Representation and structural biases in CGP

Payne, Andrew J.; Stepney, Susan

doi:10.1109/cec.2009.4983064

Cited by 5 publications

(5 citation statements)

References 15 publications

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“…Similar to Depth, Flat has exactly one solution. In [9] some evidence was found that solutions that appear less often in the search space may be harder to find. If this is the reason Depth was more difficult than Breadth, then Flat should also be difficult to solve.…”

Section: Flatmentioning

confidence: 96%

“…Also in contrast to Breadth, Depth has a unique solution for Normal and Reorder, with DAG having multiple ways of representing the same graph by encoding nodes in different orders. This problem is similar to the linear graph proposed in [9], except the problem scales such that all nodes must always be active and the fitness function involves individual execution instead of graph edit distance. Figure 5 and Table 2 both show how Normal is effectively unable to solve this problem.…”

Section: Depthmentioning

confidence: 97%

“…In fact, [9] showed that certain types of structures are more difficult to evolve than others. In particular, larger structures may be more difficult to evolve as they are less common in the search space.…”

Section: Length and Positional Biasingmentioning

confidence: 97%

“…As a result, the fitness of an individual is equal to the number of inputs connected to the output. This problem is similar to the tree graph proposed in [9], except the problem scales such that all nodes must always be active, multiple inputs are used, and the fitness function involves individual execution instead of graph edit distance.…”

Section: Breadthmentioning

confidence: 98%

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Length bias and search limitations in cartesian genetic programming

Goldman

Punch

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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In this paper we examine how Cartesian Genetic Programming's (CGP's) method for encoding directed acyclic graphs (DAGs) and its mutation operator bias the effective length of individuals as well as the distribution of inactive nodes in the genome. We investigate these biases experimentally using two CGP variants as comparisons: Reorder, a method for shuffling node ordering without effecting individual evaluation, and DAG, a method for removing the concept of node position. Experiments were performed on four problems tailored to highlight potential search limitations, with further testing on the 3-bit multiplier problem.Unlike previous work, our experiments show that CGP has an innate parsimony pressure that makes it very difficult to evolve individuals with a high percentage of active nodes. This bias is particularly prevalent as the length of an individual increases. Furthermore, these problems are compounded by CGP's positional biases which can make some problems effectively unsolvable. Both Reorder and DAG appear to avoid these problems and outperform Normal CGP on preliminary benchmark testing. Finally, these new techniques require more reasonable genome sizes than those suggested in current CGP, with some evidence that solutions are also more terse.

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Section: Flatmentioning

confidence: 96%

Section: Depthmentioning

confidence: 97%

Section: Length and Positional Biasingmentioning

confidence: 97%

Section: Breadthmentioning

confidence: 98%

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Length bias and search limitations in cartesian genetic programming

Goldman

Punch

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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“…This leads to some drawbacks, as this limitation makes it difficult or impossible to solve certain problems [5,20]. As a remedy, Goldman and Punch [5] proposed two new variants of CGP: One of those is Dag, which removes the constraint of only allowing connections that go from left to right in the grid.…”

Section: Extension: Dagmentioning

confidence: 99%

Weighted Mutation of Connections To Mitigate Search Space Limitations in Cartesian Genetic Programming

Cui

Pätzel

Margraf

et al. 2023

Proceedings of the 17th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

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This work presents and evaluates a novel modification to existing mutation operators for Cartesian Genetic Programming (CGP). We discuss and highlight a so far unresearched limitation of how CGP explores its search space which is caused by certain nodes being inactive for long periods of time. Our new mutation operator is intended to avoid this by associating each node with a dynamically changing weight. When mutating a connection between nodes, those weights are then used to bias the probability distribution in favour of inactive nodes. This way, inactive nodes have a higher probability of becoming active again. We include our mutation operator into two variants of CGP and benchmark both versions on four Boolean learning tasks. We analyse the average numbers of iterations a node is inactive and show that our modification has the intended effect on node activity. The influence of our modification on the number of iterations until a solution is reached is ambiguous if the same number of nodes is used as in the baseline without our modification. However, our results show that our new mutation operator leads to fewer nodes being required for the same performance; this saves CPU time in each iteration. CCS CONCEPTS• Computing methodologies → Genetic programming.

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