also seen in the context of the multiobjective optimisation of size and quality =-=[17]-=-, where it was easier to reduce tree size than improve quality. Runs converged toward improving the easier objective of size rather than equally improving size and quality simultaneously.sstructure ob... |

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Citation Context ...e complex Royal-Tree-like problem was defined in [12] that consisted of finding the correct proportions of subprograms using multiarity nodes. This problem, along with the ORDER and MAJORITY problems =-=[13, 14]-=-, investigated the relationship between content and structure, where the latter two were mainly concerned with the occurrence and location of primitives in solutions. Again, while these problems addre... |

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Citation Context ...e complex Royal-Tree-like problem was defined in [12] that consisted of finding the correct proportions of subprograms using multiarity nodes. This problem, along with the ORDER and MAJORITY problems =-=[13, 14]-=-, investigated the relationship between content and structure, where the latter two were mainly concerned with the occurrence and location of primitives in solutions. Again, while these problems addre... |

9 | The Impact of External Dependency in Genetic Programming Primitives
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Citation Context ...hat may not accurately reflect real-world problems and are somewhat limited in their flexibility for producing random instances that are tunable. A more complex Royal-Tree-like problem was defined in =-=[12]-=- that consisted of finding the correct proportions of subprograms using multiarity nodes. This problem, along with the ORDER and MAJORITY problems [13, 14], investigated the relationship between conte... |

7 |
et al. Genetic Programming IV: Routine Human-Competitive Machine Intelligence
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(Show Context)
Citation Context ...ns, it is not known whether the way it deals with structure and content is optimal or particularly good. Genetic programming is an evolutionary algorithm that represents solutions as computer programs=-=[4]-=-. Artificial domains are frequently used as testbed problems: the most popular being the Artificial Ant problem, the family of Boolean problems (e.g. even-parity), and symbolic regression problems. Th... |

7 |
et al., "What Makes a Problem GP-Hard? Analysis of a Tunably Difficult Problem in Genetic Programming
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(Show Context)
Citation Context ... problem to complement the existing use of the the Santa Fe trail [5]. While investigating hardness in genetic programming, tunably difficult instances of the Binomial-3 regression problem were found =-=[6]-=-. In this case, genetic programming was shown to have a harder time dealing with ill-suited constants. Also in the regression domain, tunably difficult random polynomials were created by considering t... |

3 |
An evaluation of evolutionary generalisation in genetic programming
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(Show Context)
Citation Context ...the community to address these issues. To improve solution generalisation, a random trail generator was created for the Artificial Ant problem to complement the existing use of the the Santa Fe trail =-=[5]-=-. While investigating hardness in genetic programming, tunably difficult instances of the Binomial-3 regression problem were found [6]. In this case, genetic programming was shown to have a harder tim... |

3 | A data structure for improved GP analysis via efficient computation and visualisation of population measures
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- 2004
(Show Context)
Citation Context ... tree traversals and longest common substring). We are currently developing a very simple genetic programming system for the Tree-String problem that incorporates efficiency improvements described in =-=[18]-=- for the iTree data structure. It is our goal that the Tree-String problem allows for efficient research to take place on a complex problem, ultimately making significant contributions to the scientif... |